* [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: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 256 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 200 additional inputs, on iter 1 have 56 / 256 * * * * [misc]points: Computing exacts on every 12 of 200 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 200 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 200 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 200 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 144 additional inputs, on iter 3 have 112 / 256 * * * * [misc]points: Computing exacts on every 9 of 144 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 4 of 144 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 144 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 144 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 114 additional inputs, on iter 4 have 142 / 256 * * * * [misc]points: Computing exacts on every 7 of 114 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 114 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 114 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 97 additional inputs, on iter 5 have 159 / 256 * * * * [misc]points: Computing exacts on every 6 of 97 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 97 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 97 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 73 additional inputs, on iter 6 have 183 / 256 * * * * [misc]points: Computing exacts on every 4 of 73 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 73 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 73 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 56 additional inputs, on iter 7 have 200 / 256 * * * * [misc]points: Computing exacts on every 3 of 56 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 56 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 45 additional inputs, on iter 8 have 211 / 256 * * * * [misc]points: Computing exacts on every 2 of 45 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 45 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 33 additional inputs, on iter 9 have 223 / 256 * * * * [misc]points: Computing exacts on every 2 of 33 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 33 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 27 additional inputs, on iter 10 have 229 / 256 * * * * [misc]points: Computing exacts for 27 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 22 additional inputs, on iter 11 have 234 / 256 * * * * [misc]points: Computing exacts for 22 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 17 additional inputs, on iter 12 have 239 / 256 * * * * [misc]points: Computing exacts for 17 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 17 additional inputs, on iter 13 have 239 / 256 * * * * [misc]points: Computing exacts for 17 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 16 additional inputs, on iter 14 have 240 / 256 * * * * [misc]points: Computing exacts for 16 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 14 additional inputs, on iter 15 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 16 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 9 additional inputs, on iter 17 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 18 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 19 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 20 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 21 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 22 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 23 have 254 / 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 254 / 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 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 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (- 1/2 (/ 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 (* PI (* n 2)) (- 1/2 (/ k 2))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (- 1/2 (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* PI (* n 2))))) in k * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* PI (* n 2)))) in k * [misc]taylor: Taking taylor expansion of (- 1/2 (/ k 2)) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ k 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 (* PI (* n 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (* 2 n)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 * [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 (* PI (* n 2)) (- 1/2 (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* PI (* n 2))))) in n * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* PI (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (- 1/2 (/ k 2)) 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 (/ 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 (* 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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (- 1/2 (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* PI (* n 2))))) in n * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* PI (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (- 1/2 (/ k 2)) 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 (/ 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 (* 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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 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 (* 1/2 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 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 (* 1/2 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 * [misc]backup-simplify: Simplify (+ (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 (+ (* PI 0) (+ (* 0 2) (* 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 2) (+ (* (* 1/2 k) (/ 0 2)))) 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 n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 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 (+ (* 1/2 1) (* 0 0)) into 1/2 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) * [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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 2) (* 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 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) 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 n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [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 (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) * [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 (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2)))) in k * [misc]taylor: Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) 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) 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 (* PI (* (/ 1 n) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ 2 n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 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 (* PI (* (/ 1 n) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 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 (* PI (* (/ 1 n) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 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 (* 1/2 (/ 1 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 (/ 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 (* 1/2 1) into 1/2 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 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 (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 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 (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 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 (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 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 (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]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 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) * [misc]approximate: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2)))) in k * [misc]taylor: Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) 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)) 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 (* PI (* (/ 1 (- n)) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ -2 n)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (- -1/2) into 1/2 * [misc]backup-simplify: Simplify (+ 0 1/2) into 1/2 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 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 (* PI (* (/ 1 (- n)) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* PI -2) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 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 (* PI (* (/ 1 (- n)) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* PI -2) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 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 (/ 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 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) * [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 (+ (* PI 0) (* 0 -2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 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 (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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 (+ (* PI 0) (+ (* 0 0) (* 0 -2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 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 (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2)))) 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 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) 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 (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [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)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1) * [misc]approximate: Taking taylor expansion of (* PI (* n 2)) in (n) around 0 * [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]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 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 (* 2 PI) into (* 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 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 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 (* PI (* (/ 1 n) 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* (/ 1 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 (* (/ 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 (* PI 2) 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 (+ (* PI 0) (* 0 2)) 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 (+ (* PI 0) (+ (* 0 0) (* 0 2))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) 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 (* PI (* (/ 1 (- n)) 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* (/ 1 (- 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 (* (/ 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 (* PI -2) 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 (+ (* PI 0) (* 0 -2)) 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 (+ (* PI 0) (+ (* 0 0) (* 0 -2))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2)))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2)))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2))))))) 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 (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (- 1/2 (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* PI (* n 2))))) in k * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* PI (* n 2)))) in k * [misc]taylor: Taking taylor expansion of (- 1/2 (/ k 2)) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ k 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 (* PI (* n 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (* 2 n)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 * [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 (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (- 1/2 (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* PI (* n 2))))) in n * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* PI (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (- 1/2 (/ k 2)) 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 (/ 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 (* 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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) * [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 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (- 1/2 (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ k 2)) (log (* PI (* n 2))))) in n * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ k 2)) (log (* PI (* n 2)))) in n * [misc]taylor: Taking taylor expansion of (- 1/2 (/ k 2)) 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 (/ 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 (* 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 (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) * [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 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 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 (* 1/2 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 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 (* 1/2 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 * [misc]backup-simplify: Simplify (+ (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 (* 0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) 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 (+ (* PI 0) (+ (* 0 2) (* 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 2) (+ (* (* 1/2 k) (/ 0 2)))) 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 n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (/ 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 (+ (* 1/2 1) (* 0 0)) into 1/2 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (+ (* 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))))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 2) (* 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 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) 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 n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (/ 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 (/ (* (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 (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (* (exp (* 1/2 (+ (log 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 (* (+ (* 1/2 (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)))))))) into (- (+ (* +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))) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))) * [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))))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (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 (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (* -1 (* (+ (* 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)))))))) (+ (* +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 (* (+ (* 1/2 (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))))))))) into (- (+ (* +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))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +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))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))))))))))))) into (- (+ (* +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))))) (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)))))) (- (+ (* +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))))) (log n)))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +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))))) (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)))))) (- (+ (* +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))))) (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 (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2)))) in k * [misc]taylor: Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) 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) 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 (* PI (* (/ 1 n) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ 2 n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) into (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 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 (* PI (* (/ 1 n) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) * [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 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt (/ 1 k))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (/ (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ (/ 1 k) 2)) (log (* PI (* (/ 1 n) 2)))) in n * [misc]taylor: Taking taylor expansion of (- 1/2 (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 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 (* PI (* (/ 1 n) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) * [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 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt (/ 1 k))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 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 (* 1/2 (/ 1 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 (/ 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 (* 1/2 1) into 1/2 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 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 (* 1/2 (/ 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 (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 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 (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* (- 1/2 (* 1/2 (/ 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 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) * [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 (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 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 (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [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 (* 1/2 (/ 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 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) * [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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 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 (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 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 (* 1/2 (/ 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 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2)))) in k * [misc]taylor: Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) 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)) 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 (* PI (* (/ 1 (- n)) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ -2 n)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (- -1/2) into 1/2 * [misc]backup-simplify: Simplify (+ 0 1/2) into 1/2 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 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]taylor: Taking 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 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) * [misc]taylor: Taking taylor expansion of (/ (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 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 (* PI (* (/ 1 (- n)) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* PI -2) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) * [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)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (/ (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (- 1/2 (/ (/ 1 (- k)) 2)) (log (* PI (* (/ 1 (- n)) 2)))) in n * [misc]taylor: Taking taylor expansion of (- 1/2 (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 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 (* PI (* (/ 1 (- n)) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* PI -2) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (- (/ -1/2 k)) into (* 1/2 (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1/2 (* 1/2 (/ 1 k))) into (+ (* 1/2 (/ 1 k)) 1/2) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) * [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)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 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 (/ 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 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k * [misc]taylor: Taking taylor expansion of (/ -1 k) in k * [misc]taylor: Taking taylor expansion of -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)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) * [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 (+ (* PI 0) (* 0 -2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 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 (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (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)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-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 (+ (* PI 0) (+ (* 0 0) (* 0 -2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 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 (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [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)) 1/2) (- (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)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 3 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (113 enodes) * * [misc]simplify: iters left: 2 (328 enodes) * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k))) * * * * [misc]progress: [ 4 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 5 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (* PI (* n 2)) * * [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 n) PI) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) * * * * [misc]progress: [ 6 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ 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 1 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 7 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * * [misc]simplify: iters left: 3 (11 enodes) * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))) * * * * [misc]progress: [ 8 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * * [misc]simplify: iters left: 3 (11 enodes) * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))) * * * * [misc]progress: [ 9 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (- 1/2 (/ k 2)) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * * [misc]simplify: iters left: 2 (10 enodes) * [exit]simplify: Simplified to (- 1/2 (/ k 2)) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 10 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (22 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) * * * * [misc]progress: [ 11 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * * [misc]simplify: iters left: 2 (22 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) * * * * [misc]progress: [ 12 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (9 enodes) * * [misc]simplify: iters left: 3 (12 enodes) * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))) * * * * [misc]progress: [ 13 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 14 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 15 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 16 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 17 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 18 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 19 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 20 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 21 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 22 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 23 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 24 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 25 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 26 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 28 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 29 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 30 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 31 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 32 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 33 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 34 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) * * * * [misc]progress: [ 35 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) * * * * [misc]progress: [ 36 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (220 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI 2) n)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* PI 2) n)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) * * * * [misc]progress: [ 37 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 38 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 39 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (124 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (309 enodes) * [exit]simplify: Simplified to (* (* (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (* k (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (* k (sqrt k)))))) * * * * [misc]progress: [ 40 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 41 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 42 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 43 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 44 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))))) * * * * [misc]progress: [ 45 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 46 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) * * [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 (26 enodes) * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) * * * * [misc]progress: [ 47 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))))) * * * * [misc]progress: [ 48 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 49 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) * * [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 (26 enodes) * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) * * * * [misc]progress: [ 50 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) * * * * [misc]progress: [ 51 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 52 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) * * * * [misc]progress: [ 53 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) * * * * [misc]progress: [ 54 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 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 (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 55 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)))) * * * * [misc]progress: [ 56 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) * * * * [misc]progress: [ 57 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 58 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)))) * * * * [misc]progress: [ 59 / 83 ] 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 (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) * * * * [misc]progress: [ 60 / 83 ] 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 (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 61 / 83 ] 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 (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) * * * * [misc]progress: [ 62 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 63 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 64 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 65 / 83 ] 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 (* PI (* n 2)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))) * * * * [misc]progress: [ 66 / 83 ] 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 (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) * * * * [misc]progress: [ 67 / 83 ] 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 (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k))) * * * * [misc]progress: [ 68 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) * * [misc]simplify: iters left: 5 (7 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 (sqrt (* (* 2 n) PI)) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) * * * * [misc]progress: [ 69 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) * * [misc]simplify: iters left: 5 (7 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 (sqrt (* (* 2 n) PI)) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) * * * * [misc]progress: [ 70 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (9 enodes) * * [misc]simplify: iters left: 3 (12 enodes) * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) * * * * [misc]progress: [ 71 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) * * * * [misc]progress: [ 72 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) * * * * [misc]progress: [ 73 / 83 ] simplifiying candidate # * * * * [misc]progress: [ 74 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) * * [misc]simplify: iters left: 5 (7 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 (sqrt (* (* 2 n) PI)) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) * * * * [misc]progress: [ 75 / 83 ] 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 (368 enodes) * [exit]simplify: Simplified to (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (fma -1/2 (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) (fma (* (* (* k k) (log n)) (* (log (* PI 2)) 1/4)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (fma (* (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) 1/8) (fma (* (* (* k k) (log n)) (* (log n) 1/8)) (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (pow n 1/2) (pow (* PI 2) 1/2)))))) (sqrt k))) * * * * [misc]progress: [ 76 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * [exit]simplify: Simplified to (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (fma -1/2 k 1/2)) (pow n (fma -1/2 k 1/2))) (sqrt k))) * * * * [misc]progress: [ 77 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (208 enodes) * [exit]simplify: Simplified to (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (fma -1/2 k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) * * * * [misc]progress: [ 78 / 83 ] 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) (- 1/2 (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 79 / 83 ] 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) (- 1/2 (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 80 / 83 ] 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) (- 1/2 (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 81 / 83 ] 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: [ 82 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) * * * * [misc]progress: [ 83 / 83 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) * [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 1 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 2 1) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1 1 1) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 1) * [misc]approximate: Taking taylor expansion of (pow (* PI (* n 2)) 1/2) in (n) around 0 * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) 1/2) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* PI (* n 2))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* PI (* n 2)))) 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 (* 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 (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 (+ (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 (pow (* PI (* n 2)) 1/2) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* PI (* n 2))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* PI (* n 2)))) 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 (* 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 (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 (+ (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 (+ (* PI 0) (+ (* 0 2) (* 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 (+ (* 1/2 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 2) (* 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 (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))) 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) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (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 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 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 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) * [misc]approximate: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) 1/2) in (n) around 0 * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) 1/2) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* PI (* (/ 1 n) 2))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* PI (* (/ 1 n) 2)))) 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 (* PI (* (/ 1 n) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) 1/2) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* PI (* (/ 1 n) 2))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* PI (* (/ 1 n) 2)))) 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 (* PI (* (/ 1 n) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) 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) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) 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) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) * [misc]approximate: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) 1/2) in (n) around 0 * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) 1/2) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* PI (* (/ 1 (- n)) 2))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* PI (* (/ 1 (- n)) 2)))) 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 (* PI (* (/ 1 (- n)) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* PI -2) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) 1/2) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* PI (* (/ 1 (- n)) 2))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* PI (* (/ 1 (- n)) 2)))) 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 (* PI (* (/ 1 (- n)) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* PI -2) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (- 0) 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 (+ (* PI 0) (* 0 -2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-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 (+ (* PI 0) (+ (* 0 0) (* 0 -2))) 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) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2)))) 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) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* -2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* -2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* -2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 1)))) 24) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* -2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* -2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 1)))) 120) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* -2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* -2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* -2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* -2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* -2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* -2 PI) 1)))) 720) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 2 1) * [misc]approximate: Taking taylor expansion of (* PI (* n 2)) in (n) around 0 * [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]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 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 (* 2 PI) into (* 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 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 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 (* PI (* (/ 1 n) 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* (/ 1 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 (* (/ 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 (* PI 2) 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 (+ (* PI 0) (* 0 2)) 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 (+ (* PI 0) (+ (* 0 0) (* 0 2))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) 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 (* PI (* (/ 1 (- n)) 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* (/ 1 (- 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 (* (/ 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 (* PI -2) 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 (+ (* PI 0) (* 0 -2)) 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 (+ (* PI 0) (+ (* 0 0) (* 0 -2))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2)))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2)))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1 1 1) * [misc]approximate: Taking taylor expansion of (* PI (* n 2)) in (n) around 0 * [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]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 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 (* 2 PI) into (* 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 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 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 (* PI (* (/ 1 n) 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* (/ 1 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 (* (/ 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 (* PI 2) 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 (+ (* PI 0) (* 0 2)) 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 (+ (* PI 0) (+ (* 0 0) (* 0 2))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) 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 (* PI (* (/ 1 (- n)) 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* (/ 1 (- 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 (* (/ 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 (* PI -2) 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 (+ (* PI 0) (* 0 -2)) 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 (+ (* PI 0) (+ (* 0 0) (* 0 -2))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2)))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2)))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 4 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt k)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) 1/2) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* PI (* n 2))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* PI (* n 2)))) 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 (* PI (* n 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (* 2 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 (* PI (* n 2)) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* PI (* n 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* PI (* 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 (* PI (* n 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (* 2 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 0) into 1 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* n PI)) 1/2) 1) into (sqrt (* PI (* n 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 (/ (sqrt (* PI (* n 2))) +nan.0) into (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) 1/2) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* PI (* n 2))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* PI (* n 2)))) 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 (* 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 (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 (+ (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 (pow (* PI (* n 2)) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* PI (* n 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* PI (* 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 (* 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 (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 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) into (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (sqrt k)) into (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) 1/2) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* PI (* n 2))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* PI (* n 2)))) 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 (* 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 (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 (+ (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 (pow (* PI (* n 2)) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* PI (* n 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* PI (* 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 (* 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 (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 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) into (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (sqrt k)) into (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (+ (log n) (log (* 2 PI))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (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 (+ (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 (+ (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 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (log n) (log (* 2 PI))) 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 n) (log (* 2 PI))) k) in k * [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]taylor: Taking 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) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (* (+ (log n) (log (* 2 PI))) 0) into 0 * [misc]backup-simplify: Simplify (* 1/2 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 (+ (* (+ (log n) (log (* 2 PI))) 1) (* 0 0)) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* 1/2 (+ (log n) (log (* 2 PI)))) (* 0 0)) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1) 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 (+ (* PI 0) (+ (* 0 2) (* 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 (+ (* 1/2 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (+ (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (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 (+ (* 1/2 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1) 1)))) into (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (/ (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1)))) into (- (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 2) (* 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 (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 2) (* 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 2) (+ (* (* 1/2 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 k) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (+ (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) (* 0 (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (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 (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) 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 (+ (* (+ (log n) (log (* 2 PI))) 0) (+ (* 0 1) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (+ (log n) (log (* 2 PI)))) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (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)))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))) (/ (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1)))) into (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (+ (* 1/4 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))) +nan.0) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (+ (* 1/4 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))) 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) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (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 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (+ (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) (* 0 (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) (* 0 (/ 0 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (/ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) (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 (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (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 (/ (+ (* 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 (+ (* (+ (log n) (log (* 2 PI))) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (+ (log n) (log (* 2 PI)))) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (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 (+ (* 1/48 (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))))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (/ (+ (* 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))))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))) (/ (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))) 1)) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (+ (* 1/4 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))))) (/ (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) 1)))) into (- (+ (* 1/48 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 3))) (+ (* 1/16 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow (log (* 2 PI)) 2)))) (+ (* 1/16 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (log (* 2 PI))))) (* 1/48 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 3))))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))) +nan.0) (+ (* (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (+ (* 1/4 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))))) +nan.0) (* (- (+ (* 1/48 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 3))) (+ (* 1/16 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow (log (* 2 PI)) 2)))) (+ (* 1/16 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (log (* 2 PI))))) (* 1/48 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 3))))))) 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 (* PI (* (/ 1 n) 2)) 1/2) (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* PI (* (/ 1 n) 2)) 1/2) (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* PI (* (/ 1 n) 2)) 1/2) (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) 1/2) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* PI (* (/ 1 n) 2))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* PI (* (/ 1 n) 2)))) 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 (* PI (* (/ 1 n) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ 2 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 (* 1/2 (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* PI (* (/ 1 n) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 n) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ 2 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 k) 2) (log (* PI (* (/ 1 n) 2))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (/ (pow (* 2 (/ PI n)) 1/2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (* (sqrt (/ (* PI 2) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]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 (/ (* PI 2) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) +nan.0) into (* +nan.0 (* (/ (sqrt 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) (sqrt (/ PI n)))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* PI (* (/ 1 n) 2)) 1/2) (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* PI (* (/ 1 n) 2)) 1/2) (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) 1/2) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* PI (* (/ 1 n) 2))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* PI (* (/ 1 n) 2)))) 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 (* PI (* (/ 1 n) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* PI (* (/ 1 n) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 n) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt (/ 1 k))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* PI (* (/ 1 n) 2)) 1/2) (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* PI (* (/ 1 n) 2)) 1/2) (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) 1/2) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* PI (* (/ 1 n) 2))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* PI (* (/ 1 n) 2)))) 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 (* PI (* (/ 1 n) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* PI (* (/ 1 n) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 n) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt (/ 1 k))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) 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) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (+ (* 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) 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) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 3)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 2))))))))) * [misc]approximate: Taking taylor expansion of (/ (/ (pow (* PI (* (/ 1 (- n)) 2)) 1/2) (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* PI (* (/ 1 (- n)) 2)) 1/2) (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* PI (* (/ 1 (- n)) 2)) 1/2) (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) 1/2) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* PI (* (/ 1 (- n)) 2))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* PI (* (/ 1 (- n)) 2)))) 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 (* PI (* (/ 1 (- n)) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ -2 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 (* 1/2 (log (* -2 (/ PI n))))) into (pow (* -2 (/ PI n)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 (- n)) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ -2 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 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (/ (pow (* -2 (/ PI n)) 1/2) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into (* (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) (sqrt (/ (* PI -2) n))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (* (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) (sqrt (/ (* PI -2) n))) +nan.0) into (* +nan.0 (/ (sqrt (* -2 (/ PI n))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* PI (* (/ 1 (- n)) 2)) 1/2) (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* PI (* (/ 1 (- n)) 2)) 1/2) (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) 1/2) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* PI (* (/ 1 (- n)) 2))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* PI (* (/ 1 (- n)) 2)))) 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 (* PI (* (/ 1 (- n)) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* PI -2) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 (- n)) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* PI -2) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* PI (* (/ 1 (- n)) 2)) 1/2) (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* PI (* (/ 1 (- n)) 2)) 1/2) (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) 1/2) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (* PI (* (/ 1 (- n)) 2))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (log (* PI (* (/ 1 (- n)) 2)))) 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 (* PI (* (/ 1 (- n)) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* PI -2) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 (- n)) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* PI -2) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) 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]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of -1/2 in k * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (* 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (- 0) 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 (+ (* PI 0) (* 0 -2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 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 (+ (* PI 0) (* 0 -2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-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 (+ (* PI 0) (+ (* 0 0) (* 0 -2))) 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) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 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 (+ (* PI 0) (+ (* 0 0) (* 0 -2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))))))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 3 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* PI (* n 2))) 1/2) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (115 enodes) * [exit]simplify: Simplified to (fma 1/2 (log (* 2 n)) (* 1/2 (log PI))) * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (/ (exp (fma 1/2 (log (* 2 n)) (* 1/2 (log PI)))) (pow (* PI (* n 2)) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 4 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 5 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (* PI (* n 2)) * * [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 n) PI) * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (/ (pow (* (* 2 n) PI) (* 1 1/2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 6 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (pow PI 1/2) * * [misc]simplify: iters left: 1 (3 enodes) * [exit]simplify: Simplified to (sqrt PI) * [misc]simplify: Simplified (2 1 1 1) to (λ (k n) (/ (/ (* (sqrt PI) (pow (* n 2) 1/2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 7 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 8 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 9 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 11 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 12 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 13 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 14 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 15 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 16 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 17 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 18 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 19 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 20 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 21 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 22 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 23 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 24 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 25 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 26 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 28 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 29 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 30 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 31 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 32 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 33 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 34 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 35 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 36 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 37 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 38 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 39 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 40 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* PI (* n 2))) 1/2) (* (log (* PI (* n 2))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (246 enodes) * [exit]simplify: Simplified to (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) * * * * [misc]progress: [ 41 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* PI (* n 2))) 1/2) (* (log (* PI (* n 2))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (246 enodes) * [exit]simplify: Simplified to (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) * * * * [misc]progress: [ 42 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* PI (* n 2))) 1/2) (log (pow (* PI (* n 2)) (/ k 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (231 enodes) * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) * * * * [misc]progress: [ 43 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* PI (* n 2))) 1/2) (* (log (* PI (* n 2))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (246 enodes) * [exit]simplify: Simplified to (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) * * * * [misc]progress: [ 44 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* PI (* n 2))) 1/2) (* (log (* PI (* n 2))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (246 enodes) * [exit]simplify: Simplified to (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) * * * * [misc]progress: [ 45 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* PI (* n 2))) 1/2) (log (pow (* PI (* n 2)) (/ k 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (231 enodes) * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) * * * * [misc]progress: [ 46 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (pow (* PI (* n 2)) 1/2)) (* (log (* PI (* n 2))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (240 enodes) * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) * * * * [misc]progress: [ 47 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (pow (* PI (* n 2)) 1/2)) (* (log (* PI (* n 2))) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (240 enodes) * [exit]simplify: Simplified to (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (- 1/2 (/ k 2)) (log (* (* 2 n) PI)) (- (log (sqrt k)))))) * * * * [misc]progress: [ 48 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (pow (* PI (* n 2)) 1/2)) (log (pow (* PI (* n 2)) (/ k 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (184 enodes) * [exit]simplify: Simplified to (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) * * * * [misc]progress: [ 49 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (249 enodes) * [exit]simplify: Simplified to (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (fma (log (* (* 2 n) PI)) (- 1/2 (/ k 2)) (- (log (sqrt k)))))) * * * * [misc]progress: [ 50 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 51 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 52 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (* (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) 1/2)) (pow (* PI (* n 2)) 1/2)) (* (* (pow (* PI (* n 2)) (/ k 2)) (pow (* PI (* n 2)) (/ k 2))) (pow (* PI (* n 2)) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (109 enodes) * * [misc]simplify: iters left: 3 (485 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (* (* 2 n) PI)) (* (/ 2 k) (/ (* PI n) (sqrt k)))) (pow (pow (* (* 2 n) PI) (/ k 2)) 3)) * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (/ (* (sqrt (* (* 2 n) PI)) (* (/ 2 k) (/ (* PI n) (sqrt k)))) (pow (pow (* (* 2 n) PI) (/ k 2)) 3)))) * * * * [misc]progress: [ 53 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (262 enodes) * [exit]simplify: Simplified to (* (/ (/ (* (* 2 n) PI) (pow (* (* 2 n) PI) (/ k 2))) (* (pow (* (* 2 n) PI) (/ k 2)) (sqrt k))) (/ (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2))) k)) * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (/ (/ (* (* 2 n) PI) (pow (* (* 2 n) PI) (/ k 2))) (* (pow (* (* 2 n) PI) (/ k 2)) (sqrt k))) (/ (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2))) k)))) * * * * [misc]progress: [ 54 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 55 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 56 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 57 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 58 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (cbrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt k))))) * * * * [misc]progress: [ 59 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (* (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (cbrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 60 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2))))) (/ (cbrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2))))) (/ (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (sqrt k)))) * * * * [misc]progress: [ 61 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt k))))) * * * * [misc]progress: [ 62 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 63 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (sqrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (sqrt k)))) * * * * [misc]progress: [ 64 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow PI 1/2) (pow PI (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt PI) (pow PI (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ (sqrt PI) (pow PI (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* n 2) 1/2) (pow (* n 2) (/ k 2))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* n 2) 1/2) (pow (* n 2) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* n 2)) (pow (* n 2) (/ k 2))) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt PI) (pow PI (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (* n 2)) (pow (* n 2) (/ k 2))) (cbrt (sqrt k))))) * * * * [misc]progress: [ 65 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow PI 1/2) (pow PI (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt PI) (sqrt (sqrt k))) (pow PI (/ k 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ (sqrt PI) (sqrt (sqrt k))) (pow PI (/ k 2))) (/ (/ (pow (* n 2) 1/2) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* n 2) 1/2) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* n 2)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt PI) (sqrt (sqrt k))) (pow PI (/ k 2))) (/ (/ (sqrt (* n 2)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))))) * * * * [misc]progress: [ 66 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow PI 1/2) (pow PI (/ k 2))) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (sqrt PI) (pow PI (/ k 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt PI) (pow PI (/ k 2))) (/ (/ (pow (* n 2) 1/2) (pow (* n 2) (/ k 2))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (* n 2) 1/2) (pow (* n 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* n 2)) (pow (* n 2) (/ k 2))) (sqrt k)) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt PI) (pow PI (/ k 2))) (/ (/ (sqrt (* n 2)) (pow (* n 2) (/ k 2))) (sqrt k)))) * * * * [misc]progress: [ 67 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow PI 1/2) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (71 enodes) * * [misc]simplify: iters left: 1 (74 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt PI) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ (sqrt PI) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (pow (* n 2) 1/2) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* n 2) 1/2) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* n 2)) (cbrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt PI) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (* n 2)) (cbrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2)))))) * * * * [misc]progress: [ 68 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow PI 1/2) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt PI) (sqrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ k 2))) (cbrt (pow (* n (* 2 PI)) (/ k 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ (sqrt PI) (sqrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ k 2))) (cbrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (pow (* n 2) 1/2) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* n 2) 1/2) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* n 2)) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt PI) (sqrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ k 2))) (cbrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt (* n 2)) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2)))))) * * * * [misc]progress: [ 69 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow PI 1/2) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * [exit]simplify: Simplified to (/ (sqrt PI) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt PI) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (pow (* n 2) 1/2) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (* n 2) 1/2) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* n 2)) (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt PI) (* (cbrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (* n 2)) (sqrt k)) (cbrt (pow (* (* n 2) PI) (/ k 2)))))) * * * * [misc]progress: [ 70 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow PI 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt PI) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* n (* 2 PI)) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ (sqrt PI) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* n 2)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt PI) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (/ (sqrt (* n 2)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * * * * [misc]progress: [ 71 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow PI 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt PI) (sqrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ (sqrt PI) (sqrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* n 2)) (sqrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt PI) (sqrt (sqrt k))) (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (/ (sqrt (* n 2)) (sqrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * * * * [misc]progress: [ 72 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow PI 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt PI) (sqrt (pow (* n (* 2 PI)) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt PI) (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* n 2)) (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt PI) (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (/ (sqrt (* n 2)) (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * * * * [misc]progress: [ 73 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow PI 1/2) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (/ (pow (* n 2) 1/2) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* n 2) 1/2) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* n 2)) (cbrt (sqrt k))) (pow (* (* n 2) PI) (/ k 2))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (/ (sqrt (* n 2)) (cbrt (sqrt k))) (pow (* (* n 2) PI) (/ k 2))))) * * * * [misc]progress: [ 74 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow PI 1/2) 1) (sqrt (sqrt k))) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * [exit]simplify: Simplified to (/ (sqrt PI) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt PI) (sqrt (sqrt k))) (/ (/ (pow (* n 2) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* n 2) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* n 2)) (sqrt (sqrt k))) (pow (* (* n 2) PI) (/ k 2))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt PI) (sqrt (sqrt k))) (/ (/ (sqrt (* n 2)) (sqrt (sqrt k))) (pow (* (* n 2) PI) (/ k 2))))) * * * * [misc]progress: [ 75 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow PI 1/2) 1) 1) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * [exit]simplify: Simplified to (sqrt PI) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt PI) (/ (/ (pow (* n 2) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (* n 2) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* n 2)) (sqrt k)) (pow (* n (* PI 2)) (/ k 2))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt PI) (/ (/ (sqrt (* n 2)) (sqrt k)) (pow (* n (* PI 2)) (/ k 2))))) * * * * [misc]progress: [ 76 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) 1/2))) (pow PI (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (123 enodes) * * [misc]simplify: iters left: 1 (141 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (* (* PI 2) n))) (pow PI (/ k 2))) (/ (cbrt (sqrt (* (* PI 2) n))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (sqrt (* (* PI 2) n))) (pow PI (/ k 2))) (/ (cbrt (sqrt (* (* PI 2) n))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (pow (* n 2) (/ k 2))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (pow (* n 2) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* (* 2 n) PI))) (* (pow (* 2 n) (/ k 2)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (cbrt (sqrt (* (* PI 2) n))) (pow PI (/ k 2))) (/ (cbrt (sqrt (* (* PI 2) n))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (sqrt (* (* 2 n) PI))) (* (pow (* 2 n) (/ k 2)) (cbrt (sqrt k)))))) * * * * [misc]progress: [ 77 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) 1/2))) (pow PI (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (* (sqrt (sqrt k)) (pow PI (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (* (sqrt (sqrt k)) (pow PI (/ k 2)))) (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* (* 2 n) PI))) (* (pow (* 2 n) (/ k 2)) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (* (sqrt (sqrt k)) (pow PI (/ k 2)))) (/ (cbrt (sqrt (* (* 2 n) PI))) (* (pow (* 2 n) (/ k 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 78 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) 1/2))) (pow PI (/ k 2))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (146 enodes) * * [misc]simplify: iters left: 1 (150 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* (* 2 n) PI))) (/ (pow PI (/ k 2)) (cbrt (sqrt (* (* 2 n) PI))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (cbrt (sqrt (* (* 2 n) PI))) (/ (pow PI (/ k 2)) (cbrt (sqrt (* (* 2 n) PI))))) (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (pow (* n 2) (/ k 2))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (pow (* n 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* (* 2 n) PI))) (* (sqrt k) (pow (* 2 n) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (cbrt (sqrt (* (* 2 n) PI))) (/ (pow PI (/ k 2)) (cbrt (sqrt (* (* 2 n) PI))))) (/ (cbrt (sqrt (* (* 2 n) PI))) (* (sqrt k) (pow (* 2 n) (/ k 2)))))) * * * * [misc]progress: [ 79 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) 1/2))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (249 enodes) * * [misc]simplify: iters left: 1 (308 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 80 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) 1/2))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (139 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (* (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (sqrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (sqrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 81 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) 1/2))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * * [misc]simplify: iters left: 1 (343 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* (* 2 n) PI))) (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (cbrt (sqrt (* (* 2 n) PI))) (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))))) * * * * [misc]progress: [ 82 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) 1/2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (123 enodes) * * [misc]simplify: iters left: 1 (142 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (* (sqrt (pow (* (* 2 n) PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (* (sqrt (pow (* (* 2 n) PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (* (sqrt (pow (* (* 2 n) PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 83 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) 1/2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI))))) (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (sqrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI))))) (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (sqrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 84 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) 1/2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (146 enodes) * * [misc]simplify: iters left: 1 (150 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* (* 2 n) PI))) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (cbrt (sqrt (* (* 2 n) PI))) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI))))) (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* (* 2 n) PI))) (* (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (cbrt (sqrt (* (* 2 n) PI))) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt (* (* 2 n) PI))))) (/ (cbrt (sqrt (* (* 2 n) PI))) (* (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))))) * * * * [misc]progress: [ 85 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) 1/2))) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (124 enodes) * * [misc]simplify: iters left: 2 (335 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k))) (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k))) (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k)))) (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* (* 2 n) PI))) (* (pow (* (* 2 n) PI) (/ k 2)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k))) (/ (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k)))) (/ (cbrt (sqrt (* (* 2 n) PI))) (* (pow (* (* 2 n) PI) (/ k 2)) (cbrt (sqrt k)))))) * * * * [misc]progress: [ 86 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) 1/2))) 1) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (301 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (sqrt (sqrt k))) (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* (* 2 n) PI))) (* (pow (* (* 2 n) PI) (/ k 2)) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (sqrt (sqrt k))) (/ (cbrt (sqrt (* (* 2 n) PI))) (* (pow (* (* 2 n) PI) (/ k 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 87 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) 1/2))) 1) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* PI (* n 2)) 1/2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* (* 2 n) PI))) (* (sqrt k) (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (/ (cbrt (sqrt (* (* 2 n) PI))) (* (sqrt k) (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 88 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow PI (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* 2 n) PI))) (* (* (pow PI (/ k 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (sqrt (* (* 2 n) PI))) (* (* (pow PI (/ k 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow (* n 2) (/ k 2))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow (* n 2) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* 2 n) PI))) (* (pow (* 2 n) (/ k 2)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (sqrt (* (* 2 n) PI))) (* (* (pow PI (/ k 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))) (/ (sqrt (sqrt (* (* 2 n) PI))) (* (pow (* 2 n) (/ k 2)) (cbrt (sqrt k)))))) * * * * [misc]progress: [ 89 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow PI (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* 2 n) PI))) (* (pow PI (/ k 2)) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (sqrt (* (* 2 n) PI))) (* (pow PI (/ k 2)) (sqrt (sqrt k)))) (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* 2 n) PI))) (* (pow (* 2 n) (/ k 2)) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (sqrt (* (* 2 n) PI))) (* (pow PI (/ k 2)) (sqrt (sqrt k)))) (/ (sqrt (sqrt (* (* 2 n) PI))) (* (pow (* 2 n) (/ k 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 90 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow PI (/ k 2))) 1) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* 2 n) PI))) (pow PI (/ k 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (sqrt (* (* 2 n) PI))) (pow PI (/ k 2))) (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow (* n 2) (/ k 2))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow (* n 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* 2 n) PI))) (* (sqrt k) (pow (* 2 n) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (sqrt (* (* 2 n) PI))) (pow PI (/ k 2))) (/ (sqrt (sqrt (* (* 2 n) PI))) (* (sqrt k) (pow (* 2 n) (/ k 2)))))) * * * * [misc]progress: [ 91 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 92 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt k)))) (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt k)))) (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 93 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* 2 n) PI))) (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (sqrt (* (* 2 n) PI))) (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))))) * * * * [misc]progress: [ 94 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt (* (* PI 2) n))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* PI 2) n) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ (sqrt (sqrt (* (* PI 2) n))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt (sqrt (* (* PI 2) n))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 95 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 96 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* 2 n) PI))) (* (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (sqrt (* (* 2 n) PI))) (* (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))))) * * * * [misc]progress: [ 97 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) 1) (* (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 (40 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* PI 2) n))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (sqrt (* (* PI 2) n))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* 2 n) PI))) (* (pow (* (* 2 n) PI) (/ k 2)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (sqrt (* (* PI 2) n))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (sqrt (* (* 2 n) PI))) (* (pow (* (* 2 n) PI) (/ k 2)) (cbrt (sqrt k)))))) * * * * [misc]progress: [ 98 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) 1) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt (sqrt k))) (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* 2 n) PI))) (* (pow (* (* 2 n) PI) (/ k 2)) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt (sqrt k))) (/ (sqrt (sqrt (* (* 2 n) PI))) (* (pow (* (* 2 n) PI) (/ k 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 99 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) 1) 1) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (* (* 2 n) PI))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (sqrt (* (* 2 n) PI))) (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* 2 n) PI))) (* (sqrt k) (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (sqrt (* (* 2 n) PI))) (/ (sqrt (sqrt (* (* 2 n) PI))) (* (sqrt k) (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 100 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow PI (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * [exit]simplify: Simplified to (/ (/ 1 (pow PI (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ 1 (pow PI (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* n 2) (/ k 2))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* n 2) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (pow (* 2 n) (/ k 2)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ 1 (pow PI (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (* (* 2 n) PI)) (* (pow (* 2 n) (/ k 2)) (cbrt (sqrt k)))))) * * * * [misc]progress: [ 101 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow PI (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (/ 1 (pow PI (/ k 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ 1 (pow PI (/ k 2))) (sqrt (sqrt k))) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* n 2) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (pow (* 2 n) (/ k 2)) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ 1 (pow PI (/ k 2))) (sqrt (sqrt k))) (/ (sqrt (* (* 2 n) PI)) (* (pow (* 2 n) (/ k 2)) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 102 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow PI (/ k 2))) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * [exit]simplify: Simplified to (/ 1 (pow PI (/ k 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (pow PI (/ k 2))) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* n 2) (/ k 2))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* n 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* 2 n) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (pow PI (/ k 2))) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* 2 n) (/ k 2)))))) * * * * [misc]progress: [ 103 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (71 enodes) * * [misc]simplify: iters left: 1 (74 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ k 2))) (cbrt (pow (* n (* 2 PI)) (/ k 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (* (cbrt (pow (* n (* 2 PI)) (/ k 2))) (cbrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (pow (* PI (* n 2)) 1/2) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* PI (* n 2)) 1/2) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* (* 2 n) PI)) (cbrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ 1 (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (* (* 2 n) PI)) (cbrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 104 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (sqrt k))) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ (/ 1 (sqrt (sqrt k))) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (/ (pow (* PI (* n 2)) 1/2) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* PI (* n 2)) 1/2) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ 1 (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 105 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (40 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (pow (* PI (* n 2)) 1/2) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (* PI (* n 2)) 1/2) (cbrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* (* 2 n) PI)) (sqrt k)) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (sqrt (* (* 2 n) PI)) (sqrt k)) (cbrt (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 106 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (/ (pow (* PI (* n 2)) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* PI (* n 2)) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* (* 2 n) PI)) (cbrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ 1 (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (* (* 2 n) PI)) (cbrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 107 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (pow (* PI (* n 2)) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* PI (* n 2)) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (/ 1 (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 108 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (pow (* PI (* n 2)) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (pow (* (* n PI) 2) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (/ (pow (* PI (* n 2)) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (* PI (* n 2)) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* (* 2 n) PI)) (sqrt k)) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (/ (sqrt (* (* 2 n) PI)) (sqrt k)) (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 109 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* (* 2 n) PI)) (cbrt (sqrt k))) (pow (* (* 2 n) PI) (/ k 2))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (* (* 2 n) PI)) (cbrt (sqrt k))) (pow (* (* 2 n) PI) (/ k 2))))) * * * * [misc]progress: [ 110 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (6 enodes) * * [misc]simplify: iters left: 3 (8 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt k))) (pow (* (* 2 n) PI) (/ k 2))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt k))) (pow (* (* 2 n) PI) (/ k 2))))) * * * * [misc]progress: [ 111 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) 1) * * [misc]simplify: iters left: 4 (3 enodes) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 112 / 156 ] 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 (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* (* 2 n) PI)) (cbrt (sqrt k))) (pow (* (* 2 n) PI) (/ k 2))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt (* (* 2 n) PI)) (cbrt (sqrt k))) (pow (* (* 2 n) PI) (/ k 2))))) * * * * [misc]progress: [ 113 / 156 ] 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 (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt k))) (pow (* (* 2 n) PI) (/ k 2))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (/ (sqrt (* (* 2 n) PI)) (sqrt (sqrt k))) (pow (* (* 2 n) PI) (/ k 2))))) * * * * [misc]progress: [ 114 / 156 ] 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 (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 115 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ 1 (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ 1 (pow (* PI (* n 2)) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (pow (* (* n PI) 2) (/ k 2))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ 1 (cbrt (sqrt k))) (pow (* (* n PI) 2) (/ k 2))))) * * * * [misc]progress: [ 116 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (/ 1 (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ 1 (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow (* (* n PI) 2) (/ k 2))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt k))) (pow (* (* n PI) 2) (/ k 2))))) * * * * [misc]progress: [ 117 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) * * [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 (26 enodes) * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (/ 1 (pow (* PI (* n 2)) (/ k 2))) (sqrt k)))) * [enter]simplify: Simplifying (/ (/ 1 (pow (* PI (* n 2)) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt k)) (pow (* (* n PI) 2) (/ k 2))) * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (/ 1 (sqrt k)) (pow (* (* n PI) 2) (/ k 2))))) * * * * [misc]progress: [ 118 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 119 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 120 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 121 / 156 ] 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 (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))) * * * * [misc]progress: [ 122 / 156 ] 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 (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) * * * * [misc]progress: [ 123 / 156 ] 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 (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))) 1) (sqrt k))) * * * * [misc]progress: [ 124 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) (cbrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt k) (cbrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 125 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (sqrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (/ (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 126 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI 1/2) (pow PI (/ k 2))) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (9 enodes) * [exit]simplify: Simplified to (/ (sqrt PI) (pow PI (/ k 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (/ (sqrt PI) (pow PI (/ k 2))) (/ (sqrt k) (/ (pow (* n 2) 1/2) (pow (* n 2) (/ k 2)))))) * * * * [misc]progress: [ 127 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI 1/2) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt PI) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (/ (/ (sqrt PI) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt k) (/ (pow (* n 2) 1/2) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 128 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 129 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow PI 1/2) 1) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (8 enodes) * * [misc]simplify: iters left: 1 (10 enodes) * [exit]simplify: Simplified to (sqrt PI) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt PI) (/ (sqrt k) (/ (pow (* n 2) 1/2) (pow (* PI (* n 2)) (/ k 2)))))) * * * * [misc]progress: [ 130 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) 1/2))) (pow PI (/ k 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* (* 2 n) PI))) (/ (pow PI (/ k 2)) (cbrt (sqrt (* (* 2 n) PI))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (/ (cbrt (sqrt (* (* 2 n) PI))) (/ (pow PI (/ k 2)) (cbrt (sqrt (* (* 2 n) PI))))) (/ (sqrt k) (/ (cbrt (pow (* PI (* n 2)) 1/2)) (pow (* n 2) (/ k 2)))))) * * * * [misc]progress: [ 131 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) 1/2))) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (* (* PI 2) n))) (cbrt (pow (* (* PI 2) n) (/ k 2)))) (/ (cbrt (sqrt (* (* PI 2) n))) (cbrt (pow (* (* PI 2) n) (/ k 2))))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (/ (cbrt (sqrt (* (* PI 2) n))) (cbrt (pow (* (* PI 2) n) (/ k 2)))) (/ (cbrt (sqrt (* (* PI 2) n))) (cbrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt k) (/ (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 132 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) 1/2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (/ (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (/ (cbrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 133 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) 1/2))) 1) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (cbrt (sqrt (* (* 2 n) PI))) (cbrt (sqrt (* (* 2 n) PI)))) (/ (sqrt k) (/ (cbrt (pow (* PI (* n 2)) 1/2)) (pow (* PI (* n 2)) (/ k 2)))))) * * * * [misc]progress: [ 134 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow PI (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* 2 n) PI))) (pow PI (/ k 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (pow PI (/ k 2))) (/ (sqrt k) (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow (* n 2) (/ k 2)))))) * * * * [misc]progress: [ 135 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) 1/2)) (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (/ (sqrt (pow (* PI (* n 2)) 1/2)) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 136 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (/ (sqrt (sqrt (* (* 2 n) PI))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (/ (sqrt (pow (* PI (* n 2)) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 137 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) 1/2)) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (* (* 2 n) PI))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (sqrt (* (* 2 n) PI))) (/ (sqrt k) (/ (sqrt (pow (* PI (* n 2)) 1/2)) (pow (* PI (* n 2)) (/ k 2)))))) * * * * [misc]progress: [ 138 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (pow PI (/ k 2))) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (9 enodes) * [exit]simplify: Simplified to (/ 1 (pow PI (/ k 2))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (/ 1 (pow PI (/ k 2))) (/ (sqrt k) (/ (pow (* PI (* n 2)) 1/2) (pow (* n 2) (/ k 2)))))) * * * * [misc]progress: [ 139 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (pow (* (* n PI) 2) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (/ (/ 1 (cbrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt k) (/ (pow (* PI (* n 2)) 1/2) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 140 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (pow (* (* 2 PI) n) (/ k 2)))) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (/ 1 (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt k) (/ (pow (* PI (* n 2)) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 141 / 156 ] 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 (/ (sqrt k) (/ (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)))))) * * * * [misc]progress: [ 142 / 156 ] simplifiying candidate # * * * * [misc]progress: [ 143 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) * * [misc]simplify: iters left: 5 (7 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 (sqrt (* (* 2 n) PI)) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (/ 1 (pow (* PI (* n 2)) (/ k 2)))))) * * * * [misc]progress: [ 144 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) * * [misc]simplify: iters left: 5 (7 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 (sqrt (* (* 2 n) PI)) * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) * * * * [misc]progress: [ 145 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* 1/2 (+ (log n) (log (* 2 PI))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (155 enodes) * * [misc]simplify: iters left: 1 (189 enodes) * [exit]simplify: Simplified to (sqrt (* 2 (* PI n))) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (/ (sqrt (* 2 (* PI n))) (pow (* PI (* n 2)) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 146 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (158 enodes) * * [misc]simplify: iters left: 1 (399 enodes) * [exit]simplify: Simplified to (sqrt (* (* n PI) 2)) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (/ (sqrt (* (* n PI) 2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 147 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (242 enodes) * [exit]simplify: Simplified to (* (sqrt (* PI -2)) (pow (/ -1 n) -1/2)) * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (/ (* (sqrt (* PI -2)) (pow (/ -1 n) -1/2)) (pow (* PI (* n 2)) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 148 / 156 ] 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 2 1) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 149 / 156 ] 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 2 1) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 150 / 156 ] 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 2 1) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 151 / 156 ] 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 1) to (λ (k n) (/ (/ (pow (* (* PI n) 2) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 152 / 156 ] 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 1) to (λ (k n) (/ (/ (pow (* (* PI n) 2) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 153 / 156 ] 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 1) to (λ (k n) (/ (/ (pow (* (* PI n) 2) 1/2) (pow (* PI (* n 2)) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 154 / 156 ] 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: [ 155 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 3)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (pow k 2))))))))) * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) * * * * [misc]progress: [ 156 / 156 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))))))))) * [misc]simplify: Simplified (2) to (λ (k n) +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 1 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 2 2 1 1) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1 2 1 1 2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 1) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 2 2 1 1) * [misc]approximate: Taking taylor expansion of (* PI (* n 2)) in (n) around 0 * [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]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 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 (* 2 PI) into (* 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 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 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 (* PI (* (/ 1 n) 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* (/ 1 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 (* (/ 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 (* PI 2) 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 (+ (* PI 0) (* 0 2)) 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 (+ (* PI 0) (+ (* 0 0) (* 0 2))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) 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 (* PI (* (/ 1 (- n)) 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* (/ 1 (- 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 (* (/ 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 (* PI -2) 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 (+ (* PI 0) (* 0 -2)) 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 (+ (* PI 0) (+ (* 0 0) (* 0 -2))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2)))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2)))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1 2 1 1 2) * [misc]approximate: Taking taylor expansion of (* n PI) in (n) around 0 * [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]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 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 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 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 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 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 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* PI n) into (* n PI) * [misc]approximate: Taking taylor expansion of (* (/ 1 n) PI) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) PI) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 n) PI) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 1 PI) into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 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 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 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 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 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 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) * [misc]approximate: Taking taylor expansion of (* (/ 1 (- n)) PI) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) PI) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) PI) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 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 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 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 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 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 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 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) in n * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* 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]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 (pow (* PI (* n 2)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* PI (* n 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* PI (* 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 (* 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 (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 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) into (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) * [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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log 2) (log n)))) (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt (/ 1 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))))) * [misc]backup-simplify: Simplify (/ (sqrt k) (* (exp (* 1/2 (+ (log 2) (log n)))) (sqrt (/ 1 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into (* (/ 1 (exp (* 1/2 (+ (log 2) (log n))))) (sqrt (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) k))) * [misc]taylor: Taking taylor expansion of (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* 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]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 (pow (* PI (* n 2)) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* PI (* n 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* PI (* 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 (* PI (* n 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (* 2 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 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (/ (* 1/2 (log (* 2 (* n PI)))) (* 2 (sqrt 1))) into (* 1/4 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (/ (pow (* 2 n) 1/2) 1) into (sqrt (* n 2)) * [misc]backup-simplify: Simplify (/ +nan.0 (sqrt (* n 2))) into (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 n)))) * [misc]taylor: Taking taylor expansion of (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* 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]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 (pow (* PI (* n 2)) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* PI (* n 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* PI (* 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 (* PI (* n 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (* 2 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 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (/ (* 1/2 (log (* 2 (* n PI)))) (* 2 (sqrt 1))) into (* 1/4 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (/ (pow (* 2 n) 1/2) 1) into (sqrt (* n 2)) * [misc]backup-simplify: Simplify (/ +nan.0 (sqrt (* n 2))) into (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 n)))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt 2)) (sqrt (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt 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]backup-simplify: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ 1 (sqrt 2)) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (sqrt 2)))) * [misc]backup-simplify: Simplify (* (/ 1 (sqrt 2)) 0) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ 1 (sqrt 2))))) (* 0 0)) into (- (* +nan.0 (/ 1 (sqrt 2)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (sqrt 2)))) into (- (* +nan.0 (/ 1 (sqrt 2)))) * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 n) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (* 2 n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (sqrt (* n 2)) (/ (* 1/4 (log (* 2 (* n PI)))) 1)))) into (- (* 1/4 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt n)))) * [misc]backup-simplify: Simplify (- (/ +nan.0 (sqrt (* n 2))) (+ (* (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 n)))) (/ (- (* 1/4 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt n)))) (sqrt (* n 2)))))) into (- (+ (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 n)))) (- (* +nan.0 (* (/ (log (* 2 (* n PI))) (sqrt 2)) (sqrt (/ 1 n))))))) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 n)))) (- (* +nan.0 (* (/ (log (* 2 (* n PI))) (sqrt 2)) (sqrt (/ 1 n))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 n)))) (- (* +nan.0 (* (/ (log (* 2 (* n PI))) (sqrt 2)) (sqrt (/ 1 n)))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt 2)) (sqrt (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt 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]backup-simplify: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (/ (log (* 2 (* n PI))) (sqrt 2)) (sqrt (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (/ (log (* 2 (* n PI))) (sqrt 2)) (sqrt (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (/ (log (* 2 (* n PI))) (sqrt 2)) (sqrt (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (* n PI))) (sqrt 2)) 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]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log 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 n) (log (* 2 PI))) (sqrt 2)) into (/ (+ (log n) (log (* 2 PI))) (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ 1 (sqrt 2)) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (sqrt 2)))) * [misc]backup-simplify: Simplify (* (/ 1 (sqrt 2)) 0) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ 1 (sqrt 2))))) (* 0 0)) into (- (* +nan.0 (/ 1 (sqrt 2)))) * [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 (- (/ 0 (sqrt 2)) (+ (* (/ (+ (log n) (log (* 2 PI))) (sqrt 2)) (/ 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (+ (log n) (log (* 2 PI))) (sqrt 2)) +nan.0) (* 0 0)) into (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2)))))) * [misc]backup-simplify: Simplify (* (/ (+ (log n) (log (* 2 PI))) (sqrt 2)) 0) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2))))))) (* 0 0)) into (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2)))))) * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2))))))) into (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2)))))) * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (/ 1 (sqrt 2)))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2))))))) into (- (+ (* +nan.0 (/ 1 (sqrt 2))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2)))))))) * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (/ 1 (sqrt 2))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2))))))))) into (- (+ (* +nan.0 (/ 1 (sqrt 2))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ 1 (sqrt 2))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2)))))))) into (- (+ (* +nan.0 (/ 1 (sqrt 2))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2)))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ 1 (sqrt 2)) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ 1 (sqrt 2))))) (+ (* 0 (- (* +nan.0 (/ 1 (sqrt 2))))) (* 0 0))) into (- (* +nan.0 (/ 1 (sqrt 2)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (sqrt 2)))) into (- (* +nan.0 (/ 1 (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (sqrt 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ 1 (sqrt 2))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2)))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ 1 (sqrt 2)))) (* 1 k)))) into (- (+ (* +nan.0 (/ k (sqrt 2))) (- (+ (* +nan.0 (/ (* (log n) (pow k 2)) (sqrt 2))) (- (+ (* +nan.0 (/ (* n k) (sqrt 2))) (- (+ (* +nan.0 (/ (pow k 2) (sqrt 2))) (- (* +nan.0 (/ (* (pow k 2) (log (* 2 PI))) (sqrt 2)))))))))))) * [misc]approximate: Taking taylor expansion of (/ (sqrt (/ 1 k)) (/ (pow (* (/ 1 n) 2) 1/2) (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ 1 k)) (/ (pow (* (/ 1 n) 2) 1/2) (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) 2) 1/2) (sqrt (pow (* PI (* (/ 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]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 (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* PI (* (/ 1 n) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 n) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log 2) (log n)))) (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* (sqrt (/ 1 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (exp (* 1/2 (- (log 2) (log n))))) * [misc]backup-simplify: Simplify (/ (sqrt (/ 1 k)) (* (sqrt (/ 1 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (exp (* 1/2 (- (log 2) (log n)))))) into (* (sqrt (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) k)) (/ 1 (exp (* 1/2 (- (log 2) (log n)))))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ 1 k)) (/ (pow (* (/ 1 n) 2) 1/2) (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) 2) 1/2) (sqrt (pow (* PI (* (/ 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]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 (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* PI (* (/ 1 n) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 n) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ 2 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 k) 2) (log (* PI (* (/ 1 n) 2))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (/ (pow (/ 2 n) 1/2) (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) into (sqrt (/ 2 (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))) * [misc]backup-simplify: Simplify (/ +nan.0 (sqrt (/ 2 (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)))) into (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ 1 k)) (/ (pow (* (/ 1 n) 2) 1/2) (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) 2) 1/2) (sqrt (pow (* PI (* (/ 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]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 (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* PI (* (/ 1 n) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 n) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ 2 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 k) 2) (log (* PI (* (/ 1 n) 2))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (/ (pow (/ 2 n) 1/2) (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) into (sqrt (/ 2 (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))) * [misc]backup-simplify: Simplify (/ +nan.0 (sqrt (/ 2 (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)))) into (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 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 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt 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]backup-simplify: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)) in n * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]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 (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 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 (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) (* 0 0)) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* 2 (sqrt 0))) into (* +nan.0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (* (/ 1 (sqrt 2)) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 n) (/ 0 n)))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ 1 n) 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (/ 2 n) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (/ 2 n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (/ 2 n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) (+ (* (sqrt (/ 2 (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))) (/ 0 (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))))) into 0 * [misc]backup-simplify: Simplify (- (/ +nan.0 (sqrt (/ 2 (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)))) (+ (* (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)))) (/ 0 (sqrt (/ 2 (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))))))) into (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 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 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt 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]backup-simplify: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)) in n * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]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 (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 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 (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) (* 0 0)) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* 2 (sqrt 0))) into (* +nan.0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (* (/ 1 (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 into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ 1 (sqrt 2)) (* +nan.0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2))))) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 n) (/ 0 n)) (* 0 (/ 0 n)))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ 1 n) 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (/ 2 n) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (/ 2 n) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (log (/ 2 n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (/ 2 n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) (+ (* (sqrt (/ 2 (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))) (/ 0 (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) (* 0 (/ 0 (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))))) into 0 * [misc]backup-simplify: Simplify (- (/ +nan.0 (sqrt (/ 2 (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)))) (+ (* (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)))) (/ 0 (sqrt (/ 2 (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))))) (* (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))))) (/ 0 (sqrt (/ 2 (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))))))) into (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 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 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt 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]backup-simplify: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)) in n * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]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 (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 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 (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) (* 0 0)) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* 2 (sqrt 0))) into (* +nan.0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (* (/ 1 (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 into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ 1 (sqrt 2)) (* +nan.0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2))))) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2))))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 1) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 2) (+)) (* 2 0)) into (* +nan.0 (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ 1 (sqrt 2)) (* +nan.0 (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2))) (+ (* 0 (* +nan.0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 0))) into (- (* +nan.0 (/ (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2) (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2) (sqrt 2))))) (+ (* 0 (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2))))) (* 0 0))) into (- (* +nan.0 (/ (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2) (sqrt 2)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2) (sqrt 2)))) into (- (* +nan.0 (/ (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2) (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) 2) (sqrt 2)))) (pow (* (/ 1 n) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (sqrt 2)))) (* (/ 1 n) (/ 1 k))) (* (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (sqrt 2)))) (* (/ 1 n) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* n k)))) (- (+ (* +nan.0 (/ (pow (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) 2) (* (sqrt 2) (pow n 2)))) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) n)))))))) * [misc]approximate: Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (/ (pow (* (/ 1 (- n)) 2) 1/2) (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (/ (pow (* (/ 1 (- n)) 2) 1/2) (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) 2) 1/2) (sqrt (pow (* PI (* (/ 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]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 (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 (- n)) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* PI -2) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (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 (+ (* PI 0) (* 0 -2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log -2) (log n)))) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* (sqrt (/ 1 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (exp (* 1/2 (- (log -2) (log n))))) * [misc]backup-simplify: Simplify (/ (sqrt (/ -1 k)) (* (sqrt (/ 1 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (exp (* 1/2 (- (log -2) (log n)))))) into (* (/ (sqrt (/ -1 k)) (exp (* 1/2 (- (log -2) (log n))))) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (/ (pow (* (/ 1 (- n)) 2) 1/2) (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) 2) 1/2) (sqrt (pow (* PI (* (/ 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]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 (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 (- n)) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ -2 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 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (/ (pow (/ -2 n) 1/2) (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) into (sqrt (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) * [misc]backup-simplify: Simplify (/ +nan.0 (sqrt (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) into (/ +nan.0 (sqrt (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (/ (pow (* (/ 1 (- n)) 2) 1/2) (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) 2) 1/2) (sqrt (pow (* PI (* (/ 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]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 (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 (- n)) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ -2 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 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (/ (pow (/ -2 n) 1/2) (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) into (sqrt (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) * [misc]backup-simplify: Simplify (/ +nan.0 (sqrt (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) into (/ +nan.0 (sqrt (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) * [misc]taylor: Taking taylor expansion of (/ +nan.0 (sqrt (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (sqrt (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) in n * [misc]taylor: Taking taylor expansion of (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) 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 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) in n * [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 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) in n * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (* -2 (/ PI n))) k)) in n * [misc]taylor: Taking taylor expansion of -1/2 in n * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (/ (log (* -2 (/ PI n))) k) in n * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of -2 in n * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) k) into (/ (- (log (* -2 PI)) (log n)) k) * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (* 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 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 (- (/ 0 k) (+ (* (/ (- (log (* -2 PI)) (log n)) k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 0 (/ (- (log (* -2 PI)) (log n)) k))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ -2 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ -2 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (/ -2 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (* 2 (sqrt 0))) into (/ +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (/ +nan.0 (/ +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 n) (/ 0 (- n))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ -1 n) 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (/ -2 n) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (/ -2 n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (/ -2 n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) (+ (* (sqrt (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) (/ 0 (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))))) into 0 * [misc]backup-simplify: Simplify (- (/ +nan.0 (sqrt (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) (+ (* (/ +nan.0 (sqrt (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) (/ 0 (sqrt (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))))))) into (- (* +nan.0 (/ 1 (sqrt (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (/ 1 (sqrt (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (/ 1 (sqrt (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) in n * [misc]taylor: Taking taylor expansion of (/ -2 (* n (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) 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 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) in n * [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 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) in n * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (* -2 (/ PI n))) k)) in n * [misc]taylor: Taking taylor expansion of -1/2 in n * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (/ (log (* -2 (/ PI n))) k) in n * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of -2 in n * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) k) into (/ (- (log (* -2 PI)) (log n)) k) * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (* 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 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 (- (/ 0 k) (+ (* (/ (- (log (* -2 PI)) (log n)) k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 0 (/ (- (log (* -2 PI)) (log n)) k))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ -2 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ -2 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (/ -2 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (* 2 (sqrt 0))) into (/ +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (/ 1 (/ +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (* +nan.0 (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* -2 PI)) (log n)) k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 0 0) (* 0 (/ (- (log (* -2 PI)) (log n)) k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (+ (* (/ -2 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (/ +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 2) (+)) (* 2 0)) into (/ +nan.0 (pow (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 2)) * [misc]backup-simplify: Simplify (- (/ 0 (/ +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (+ (* (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ (/ +nan.0 (pow (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 2)) (/ +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* (- +nan.0) (* (/ 1 (- n)) 1)) (+ (* (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))) (- (* +nan.0 (/ 1 n))))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 3 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 4 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 5 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 6 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 7 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 8 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 9 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 11 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 12 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 13 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 14 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 15 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 16 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 17 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 18 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 19 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 20 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 21 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 22 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 23 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 24 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 25 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 26 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 28 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 29 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 30 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 31 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 32 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 33 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 34 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 35 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (sqrt k)) (- (* (log (* n 2)) 1/2) (log (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (206 enodes) * * [misc]simplify: iters left: 1 (345 enodes) * [exit]simplify: Simplified to (+ (log (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (fma (log (* n 2)) -1/2 (log (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (exp (+ (log (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (fma (log (* n 2)) -1/2 (log (sqrt k))))))) * * * * [misc]progress: [ 36 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (sqrt k)) (- (* (log (* n 2)) 1/2) (log (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (206 enodes) * * [misc]simplify: iters left: 1 (345 enodes) * [exit]simplify: Simplified to (+ (log (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (fma (log (* n 2)) -1/2 (log (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (exp (+ (log (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (fma (log (* n 2)) -1/2 (log (sqrt k))))))) * * * * [misc]progress: [ 37 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (sqrt k)) (- (log (pow (* n 2) 1/2)) (log (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (81 enodes) * * [misc]simplify: iters left: 2 (159 enodes) * * [misc]simplify: iters left: 1 (291 enodes) * [exit]simplify: Simplified to (+ (log (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (fma -1/2 (log (* n 2)) (log (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (exp (+ (log (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (fma -1/2 (log (* n 2)) (log (sqrt k))))))) * * * * [misc]progress: [ 38 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (sqrt k)) (log (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (144 enodes) * [exit]simplify: Simplified to (+ (fma (log (* n 2)) -1/2 (log (sqrt k))) (log (sqrt (pow (* 2 (* PI n)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (exp (+ (fma (log (* n 2)) -1/2 (log (sqrt k))) (log (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))) * * * * [misc]progress: [ 39 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 40 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 41 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (/ (* (* (pow (* n 2) 1/2) (pow (* n 2) 1/2)) (pow (* n 2) 1/2)) (* (* (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (115 enodes) * * [misc]simplify: iters left: 3 (405 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* PI (* n 2)) (/ k 2))) (* (pow (* PI (* n 2)) (/ k 2)) (/ (* k (sqrt k)) (pow (* n 2) 3/2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (* (sqrt (pow (* PI (* n 2)) (/ k 2))) (* (pow (* PI (* n 2)) (/ k 2)) (/ (* k (sqrt k)) (pow (* n 2) 3/2))))))) * * * * [misc]progress: [ 42 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (99 enodes) * * [misc]simplify: iters left: 3 (290 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (pow (* n (* PI 2)) (/ k 2))) k) (/ (* n 2) (* (pow (* n (* PI 2)) (/ k 2)) (/ (sqrt k) (sqrt (* n 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (/ (* (sqrt (pow (* n (* PI 2)) (/ k 2))) k) (/ (* n 2) (* (pow (* n (* PI 2)) (/ k 2)) (/ (sqrt k) (sqrt (* n 2))))))))) * * * * [misc]progress: [ 43 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 44 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 45 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ k (/ (* n 2) (pow (* PI (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (* (/ k (* 2 n)) (pow (* n (* PI 2)) (/ k 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (sqrt (* (/ k (* 2 n)) (pow (* n (* PI 2)) (/ k 2)))))) * * * * [misc]progress: [ 46 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 47 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 48 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (cbrt (sqrt k)) (cbrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (cbrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 49 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt (* n 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt (* n 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (/ (cbrt (sqrt k)) (sqrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (sqrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (sqrt (/ (sqrt (* n 2)) (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt (* n 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (/ (cbrt (sqrt k)) (sqrt (/ (sqrt (* n 2)) (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 50 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (113 enodes) * * [misc]simplify: iters left: 1 (144 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt n))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt n))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (cbrt (sqrt k)) (/ (pow 2 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (pow 2 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 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 (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt n))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2)))))) * * * * [misc]progress: [ 51 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (pow n 1/2) (sqrt (pow PI (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (50 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (* (sqrt (pow PI (/ k 2))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (pow PI (/ k 2))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n))) (/ (cbrt (sqrt k)) (/ (pow 2 1/2) (sqrt (pow (* n 2) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (pow 2 1/2) (sqrt (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (sqrt 2)) (sqrt (pow (* 2 n) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (pow PI (/ k 2))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n))) (* (/ (cbrt (sqrt k)) (sqrt 2)) (sqrt (pow (* 2 n) (/ k 2))))))) * * * * [misc]progress: [ 52 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (pow n 1/2) (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (73 enodes) * [exit]simplify: Simplified to (* (fabs (cbrt (pow (* (* PI n) 2) (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (fabs (cbrt (pow (* (* PI n) 2) (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n))) (/ (cbrt (sqrt k)) (/ (pow 2 1/2) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (pow 2 1/2) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (fabs (cbrt (pow (* (* PI n) 2) (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n))) (* (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2)))))) * * * * [misc]progress: [ 53 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (pow n 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt n) (cbrt (sqrt k))) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt n) (cbrt (sqrt k))) (cbrt (sqrt k)))) (/ (cbrt (sqrt k)) (/ (pow 2 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (pow 2 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt n) (cbrt (sqrt k))) (cbrt (sqrt k)))) (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2)))))) * * * * [misc]progress: [ 54 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (pow n 1/2) (sqrt 1))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * * [misc]simplify: iters left: 1 (49 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n)) (/ (cbrt (sqrt k)) (/ (pow 2 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (pow 2 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 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 (sqrt k)) (sqrt 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n)) (* (/ (cbrt (sqrt k)) (sqrt 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 55 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (pow n 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt n) (cbrt (sqrt k))) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt n) (cbrt (sqrt k))) (cbrt (sqrt k)))) (/ (cbrt (sqrt k)) (/ (pow 2 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (pow 2 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt n) (cbrt (sqrt k))) (cbrt (sqrt k)))) (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2)))))) * * * * [misc]progress: [ 56 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (pow n 1/2) 1)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (62 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (/ (sqrt n) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt k)) (/ (sqrt n) (cbrt (sqrt k)))) (/ (cbrt (sqrt k)) (/ (pow 2 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (pow 2 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 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 (sqrt k)) (sqrt 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt k)) (/ (sqrt n) (cbrt (sqrt k)))) (* (/ (cbrt (sqrt k)) (sqrt 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 57 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (279 enodes) * * [misc]simplify: iters left: 1 (401 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 58 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt (pow PI (/ k 2))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (81 enodes) * * [misc]simplify: iters left: 2 (134 enodes) * * [misc]simplify: iters left: 1 (165 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (pow PI (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (cbrt (sqrt (* n 2))) (cbrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (pow PI (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (cbrt (sqrt (* n 2))) (cbrt (sqrt (* n 2))))) (/ (cbrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* n 2) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 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 (* n 2) (/ k 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (pow PI (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (cbrt (sqrt (* n 2))) (cbrt (sqrt (* n 2))))) (* (sqrt (pow (* n 2) (/ k 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 59 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (152 enodes) * * [misc]simplify: iters left: 1 (185 enodes) * [exit]simplify: Simplified to (* (fabs (cbrt (pow (* PI (* n 2)) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (fabs (cbrt (pow (* PI (* n 2)) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))))) (/ (cbrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (fabs (cbrt (pow (* PI (* n 2)) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 60 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (151 enodes) * * [misc]simplify: iters left: 1 (182 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2))))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2))))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2))))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 61 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt 1))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (189 enodes) * * [misc]simplify: iters left: 1 (316 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2))))) (/ (cbrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2))))) (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 62 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (151 enodes) * * [misc]simplify: iters left: 1 (182 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2))))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2))))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2))))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 63 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) 1)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (277 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2))))) (/ (cbrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2))))) (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 64 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow (* n 2) 1/2)) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (113 enodes) * * [misc]simplify: iters left: 1 (146 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (cbrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (sqrt (sqrt (* n 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt (* n 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 65 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow PI (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt k)) (sqrt (pow PI (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (sqrt (pow PI (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt (sqrt (* n 2))))) (/ (cbrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* n 2) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 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 (* n 2) (/ k 2))) (/ (cbrt (sqrt k)) (sqrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (sqrt (pow PI (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt (sqrt (* n 2))))) (* (sqrt (pow (* n 2) (/ k 2))) (/ (cbrt (sqrt k)) (sqrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 66 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (73 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 67 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (cbrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 68 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow (* n 2) 1/2)) (sqrt 1))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) (/ (cbrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (cbrt (sqrt k)) (sqrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (cbrt (sqrt k)) (sqrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 69 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (cbrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 70 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow (* n 2) 1/2)) 1)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * * [misc]simplify: iters left: 1 (47 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) (/ (cbrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (cbrt (sqrt k)) (sqrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt (* n 2)))) (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (cbrt (sqrt k)) (sqrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 71 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (142 enodes) * * [misc]simplify: iters left: 1 (392 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt k))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt k))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (sqrt k)) (/ (pow (* n 2) 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (pow (* n 2) 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 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 (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt k))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt k)))) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt (* n 2))))))) * * * * [misc]progress: [ 72 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (sqrt (pow PI (/ k 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (138 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow PI (/ k 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow PI (/ k 2)))) (/ (cbrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (pow (* n 2) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (sqrt (* n 2))) (sqrt (pow (* n 2) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow PI (/ k 2)))) (* (/ (cbrt (sqrt k)) (sqrt (* n 2))) (sqrt (pow (* n 2) (/ k 2))))))) * * * * [misc]progress: [ 73 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (156 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (fabs (cbrt (pow (* (* PI n) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (fabs (cbrt (pow (* (* PI n) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (fabs (cbrt (pow (* (* PI n) 2) (/ k 2))))) (* (sqrt (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt (* n 2))))))) * * * * [misc]progress: [ 74 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (138 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt (* n 2))))))) * * * * [misc]progress: [ 75 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (sqrt 1))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 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 (sqrt k)) (sqrt (* n 2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (/ (cbrt (sqrt k)) (sqrt (* n 2))) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 76 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (138 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt (* n 2))))))) * * * * [misc]progress: [ 77 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 1)) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 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 (sqrt k)) (sqrt (* n 2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (/ (cbrt (sqrt k)) (sqrt (* n 2))) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 78 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * * [misc]simplify: iters left: 2 (23 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 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 (sqrt k)) (sqrt (* n 2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (/ (cbrt (sqrt k)) (sqrt (* n 2))) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 79 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* n 2) 1/2)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* n 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* n 2))) (/ (cbrt (sqrt k)) (/ 1 (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (cbrt (sqrt k)) (/ 1 (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * * [misc]simplify: iters left: 1 (49 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (* n 2))) (* (sqrt (pow (* (* n 2) PI) (/ k 2))) (cbrt (sqrt k)))))) * * * * [misc]progress: [ 80 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (* (cbrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt k)) (cbrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (cbrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt k)) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 81 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (/ (sqrt (* n 2)) (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (/ (sqrt (* n 2)) (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (/ (sqrt (* n 2)) (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (/ (sqrt (* n 2)) (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (/ (sqrt (* n 2)) (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 82 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (sqrt (sqrt k)) (/ (pow 2 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow 2 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 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 (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2)))))) * * * * [misc]progress: [ 83 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow n 1/2) (sqrt (pow PI (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt n)) (sqrt (pow PI (/ k 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt n)) (sqrt (pow PI (/ k 2)))) (/ (sqrt (sqrt k)) (/ (pow 2 1/2) (sqrt (pow (* n 2) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow 2 1/2) (sqrt (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 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 (sqrt k)) (sqrt 2)) (sqrt (pow (* 2 n) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt n)) (sqrt (pow PI (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt 2)) (sqrt (pow (* 2 n) (/ k 2))))))) * * * * [misc]progress: [ 84 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow n 1/2) (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt n))) (/ (sqrt (sqrt k)) (/ (pow 2 1/2) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow 2 1/2) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt n))) (* (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2)))))) * * * * [misc]progress: [ 85 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow n 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt n))) (/ (sqrt (sqrt k)) (/ (pow 2 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow 2 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt n))) (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2)))))) * * * * [misc]progress: [ 86 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow n 1/2) (sqrt 1))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt n)) (/ (sqrt (sqrt k)) (/ (pow 2 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow 2 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 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 (sqrt k)) (sqrt 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt n)) (* (/ (sqrt (sqrt k)) (sqrt 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 87 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow n 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt n))) (/ (sqrt (sqrt k)) (/ (pow 2 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow 2 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt n))) (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2)))))) * * * * [misc]progress: [ 88 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow n 1/2) 1)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * * [misc]simplify: iters left: 1 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt n)) (/ (sqrt (sqrt k)) (/ (pow 2 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow 2 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 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 (sqrt k)) (sqrt 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt n)) (* (/ (sqrt (sqrt k)) (sqrt 2)) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 89 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (83 enodes) * * [misc]simplify: iters left: 2 (115 enodes) * * [misc]simplify: iters left: 1 (138 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt (* n 2))) (cbrt (sqrt (* n 2))))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt (* n 2))) (cbrt (sqrt (* n 2))))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (sqrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt (* n 2))) (cbrt (sqrt (* n 2))))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 90 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt (pow PI (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (pow PI (/ k 2))) (cbrt (sqrt (* n 2)))) (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (pow PI (/ k 2))) (cbrt (sqrt (* n 2)))) (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2))))) (/ (sqrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* n 2) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 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 (* n 2) (/ k 2))) (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (pow PI (/ k 2))) (cbrt (sqrt (* n 2)))) (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2))))) (* (sqrt (pow (* n 2) (/ k 2))) (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 91 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (* n 2)))) (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (* n 2)))) (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (sqrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (* n 2)))) (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2))))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 92 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (sqrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 93 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt 1))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (83 enodes) * * [misc]simplify: iters left: 1 (114 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (* n 2)))) (/ (sqrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (* n 2)))) (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 94 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (sqrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 95 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) 1)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (78 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (* n 2)))) (/ (sqrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))) (cbrt (sqrt (* n 2)))) (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (sqrt (sqrt k)) (cbrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 96 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 97 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow PI (/ k 2))))) * * [misc]simplify: iters left: 6 (15 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 (/ k 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (pow PI (/ k 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2))))) (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* n 2) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 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 (* n 2) (/ k 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (pow PI (/ k 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2))))) (* (sqrt (pow (* n 2) (/ k 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 98 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (fabs (cbrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (fabs (cbrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (fabs (cbrt (pow (* PI (* n 2)) (/ k 2))))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 99 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 100 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt 1))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 101 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 102 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) 1)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))) (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 103 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (/ (pow (* n 2) 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow (* n 2) 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 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 (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (* n 2))))))) * * * * [misc]progress: [ 104 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ 1 (sqrt (pow PI (/ k 2))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * * [misc]simplify: iters left: 1 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt k)) (sqrt (pow PI (/ k 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt k)) (sqrt (pow PI (/ k 2)))) (/ (sqrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (pow (* n 2) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 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 (sqrt k)) (sqrt (* n 2))) (sqrt (pow (* n 2) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt k)) (sqrt (pow PI (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (* n 2))) (sqrt (pow (* n 2) (/ k 2))))))) * * * * [misc]progress: [ 105 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ 1 (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (52 enodes) * [exit]simplify: Simplified to (* (fabs (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (fabs (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (fabs (cbrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (* (sqrt (cbrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (* n 2))))))) * * * * [misc]progress: [ 106 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ 1 (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (50 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (sqrt (sqrt k))) (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (* n 2))))))) * * * * [misc]progress: [ 107 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ 1 (sqrt 1))) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 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 (sqrt k)) (sqrt (* n 2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt k)) (* (/ (sqrt (sqrt k)) (sqrt (* n 2))) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 108 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ 1 (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (50 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (sqrt (sqrt k))) (* (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (* n 2))))))) * * * * [misc]progress: [ 109 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ 1 1)) * * [misc]simplify: iters left: 4 (6 enodes) * * [misc]simplify: iters left: 3 (8 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 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 (sqrt k)) (sqrt (* n 2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt k)) (* (/ (sqrt (sqrt k)) (sqrt (* n 2))) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 110 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) 1) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * * [misc]simplify: iters left: 2 (9 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt k)) (/ (sqrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 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 (sqrt k)) (sqrt (* n 2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt k)) (* (/ (sqrt (sqrt k)) (sqrt (* n 2))) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 111 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow (* n 2) 1/2)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (* n 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (* n 2))) (/ (sqrt (sqrt k)) (/ 1 (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ 1 (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * * [misc]simplify: iters left: 1 (49 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (* n 2))) (* (sqrt (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 112 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (/ (sqrt (* 2 n)) (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (/ (sqrt (* 2 n)) (sqrt (pow (* n (* PI 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (* (cbrt (/ (sqrt (* 2 n)) (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (/ (sqrt (* 2 n)) (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (sqrt k) (cbrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (* (cbrt (/ (sqrt (* 2 n)) (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (/ (sqrt (* 2 n)) (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (sqrt k) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* 2 (* PI n)) (/ k 2))))))))) * * * * [misc]progress: [ 113 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (/ (sqrt (* 2 n)) (sqrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (/ (sqrt (* 2 n)) (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (/ (sqrt k) (sqrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (sqrt (* n 2)) (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (/ (sqrt (* 2 n)) (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (/ (sqrt k) (sqrt (/ (sqrt (* n 2)) (sqrt (pow (* 2 (* PI n)) (/ k 2))))))))) * * * * [misc]progress: [ 114 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (108 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt k) (/ (pow 2 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow 2 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 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 k) (sqrt 2)) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (sqrt k) (sqrt 2)) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * * * * [misc]progress: [ 115 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (pow n 1/2) (sqrt (pow PI (/ k 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * * [misc]simplify: iters left: 1 (41 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (/ k 2))) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (pow PI (/ k 2))) (sqrt n)) (/ (sqrt k) (/ (pow 2 1/2) (sqrt (pow (* n 2) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow 2 1/2) (sqrt (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* 2 n) (/ k 2))) (/ (sqrt k) (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (pow PI (/ k 2))) (sqrt n)) (* (sqrt (pow (* 2 n) (/ k 2))) (/ (sqrt k) (sqrt 2)))))) * * * * [misc]progress: [ 116 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (pow n 1/2) (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (52 enodes) * [exit]simplify: Simplified to (/ (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt n)) (/ (sqrt k) (/ (pow 2 1/2) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow 2 1/2) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 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 k) (sqrt 2)) (sqrt (cbrt (pow (* n (* 2 PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt n)) (* (/ (sqrt k) (sqrt 2)) (sqrt (cbrt (pow (* n (* 2 PI)) (/ k 2)))))))) * * * * [misc]progress: [ 117 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (pow n 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (55 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt n)) (/ (sqrt k) (/ (pow 2 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow 2 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 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 k) (sqrt 2)) (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt n)) (* (/ (sqrt k) (sqrt 2)) (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * * * * [misc]progress: [ 118 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (pow n 1/2) (sqrt 1))) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt n)) (/ (sqrt k) (/ (pow 2 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow 2 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (sqrt k) (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt n)) (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (sqrt k) (sqrt 2)))))) * * * * [misc]progress: [ 119 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (pow n 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (55 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt n)) (/ (sqrt k) (/ (pow 2 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow 2 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 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 k) (sqrt 2)) (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt n)) (* (/ (sqrt k) (sqrt 2)) (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * * * * [misc]progress: [ 120 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (pow n 1/2) 1)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt n)) (/ (sqrt k) (/ (pow 2 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow 2 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (sqrt k) (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt n)) (* (sqrt (pow (* n (* 2 PI)) (/ k 2))) (/ (sqrt k) (sqrt 2)))))) * * * * [misc]progress: [ 121 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (179 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (* 2 n)))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (* 2 n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (* 2 n)))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (* 2 n))))) (/ (sqrt k) (/ (cbrt (pow (* n 2) 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* n 2) 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 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 (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (* 2 n)))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (* 2 n))))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 122 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt (pow PI (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (87 enodes) * * [misc]simplify: iters left: 1 (172 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (/ k 2))) (* (cbrt (sqrt (* 2 n))) (cbrt (sqrt (* 2 n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (pow PI (/ k 2))) (* (cbrt (sqrt (* 2 n))) (cbrt (sqrt (* 2 n))))) (/ (sqrt k) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* n 2) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 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 k) (/ (cbrt (sqrt (* n 2))) (sqrt (pow (* n 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (pow PI (/ k 2))) (* (cbrt (sqrt (* 2 n))) (cbrt (sqrt (* 2 n))))) (/ (sqrt k) (/ (cbrt (sqrt (* n 2))) (sqrt (pow (* n 2) (/ k 2)))))))) * * * * [misc]progress: [ 123 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (104 enodes) * [exit]simplify: Simplified to (/ (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (* 2 n))) (cbrt (sqrt (* 2 n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (* 2 n))) (cbrt (sqrt (* 2 n))))) (/ (sqrt k) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (* 2 n))) (cbrt (sqrt (* 2 n))))) (* (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 124 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (101 enodes) * * [misc]simplify: iters left: 1 (183 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (* 2 n))) (cbrt (sqrt (* 2 n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (* 2 n))) (cbrt (sqrt (* 2 n))))) (/ (sqrt k) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (* 2 n))) (cbrt (sqrt (* 2 n))))) (* (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 125 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (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 (29 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt (* 2 n))) (cbrt (sqrt (* 2 n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (* (cbrt (sqrt (* 2 n))) (cbrt (sqrt (* 2 n))))) (/ (sqrt k) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 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 k) (cbrt (sqrt (* n 2)))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (* (cbrt (sqrt (* 2 n))) (cbrt (sqrt (* 2 n))))) (* (/ (sqrt k) (cbrt (sqrt (* n 2)))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 126 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (101 enodes) * * [misc]simplify: iters left: 1 (183 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (* 2 n))) (cbrt (sqrt (* 2 n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (* 2 n))) (cbrt (sqrt (* 2 n))))) (/ (sqrt k) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (* 2 n))) (cbrt (sqrt (* 2 n))))) (* (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 127 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) 1)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt (* 2 n)))) (cbrt (sqrt (* 2 n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (sqrt (* 2 n)))) (cbrt (sqrt (* 2 n)))) (/ (sqrt k) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 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 k) (cbrt (sqrt (* n 2)))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (sqrt (* 2 n)))) (cbrt (sqrt (* 2 n)))) (* (/ (sqrt k) (cbrt (sqrt (* n 2)))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 128 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (pow (* n 2) 1/2)) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (128 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt (* 2 n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt (* 2 n))))) (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 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 (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt (* 2 n))))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 129 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow PI (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * * [misc]simplify: iters left: 1 (52 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow PI (/ k 2))) (sqrt (sqrt (* 2 n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (pow PI (/ k 2))) (sqrt (sqrt (* 2 n)))) (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* n 2) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 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 k) (/ (sqrt (sqrt (* n 2))) (sqrt (pow (* n 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (pow PI (/ k 2))) (sqrt (sqrt (* 2 n)))) (/ (sqrt k) (/ (sqrt (sqrt (* n 2))) (sqrt (pow (* n 2) (/ k 2)))))))) * * * * [misc]progress: [ 130 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (pow (* n 2) 1/2)) (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (/ (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt (* 2 n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt (* 2 n)))) (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt (* 2 n)))) (* (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 131 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt (* 2 n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt (* 2 n)))) (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt (* 2 n)))) (* (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 132 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (pow (* n 2) 1/2)) (sqrt 1))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (* 2 n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (sqrt (* 2 n)))) (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 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 k) (sqrt (sqrt (* n 2)))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (sqrt (* 2 n)))) (* (/ (sqrt k) (sqrt (sqrt (* n 2)))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 133 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt (* 2 n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt (* 2 n)))) (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt (* n 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt (* 2 n)))) (* (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt (* n 2)))))))) * * * * [misc]progress: [ 134 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (pow (* n 2) 1/2)) 1)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt (* 2 n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (sqrt (* 2 n)))) (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 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 k) (sqrt (sqrt (* n 2)))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (sqrt (* 2 n)))) (* (/ (sqrt k) (sqrt (sqrt (* n 2)))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 135 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (40 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (/ (pow (* n 2) 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n 2) 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 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 k) (sqrt (* n 2))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (/ (sqrt k) (sqrt (* n 2))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))) * * * * [misc]progress: [ 136 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (sqrt (pow PI (/ k 2))))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * [exit]simplify: Simplified to (sqrt (pow PI (/ k 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (pow PI (/ k 2))) (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* n 2) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* n 2) (/ k 2))) (/ (sqrt k) (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (pow PI (/ k 2))) (* (sqrt (pow (* n 2) (/ k 2))) (/ (sqrt k) (sqrt (* n 2))))))) * * * * [misc]progress: [ 137 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 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 k) (sqrt (* n 2))) (sqrt (cbrt (pow (* 2 (* PI n)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2)))) (* (/ (sqrt k) (sqrt (* n 2))) (sqrt (cbrt (pow (* 2 (* PI n)) (/ k 2)))))))) * * * * [misc]progress: [ 138 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 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 k) (sqrt (* n 2))) (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (/ (sqrt k) (sqrt (* n 2))) (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))) * * * * [misc]progress: [ 139 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (sqrt 1))) * * [misc]simplify: iters left: 5 (4 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (/ (sqrt k) (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (/ (sqrt k) (sqrt (* n 2))))))) * * * * [misc]progress: [ 140 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 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 k) (sqrt (* n 2))) (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (/ (sqrt k) (sqrt (* n 2))) (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))) * * * * [misc]progress: [ 141 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 1)) * * [misc]simplify: iters left: 4 (3 enodes) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (/ (sqrt k) (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (/ (sqrt k) (sqrt (* n 2))))))) * * * * [misc]progress: [ 142 / 192 ] 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) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (/ (sqrt k) (sqrt (* n 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (/ (sqrt k) (sqrt (* n 2))))))) * * * * [misc]progress: [ 143 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (pow (* n 2) 1/2)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (* 2 n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (* 2 n))) (/ (sqrt k) (/ 1 (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * [enter]simplify: Simplifying (/ (sqrt k) (/ 1 (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * * [misc]simplify: iters left: 1 (49 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt k)) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (* 2 n))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt k))))) * * * * [misc]progress: [ 144 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 145 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 146 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 147 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (* (cbrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt (* n 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * * * * [misc]progress: [ 148 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (sqrt (/ (sqrt (* n 2)) (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (sqrt (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt (* n 2)) (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * * * * [misc]progress: [ 149 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 2 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 150 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 2 1/2) (sqrt (pow (* n 2) (/ k 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (sqrt (pow (* n 2) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (sqrt (pow PI (/ k 2))))) (/ (sqrt 2) (sqrt (pow (* n 2) (/ k 2))))))) * * * * [misc]progress: [ 151 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 2 1/2) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 152 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 2 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 153 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 2 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (sqrt 1))) (/ (sqrt 2) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 154 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 2 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 155 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow 2 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) 1)) (/ (sqrt 2) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 156 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* n 2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt (* n 2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 157 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* n 2) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* n 2))) (sqrt (pow (* n 2) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt (pow PI (/ k 2))))) (/ (cbrt (sqrt (* n 2))) (sqrt (pow (* n 2) (/ k 2))))))) * * * * [misc]progress: [ 158 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) 1/2)) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* n 2))) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt (* n 2))) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 159 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* n 2))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt (* n 2))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 160 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* n 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt 1))) (/ (cbrt (sqrt (* n 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 161 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* n 2))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt (* n 2))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 162 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (* n 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (* (cbrt (pow (* n 2) 1/2)) (cbrt (pow (* n 2) 1/2))) 1)) (/ (cbrt (sqrt (* n 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 163 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* n 2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt (* n 2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 164 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* n 2) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* n 2))) (sqrt (pow (* n 2) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow PI (/ k 2))))) (/ (sqrt (sqrt (* n 2))) (sqrt (pow (* n 2) (/ k 2))))))) * * * * [misc]progress: [ 165 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) 1/2)) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* n 2))) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt (* n 2))) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 166 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* n 2))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt (* n 2))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 167 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* n 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (sqrt 1))) (/ (sqrt (sqrt (* n 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 168 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* n 2))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt (* n 2))) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 169 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n 2) 1/2)) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt (* n 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (sqrt (pow (* n 2) 1/2)) 1)) (/ (sqrt (sqrt (* n 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 170 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (* n 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * * * * [misc]progress: [ 171 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (sqrt (pow (* n 2) (/ k 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (sqrt (pow (* n 2) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ 1 (sqrt (pow PI (/ k 2))))) (/ (sqrt (* n 2)) (sqrt (pow (* n 2) (/ k 2))))))) * * * * [misc]progress: [ 172 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (sqrt (cbrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ 1 (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (* n 2)) (sqrt (cbrt (pow (* (* n 2) PI) (/ k 2)))))))) * * * * [misc]progress: [ 173 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ 1 (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (* n 2)) (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * * * * [misc]progress: [ 174 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ 1 (sqrt 1))) (/ (sqrt (* n 2)) (sqrt (pow (* n (* PI 2)) (/ k 2))))))) * * * * [misc]progress: [ 175 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ 1 (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (* n 2)) (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * * * * [misc]progress: [ 176 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ 1 1)) (/ (sqrt (* n 2)) (sqrt (pow (* n (* PI 2)) (/ k 2))))))) * * * * [misc]progress: [ 177 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt (* n 2)) (sqrt (pow (* n (* PI 2)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) 1) (/ (sqrt (* n 2)) (sqrt (pow (* n (* PI 2)) (/ k 2))))))) * * * * [misc]progress: [ 178 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (pow (* (* 2 PI) n) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (pow (* n 2) 1/2)) (/ 1 (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * * * * [misc]progress: [ 179 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (sqrt k)) (cbrt (sqrt k))) * * [misc]simplify: iters left: 4 (4 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt k)))))) * * * * [misc]progress: [ 180 / 192 ] 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 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (/ (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))) (sqrt (sqrt k)))))) * * * * [misc]progress: [ 181 / 192 ] simplifiying candidate # * * * * [misc]progress: [ 182 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (/ k 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (/ k 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (pow (* n 2) 1/2)) (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 183 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (163 enodes) * * [misc]simplify: iters left: 1 (239 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* 2 n)) (/ (sqrt k) (sqrt PI))) (pow (* (* 2 n) PI) (/ k 2))) * [misc]simplify: Simplified (2) to (λ (k n) (/ (/ (sqrt (* 2 n)) (/ (sqrt k) (sqrt PI))) (pow (* (* 2 n) PI) (/ k 2)))) * * * * [misc]progress: [ 184 / 192 ] 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 2 2 1 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * * * * [misc]progress: [ 185 / 192 ] 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 2 2 1 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * * * * [misc]progress: [ 186 / 192 ] 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 2 2 1 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * * * * [misc]progress: [ 187 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [misc]simplify: Simplified (2 1 2 1 1 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 188 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [misc]simplify: Simplified (2 1 2 1 1 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 189 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [misc]simplify: Simplified (2 1 2 1 1 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (/ (pow (* n 2) 1/2) (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * * * [misc]progress: [ 190 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ k (sqrt 2))) (- (+ (* +nan.0 (/ (* (log n) (pow k 2)) (sqrt 2))) (- (+ (* +nan.0 (/ (* n k) (sqrt 2))) (- (+ (* +nan.0 (/ (pow k 2) (sqrt 2))) (- (* +nan.0 (/ (* (pow k 2) (log (* 2 PI))) (sqrt 2)))))))))))) * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) +nan.0)) * * * * [misc]progress: [ 191 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* n k)))) (- (+ (* +nan.0 (/ (pow (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) 2) (* (sqrt 2) (pow n 2)))) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) n)))))))) * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) +nan.0)) * * * * [misc]progress: [ 192 / 192 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))) (- (* +nan.0 (/ 1 n))))))) * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ 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 1 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1 2 1 1 2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2 2 2 1 1 1) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 1) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) in n * [misc]taylor: Taking taylor expansion of (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) in n * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]taylor: Taking taylor expansion of (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) in n * [misc]taylor: Taking taylor expansion of (pow n 1/2) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log n))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (log n)) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) * [misc]backup-simplify: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) * [misc]taylor: Taking taylor expansion of (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) in n * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) in n * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* n 2)) (/ k 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2))))) in n * [misc]taylor: Taking taylor expansion of 1/3 in n * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* n 2)) (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* n 2)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* PI (* n 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* PI (* 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 (* 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 (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 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) into (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) * [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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) into (log (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))))) into (* 1/3 (log (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into (pow (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1/3) * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) in n * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* n 2)) (/ k 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2))))) in n * [misc]taylor: Taking taylor expansion of 1/3 in n * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* n 2)) (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* n 2)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* PI (* n 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* PI (* 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 (* 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 (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 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) into (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) * [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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) into (log (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))))) into (* 1/3 (log (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into (pow (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1/3) * [misc]backup-simplify: Simplify (* (pow (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1/3) (pow (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1/3)) into (pow (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) 1/3) * [misc]backup-simplify: Simplify (/ (pow n 1/2) (pow (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) 1/3)) into (* (sqrt n) (pow (/ 1 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1/3)) * [misc]backup-simplify: Simplify (/ (sqrt k) (* (sqrt n) (pow (/ 1 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1/3))) into (* (sqrt (/ k n)) (pow (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) 1/3)) * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 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 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) in n * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* n 2)) (/ k 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2))))) in n * [misc]taylor: Taking taylor expansion of 1/3 in n * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* n 2)) (/ k 2)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* n 2)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* PI (* n 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* PI (* 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 (* 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 (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 k) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (+ (log n) (log (* 2 PI))) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) into (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) into (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) * [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 (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) into (log (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))))) into (* 1/3 (log (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))))))) into (pow (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1/3) * [misc]backup-simplify: Simplify (/ (sqrt 2) (pow (sqrt (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1/3)) into (* (sqrt 2) (pow (/ 1 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1/6)) * [misc]backup-simplify: Simplify (/ (* (sqrt (/ k n)) (pow (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) 1/3)) (* (sqrt 2) (pow (/ 1 (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k)))) 1/6))) into (* (/ 1 (sqrt 2)) (sqrt (/ (* (exp (* 1/2 (* (+ (log n) (log (* 2 PI))) k))) k) n))) * [misc]taylor: Taking taylor expansion of (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) in k * [misc]taylor: Taking taylor expansion of (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) in k * [misc]taylor: Taking taylor expansion of (pow n 1/2) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log n))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (log n)) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) * [misc]taylor: Taking taylor expansion of (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) in k * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* n 2)) (/ k 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* n 2)) (/ k 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* n 2)) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* PI (* n 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* PI (* 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 (* PI (* n 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (* 2 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 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (/ (* 1/2 (log (* 2 (* n PI)))) (* 2 (sqrt 1))) into (* 1/4 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (* 1/3 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 (* 1/4 (log (* 2 (* n PI))))) 1)) (pow 1 1)))) 1) into (* 1/4 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (+ (* 1/3 (* 1/4 (log (* 2 (* n PI))))) (* 0 0)) into (* 1/12 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* n 2)) (/ k 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* n 2)) (/ k 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* n 2)) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* PI (* n 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* PI (* 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 (* PI (* n 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (* 2 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 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (/ (* 1/2 (log (* 2 (* n PI)))) (* 2 (sqrt 1))) into (* 1/4 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (* 1/3 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 (* 1/4 (log (* 2 (* n PI))))) 1)) (pow 1 1)))) 1) into (* 1/4 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (+ (* 1/3 (* 1/4 (log (* 2 (* n PI))))) (* 0 0)) into (* 1/12 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (/ (pow n 1/2) 1) into (sqrt n) * [misc]backup-simplify: Simplify (/ +nan.0 (sqrt n)) into (* +nan.0 (sqrt (/ 1 n))) * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) in k * [misc]taylor: Taking taylor expansion of (sqrt 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [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 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* n 2)) (/ k 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* n 2)) (/ k 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* n 2)) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* PI (* n 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* PI (* 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 (* PI (* n 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (* 2 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 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (/ (* 1/2 (log (* 2 (* n PI)))) (* 2 (sqrt 1))) into (* 1/4 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (* 1/3 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 (* 1/4 (log (* 2 (* n PI))))) 1)) (pow 1 1)))) 1) into (* 1/4 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (+ (* 1/3 (* 1/4 (log (* 2 (* n PI))))) (* 0 0)) into (* 1/12 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (/ (sqrt 2) 1) into (sqrt 2) * [misc]backup-simplify: Simplify (/ (* +nan.0 (sqrt (/ 1 n))) (sqrt 2)) into (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 n)))) * [misc]taylor: Taking taylor expansion of (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) in k * [misc]taylor: Taking taylor expansion of (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) in k * [misc]taylor: Taking taylor expansion of (pow n 1/2) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log n))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (log n)) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) * [misc]taylor: Taking taylor expansion of (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) in k * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* n 2)) (/ k 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* n 2)) (/ k 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* n 2)) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* PI (* n 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* PI (* 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 (* PI (* n 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (* 2 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 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (/ (* 1/2 (log (* 2 (* n PI)))) (* 2 (sqrt 1))) into (* 1/4 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (* 1/3 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 (* 1/4 (log (* 2 (* n PI))))) 1)) (pow 1 1)))) 1) into (* 1/4 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (+ (* 1/3 (* 1/4 (log (* 2 (* n PI))))) (* 0 0)) into (* 1/12 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* n 2)) (/ k 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* n 2)) (/ k 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* n 2)) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* PI (* n 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* PI (* 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 (* PI (* n 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (* 2 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 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (/ (* 1/2 (log (* 2 (* n PI)))) (* 2 (sqrt 1))) into (* 1/4 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (* 1/3 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 (* 1/4 (log (* 2 (* n PI))))) 1)) (pow 1 1)))) 1) into (* 1/4 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (+ (* 1/3 (* 1/4 (log (* 2 (* n PI))))) (* 0 0)) into (* 1/12 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (* 1 1) into 1 * [misc]backup-simplify: Simplify (/ (pow n 1/2) 1) into (sqrt n) * [misc]backup-simplify: Simplify (/ +nan.0 (sqrt n)) into (* +nan.0 (sqrt (/ 1 n))) * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) in k * [misc]taylor: Taking taylor expansion of (sqrt 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [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 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* n 2)) (/ k 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* n 2)) (/ k 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* n 2)) (/ k 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* n 2)) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* n 2)) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* PI (* n 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* PI (* 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 (* PI (* n 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* n 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (* 2 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 0) into 1 * [misc]backup-simplify: Simplify (sqrt 1) into 1 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (/ (* 1/2 (log (* 2 (* n PI)))) (* 2 (sqrt 1))) into (* 1/4 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (* 1/3 0) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 (* 1/4 (log (* 2 (* n PI))))) 1)) (pow 1 1)))) 1) into (* 1/4 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (+ (* 1/3 (* 1/4 (log (* 2 (* n PI))))) (* 0 0)) into (* 1/12 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (/ (sqrt 2) 1) into (sqrt 2) * [misc]backup-simplify: Simplify (/ (* +nan.0 (sqrt (/ 1 n))) (sqrt 2)) into (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 n)))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt 2)) (sqrt (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt 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]backup-simplify: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ 1 (sqrt 2)) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (sqrt 2)))) * [misc]backup-simplify: Simplify (* (/ 1 (sqrt 2)) 0) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ 1 (sqrt 2))))) (* 0 0)) into (- (* +nan.0 (/ 1 (sqrt 2)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (sqrt 2)))) into (- (* +nan.0 (/ 1 (sqrt 2)))) * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log n))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/12 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/12 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/12 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/12 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (+ (* 1 (* 1/12 (log (* 2 (* n PI))))) (* (* 1/12 (log (* 2 (* n PI)))) 1)) into (* 1/6 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (sqrt n) (/ (* 1/6 (log (* 2 (* n PI)))) 1)))) into (- (* 1/6 (* (log (* 2 (* n PI))) (sqrt n)))) * [misc]backup-simplify: Simplify (- (/ +nan.0 (sqrt n)) (+ (* (* +nan.0 (sqrt (/ 1 n))) (/ (- (* 1/6 (* (log (* 2 (* n PI))) (sqrt n)))) (sqrt n))))) into (- (+ (* +nan.0 (* (log (* 2 (* n PI))) (sqrt (/ 1 n)))) (- (* +nan.0 (sqrt (/ 1 n)))))) * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/12 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/12 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (sqrt 2) (/ (* 1/12 (log (* 2 (* n PI)))) 1)))) into (- (* 1/12 (* (sqrt 2) (log (* 2 (* n PI)))))) * [misc]backup-simplify: Simplify (- (/ (- (+ (* +nan.0 (* (log (* 2 (* n PI))) (sqrt (/ 1 n)))) (- (* +nan.0 (sqrt (/ 1 n)))))) (sqrt 2)) (+ (* (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 n)))) (/ (- (* 1/12 (* (sqrt 2) (log (* 2 (* n PI)))))) (sqrt 2))))) into (- (+ (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 n)))) (- (* +nan.0 (* (/ (log (* 2 (* n PI))) (sqrt 2)) (sqrt (/ 1 n))))))) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 n)))) (- (* +nan.0 (* (/ (log (* 2 (* n PI))) (sqrt 2)) (sqrt (/ 1 n))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 n)))) (- (* +nan.0 (* (/ (log (* 2 (* n PI))) (sqrt 2)) (sqrt (/ 1 n)))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt 2)) (sqrt (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt 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]backup-simplify: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (/ (log (* 2 (* n PI))) (sqrt 2)) (sqrt (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (/ (log (* 2 (* n PI))) (sqrt 2)) (sqrt (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (/ (log (* 2 (* n PI))) (sqrt 2)) (sqrt (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (* n PI))) (sqrt 2)) 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]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log 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 n) (log (* 2 PI))) (sqrt 2)) into (/ (+ (log n) (log (* 2 PI))) (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ 1 (sqrt 2)) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (sqrt 2)))) * [misc]backup-simplify: Simplify (* (/ 1 (sqrt 2)) 0) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ 1 (sqrt 2))))) (* 0 0)) into (- (* +nan.0 (/ 1 (sqrt 2)))) * [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 (- (/ 0 (sqrt 2)) (+ (* (/ (+ (log n) (log (* 2 PI))) (sqrt 2)) (/ 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (+ (log n) (log (* 2 PI))) (sqrt 2)) +nan.0) (* 0 0)) into (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2)))))) * [misc]backup-simplify: Simplify (* (/ (+ (log n) (log (* 2 PI))) (sqrt 2)) 0) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2))))))) (* 0 0)) into (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2)))))) * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2))))))) into (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2)))))) * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (/ 1 (sqrt 2)))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2))))))) into (- (+ (* +nan.0 (/ 1 (sqrt 2))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2)))))))) * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (/ 1 (sqrt 2))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2))))))))) into (- (+ (* +nan.0 (/ 1 (sqrt 2))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ 1 (sqrt 2))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2)))))))) into (- (+ (* +nan.0 (/ 1 (sqrt 2))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2)))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ 1 (sqrt 2)) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ 1 (sqrt 2))))) (+ (* 0 (- (* +nan.0 (/ 1 (sqrt 2))))) (* 0 0))) into (- (* +nan.0 (/ 1 (sqrt 2)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ 1 (sqrt 2)))) into (- (* +nan.0 (/ 1 (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ 1 (sqrt 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ 1 (sqrt 2))) (- (+ (* +nan.0 (/ (log (* 2 PI)) (sqrt 2))) (- (* +nan.0 (/ (log n) (sqrt 2)))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ 1 (sqrt 2)))) (* 1 k)))) into (- (+ (* +nan.0 (/ k (sqrt 2))) (- (+ (* +nan.0 (/ (* (log n) (pow k 2)) (sqrt 2))) (- (+ (* +nan.0 (/ (* n k) (sqrt 2))) (- (+ (* +nan.0 (/ (pow k 2) (sqrt 2))) (- (* +nan.0 (/ (* (pow k 2) (log (* 2 PI))) (sqrt 2)))))))))))) * [misc]approximate: Taking taylor expansion of (/ (/ (sqrt (/ 1 k)) (/ (pow (/ 1 n) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (sqrt (/ 1 k)) (/ (pow (/ 1 n) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))))) in n * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ 1 k)) (/ (pow (/ 1 n) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]taylor: Taking taylor expansion of (/ (pow (/ 1 n) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))))) in n * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) 1/2) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (log (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log n))) into (* -1/2 (log n)) * [misc]backup-simplify: Simplify (exp (* -1/2 (log n))) into (pow n -1/2) * [misc]taylor: Taking taylor expansion of (* (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in n * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in n * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in n * [misc]taylor: Taking taylor expansion of 1/3 in n * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* PI (* (/ 1 n) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 n) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (log (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (* 1/3 (log (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into (pow (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1/3) * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in n * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in n * [misc]taylor: Taking taylor expansion of 1/3 in n * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* PI (* (/ 1 n) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 n) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (log (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (* 1/3 (log (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into (pow (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1/3) * [misc]backup-simplify: Simplify (* (pow (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1/3) (pow (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1/3)) into (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1/3) * [misc]backup-simplify: Simplify (/ (pow n -1/2) (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1/3)) into (* (pow (/ 1 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1/3) (sqrt (/ 1 n))) * [misc]backup-simplify: Simplify (/ (sqrt (/ 1 k)) (* (pow (/ 1 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1/3) (sqrt (/ 1 n)))) into (* (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1/3) (sqrt (/ n k))) * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 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 (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in n * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in n * [misc]taylor: Taking taylor expansion of 1/3 in n * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* PI (* (/ 1 n) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 n) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (log (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (* 1/3 (log (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into (pow (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1/3) * [misc]backup-simplify: Simplify (/ (sqrt 2) (pow (sqrt (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1/3)) into (* (sqrt 2) (pow (/ 1 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1/6)) * [misc]backup-simplify: Simplify (/ (* (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1/3) (sqrt (/ n k))) (* (sqrt 2) (pow (/ 1 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 1/6))) into (* (/ 1 (sqrt 2)) (sqrt (/ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) n) k))) * [misc]taylor: Taking taylor expansion of (/ (/ (sqrt (/ 1 k)) (/ (pow (/ 1 n) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))))) in k * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ 1 k)) (/ (pow (/ 1 n) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ (pow (/ 1 n) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))))) in k * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) 1/2) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (log (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 1 n))) into (* 1/2 (log (/ 1 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ 1 n)))) into (pow (/ 1 n) 1/2) * [misc]taylor: Taking taylor expansion of (* (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in k * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* PI (* (/ 1 n) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 n) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ 2 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 k) 2) (log (* PI (* (/ 1 n) 2))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) into (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) into (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* PI (* (/ 1 n) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 n) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ 2 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 k) 2) (log (* PI (* (/ 1 n) 2))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) into (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) into (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) * [misc]backup-simplify: Simplify (* (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3)) into (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3) * [misc]backup-simplify: Simplify (/ (pow (/ 1 n) 1/2) (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3)) into (* (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) (sqrt (/ 1 n))) * [misc]backup-simplify: Simplify (/ +nan.0 (* (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) (sqrt (/ 1 n)))) into (* +nan.0 (* (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3) (sqrt n))) * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in k * [misc]taylor: Taking taylor expansion of (sqrt 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [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 (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* PI (* (/ 1 n) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 n) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ 2 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 k) 2) (log (* PI (* (/ 1 n) 2))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) into (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) into (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) * [misc]backup-simplify: Simplify (/ (sqrt 2) (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3)) into (* (sqrt 2) (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/6)) * [misc]backup-simplify: Simplify (/ (* +nan.0 (* (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3) (sqrt n))) (* (sqrt 2) (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/6))) into (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)))) * [misc]taylor: Taking taylor expansion of (/ (/ (sqrt (/ 1 k)) (/ (pow (/ 1 n) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))))) in k * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ 1 k)) (/ (pow (/ 1 n) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ (pow (/ 1 n) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))))) in k * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) 1/2) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (log (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ 1 n))) into (* 1/2 (log (/ 1 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ 1 n)))) into (pow (/ 1 n) 1/2) * [misc]taylor: Taking taylor expansion of (* (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in k * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* PI (* (/ 1 n) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 n) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ 2 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 k) 2) (log (* PI (* (/ 1 n) 2))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) into (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) into (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* PI (* (/ 1 n) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 n) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ 2 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 k) 2) (log (* PI (* (/ 1 n) 2))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) into (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) into (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) * [misc]backup-simplify: Simplify (* (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3)) into (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3) * [misc]backup-simplify: Simplify (/ (pow (/ 1 n) 1/2) (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3)) into (* (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) (sqrt (/ 1 n))) * [misc]backup-simplify: Simplify (/ +nan.0 (* (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) (sqrt (/ 1 n)))) into (* +nan.0 (* (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3) (sqrt n))) * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in k * [misc]taylor: Taking taylor expansion of (sqrt 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [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 (cbrt (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 n) 2)) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* PI (* (/ 1 n) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 n) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 n) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ 2 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 k) 2) (log (* PI (* (/ 1 n) 2))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) into (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) into (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) * [misc]backup-simplify: Simplify (/ (sqrt 2) (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3)) into (* (sqrt 2) (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/6)) * [misc]backup-simplify: Simplify (/ (* +nan.0 (* (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3) (sqrt n))) (* (sqrt 2) (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/6))) into (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 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 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt 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]backup-simplify: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)) in n * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]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 (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 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 (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) (* 0 0)) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* 2 (sqrt 0))) into (* +nan.0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (* (/ 1 (sqrt 2)) 0) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 n) (/ 0 n)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (/ 1 n) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (/ 1 n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (/ 1 n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* 1/3 0) (* 0 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* 1/3 0) (* 0 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) 0) (* 0 (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3)) (+ (* (* (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) (sqrt (/ 1 n))) (/ 0 (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3))))) into 0 * [misc]backup-simplify: Simplify (- (/ +nan.0 (* (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) (sqrt (/ 1 n)))) (+ (* (* +nan.0 (* (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3) (sqrt n))) (/ 0 (* (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) (sqrt (/ 1 n))))))) into (- (* +nan.0 (* (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3) (sqrt n)))) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* 1/3 0) (* 0 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3)) (+ (* (* (sqrt 2) (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/6)) (/ 0 (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3))))) into 0 * [misc]backup-simplify: Simplify (- (/ (- (* +nan.0 (* (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3) (sqrt n)))) (* (sqrt 2) (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/6))) (+ (* (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)))) (/ 0 (* (sqrt 2) (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/6)))))) into (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 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 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt 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]backup-simplify: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)) in n * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]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 (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 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 (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) (* 0 0)) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* 2 (sqrt 0))) into (* +nan.0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (* (/ 1 (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 into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ 1 (sqrt 2)) (* +nan.0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2))))) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 n) (/ 0 n)) (* 0 (/ 0 n)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (/ 1 n) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (/ 1 n) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (log (/ 1 n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (/ 1 n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) 0) (+ (* 0 0) (* 0 (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3)) (+ (* (* (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) (sqrt (/ 1 n))) (/ 0 (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3))) (* 0 (/ 0 (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3))))) into 0 * [misc]backup-simplify: Simplify (- (/ +nan.0 (* (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) (sqrt (/ 1 n)))) (+ (* (* +nan.0 (* (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3) (sqrt n))) (/ 0 (* (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) (sqrt (/ 1 n))))) (* (- (* +nan.0 (* (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3) (sqrt n)))) (/ 0 (* (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3) (sqrt (/ 1 n))))))) into (- (* +nan.0 (* (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3) (sqrt n)))) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/3 (log (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3)) (+ (* (* (sqrt 2) (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/6)) (/ 0 (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3))) (* 0 (/ 0 (pow (sqrt (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/3))))) into 0 * [misc]backup-simplify: Simplify (- (/ (- (* +nan.0 (* (pow (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 1/3) (sqrt n)))) (* (sqrt 2) (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/6))) (+ (* (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)))) (/ 0 (* (sqrt 2) (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/6)))) (* (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))))) (/ 0 (* (sqrt 2) (pow (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) 1/6)))))) into (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) 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 (* (/ 1 (sqrt 2)) (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt 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]backup-simplify: Simplify (/ 1 (sqrt 2)) into (/ 1 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n)) in n * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) n) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) k) into (/ (- (log (* 2 PI)) (log n)) k) * [misc]backup-simplify: Simplify (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]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 (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 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 (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 1) (* 0 0)) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (* 2 (sqrt 0))) into (* +nan.0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (* (/ 1 (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 into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ 1 (sqrt 2)) (* +nan.0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2))))) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) * [misc]backup-simplify: Simplify (- (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2))))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) into (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2)))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ (- (log (* 2 PI)) (log n)) k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ (- (log (* 2 PI)) (log n)) k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 0) (+ (* 0 1) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 2) (+)) (* 2 0)) into (* +nan.0 (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2)) * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 (sqrt 2)) (/ 0 (sqrt 2))) (* 0 (/ 0 (sqrt 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ 1 (sqrt 2)) (* +nan.0 (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2))) (+ (* 0 (* +nan.0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 0))) into (- (* +nan.0 (/ (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2) (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2) (sqrt 2))))) (+ (* 0 (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (sqrt 2))))) (* 0 0))) into (- (* +nan.0 (/ (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2) (sqrt 2)))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2) (sqrt 2)))) into (- (* +nan.0 (/ (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) 2) (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (pow (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) 2) (sqrt 2)))) (pow (* (/ 1 n) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (sqrt 2)))) (* (/ 1 n) (/ 1 k))) (* (- (* +nan.0 (/ (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))) (sqrt 2)))) (* (/ 1 n) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* n k)))) (- (+ (* +nan.0 (/ (pow (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) 2) (* (sqrt 2) (pow n 2)))) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) n)))))))) * [misc]approximate: Taking taylor expansion of (/ (/ (sqrt (/ 1 (- k))) (/ (pow (/ 1 (- n)) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (sqrt (/ 1 (- k))) (/ (pow (/ 1 (- n)) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))))) in n * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (/ (pow (/ 1 (- n)) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]taylor: Taking taylor expansion of (/ (pow (/ 1 (- n)) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))))) in n * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) 1/2) in n * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (log (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (log -1) into (log -1) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log -1) (log n)))) into (exp (* 1/2 (- (log -1) (log n)))) * [misc]taylor: Taking taylor expansion of (* (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in n * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in n * [misc]taylor: Taking taylor expansion of 1/3 in n * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 (- n)) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* PI -2) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (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 (+ (* PI 0) (* 0 -2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (log (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* 1/3 (log (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (pow (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1/3) * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in n * [misc]taylor: Taking taylor expansion of 1/3 in n * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 (- n)) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* PI -2) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (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 (+ (* PI 0) (* 0 -2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (log (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* 1/3 (log (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (pow (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1/3) * [misc]backup-simplify: Simplify (* (pow (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1/3) (pow (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1/3)) into (pow (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1/3) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log -1) (log n)))) (pow (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1/3)) into (* (exp (* 1/2 (- (log -1) (log n)))) (pow (/ 1 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1/3)) * [misc]backup-simplify: Simplify (/ (sqrt (/ -1 k)) (* (exp (* 1/2 (- (log -1) (log n)))) (pow (/ 1 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1/3))) into (* (/ (sqrt (/ -1 k)) (exp (* 1/2 (- (log -1) (log n))))) (pow (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1/3)) * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 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 (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in n * [misc]taylor: Taking taylor expansion of 1/3 in n * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 (- n)) 2))) in n * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* PI -2) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (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 (+ (* PI 0) (* 0 -2)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (log (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* 1/3 (log (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (pow (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1/3) * [misc]backup-simplify: Simplify (/ (sqrt 2) (pow (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1/3)) into (* (sqrt 2) (pow (/ 1 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1/6)) * [misc]backup-simplify: Simplify (/ (* (/ (sqrt (/ -1 k)) (exp (* 1/2 (- (log -1) (log n))))) (pow (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 1/3)) (* (sqrt 2) (pow (/ 1 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) 1/6))) into (* (/ (sqrt (/ -1 k)) (* (sqrt 2) (exp (* 1/2 (- (log -1) (log n)))))) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]taylor: Taking taylor expansion of (/ (/ (sqrt (/ 1 (- k))) (/ (pow (/ 1 (- n)) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))))) in k * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (/ (pow (/ 1 (- n)) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ (pow (/ 1 (- n)) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))))) in k * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) 1/2) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (log (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ -1 n)))) into (pow (/ -1 n) 1/2) * [misc]taylor: Taking taylor expansion of (* (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in k * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 (- n)) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ -2 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 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) into (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) into (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3) * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 (- n)) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ -2 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 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) into (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) into (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3) * [misc]backup-simplify: Simplify (* (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3) (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3)) into (pow (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1/3) * [misc]backup-simplify: Simplify (/ (pow (/ -1 n) 1/2) (pow (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1/3)) into (* (sqrt (/ -1 n)) (pow (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3)) * [misc]backup-simplify: Simplify (/ +nan.0 (* (sqrt (/ -1 n)) (pow (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3))) into (* +nan.0 (* (/ 1 (sqrt (/ -1 n))) (pow (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1/3))) * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in k * [misc]taylor: Taking taylor expansion of (sqrt 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [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 (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 (- n)) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ -2 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 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) into (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) into (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3) * [misc]backup-simplify: Simplify (/ (sqrt 2) (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3)) into (* (sqrt 2) (pow (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/6)) * [misc]backup-simplify: Simplify (/ (* +nan.0 (* (/ 1 (sqrt (/ -1 n))) (pow (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1/3))) (* (sqrt 2) (pow (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/6))) into (* +nan.0 (* (/ 1 (* (sqrt 2) (sqrt (/ -1 n)))) (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) * [misc]taylor: Taking taylor expansion of (/ (/ (sqrt (/ 1 (- k))) (/ (pow (/ 1 (- n)) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))))) in k * [misc]taylor: Taking taylor expansion of (/ (sqrt (/ 1 (- k))) (/ (pow (/ 1 (- n)) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ (pow (/ 1 (- n)) 1/2) (* (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))))) in k * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- n)) 1/2) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (log (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (log (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (/ -1 n)))) into (pow (/ -1 n) 1/2) * [misc]taylor: Taking taylor expansion of (* (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in k * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 (- n)) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ -2 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 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) into (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) into (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3) * [misc]taylor: Taking taylor expansion of (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 (- n)) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ -2 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 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) into (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) into (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3) * [misc]backup-simplify: Simplify (* (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3) (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3)) into (pow (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1/3) * [misc]backup-simplify: Simplify (/ (pow (/ -1 n) 1/2) (pow (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1/3)) into (* (sqrt (/ -1 n)) (pow (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3)) * [misc]backup-simplify: Simplify (/ +nan.0 (* (sqrt (/ -1 n)) (pow (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3))) into (* +nan.0 (* (/ 1 (sqrt (/ -1 n))) (pow (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1/3))) * [misc]taylor: Taking taylor expansion of (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in k * [misc]taylor: Taking taylor expansion of (sqrt 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [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 (cbrt (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Rewrote expression to (pow (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) 1/3) * [misc]taylor: Taking taylor expansion of (exp (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))))) in k * [misc]taylor: Taking taylor expansion of (* 1/3 (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))))) in k * [misc]taylor: Taking taylor expansion of 1/3 in k * [misc]backup-simplify: Simplify 1/3 into 1/3 * [misc]taylor: Taking taylor expansion of (log (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* PI (* (/ 1 (- n)) 2)) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* PI (* (/ 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 (* PI (* (/ 1 (- n)) 2))) in k * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- n)) 2)) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [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 (* PI (/ -2 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 (- k)) 2) (log (* PI (* (/ 1 (- n)) 2))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into 0 * [misc]backup-simplify: Simplify (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) into (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) * [misc]backup-simplify: Simplify (exp (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) into (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3) * [misc]backup-simplify: Simplify (/ (sqrt 2) (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3)) into (* (sqrt 2) (pow (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/6)) * [misc]backup-simplify: Simplify (/ (* +nan.0 (* (/ 1 (sqrt (/ -1 n))) (pow (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1/3))) (* (sqrt 2) (pow (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/6))) into (* +nan.0 (* (/ 1 (* (sqrt 2) (sqrt (/ -1 n)))) (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (/ 1 (* (sqrt 2) (sqrt (/ -1 n)))) (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (* (sqrt 2) (sqrt (/ -1 n)))) (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt 2) (sqrt (/ -1 n)))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (/ -1 n))) in n * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 n)) in n * [misc]taylor: Taking taylor expansion of (/ -1 n) in n * [misc]taylor: Taking taylor expansion of -1 in n * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ -1 1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) +nan.0) (* 0 0)) into (- (* +nan.0 (sqrt 2))) * [misc]backup-simplify: Simplify (/ 1 (- (* +nan.0 (sqrt 2)))) into (/ +nan.0 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) in n * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) in n * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (* -2 (/ PI n))) k)) in n * [misc]taylor: Taking taylor expansion of -1/2 in n * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (/ (log (* -2 (/ PI n))) k) in n * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of -2 in n * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) k) into (/ (- (log (* -2 PI)) (log n)) k) * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [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 (- (/ 0 k) (+ (* (/ (- (log (* -2 PI)) (log n)) k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 0 (/ (- (log (* -2 PI)) (log n)) k))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (* (/ +nan.0 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (* +nan.0 (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (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 (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 n) (/ 0 (- n))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (/ -1 n) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (log (/ -1 n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (/ -1 n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* 1/3 0) (* 0 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* 1/3 0) (* 0 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3) 0) (* 0 (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1/3)) (+ (* (* (sqrt (/ -1 n)) (pow (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3)) (/ 0 (pow (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1/3))))) into 0 * [misc]backup-simplify: Simplify (- (/ +nan.0 (* (sqrt (/ -1 n)) (pow (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3))) (+ (* (* +nan.0 (* (/ 1 (sqrt (/ -1 n))) (pow (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1/3))) (/ 0 (* (sqrt (/ -1 n)) (pow (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3)))))) into (- (* +nan.0 (* (/ 1 (sqrt (/ -1 n))) (pow (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1/3)))) * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* 1/3 0) (* 0 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/3 (log (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3)) (+ (* (* (sqrt 2) (pow (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/6)) (/ 0 (pow (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/3))))) into 0 * [misc]backup-simplify: Simplify (- (/ (- (* +nan.0 (* (/ 1 (sqrt (/ -1 n))) (pow (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) 1/3)))) (* (sqrt 2) (pow (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/6))) (+ (* (* +nan.0 (* (/ 1 (* (sqrt 2) (sqrt (/ -1 n)))) (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) (/ 0 (* (sqrt 2) (pow (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) 1/6)))))) into (- (* +nan.0 (* (/ 1 (* (sqrt 2) (sqrt (/ -1 n)))) (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (/ 1 (* (sqrt 2) (sqrt (/ -1 n)))) (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (/ 1 (* (sqrt 2) (sqrt (/ -1 n)))) (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (* (sqrt 2) (sqrt (/ -1 n)))) (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (* (sqrt 2) (sqrt (/ -1 n)))) in n * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (/ -1 n))) in n * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 n)) in n * [misc]taylor: Taking taylor expansion of (/ -1 n) in n * [misc]taylor: Taking taylor expansion of -1 in n * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ -1 1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) +nan.0) (* 0 0)) into (- (* +nan.0 (sqrt 2))) * [misc]backup-simplify: Simplify (/ 1 (- (* +nan.0 (sqrt 2)))) into (/ +nan.0 (sqrt 2)) * [misc]taylor: Taking taylor expansion of (sqrt (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) in n * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) in n * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (log (* -2 (/ PI n))) k)) in n * [misc]taylor: Taking taylor expansion of -1/2 in n * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (/ (log (* -2 (/ PI n))) k) in n * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of -2 in n * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) k) into (/ (- (log (* -2 PI)) (log n)) k) * [misc]backup-simplify: Simplify (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [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 (- (/ 0 k) (+ (* (/ (- (log (* -2 PI)) (log n)) k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 0 (/ (- (log (* -2 PI)) (log n)) k))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (* (/ +nan.0 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (* +nan.0 (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) * [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 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (sqrt 2))) * [misc]backup-simplify: Simplify (- (+ (* (/ +nan.0 (sqrt 2)) (/ (- (* +nan.0 (sqrt 2))) (- (* +nan.0 (sqrt 2))))))) into (- (* +nan.0 (/ 1 (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (* (/ +nan.0 (sqrt 2)) 0) (* (- (* +nan.0 (/ 1 (sqrt 2)))) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))))) (* 0 (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))))) into (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) into (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) (* (/ 1 (- n)) 1)) (+ (* (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))))) into (- (+ (* +nan.0 (* (/ 1 (* (sqrt 2) n)) (sqrt (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))))) (- (+ (* +nan.0 (* (/ 1 (* (sqrt 2) k)) (sqrt (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))))) (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))))))))))) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1 2 1 1 2) * [misc]approximate: Taking taylor expansion of (* n PI) in (n) around 0 * [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]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 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 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 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 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 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 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* PI n) into (* n PI) * [misc]approximate: Taking taylor expansion of (* (/ 1 n) PI) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) PI) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 n) PI) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 1 PI) into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 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 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 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 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 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 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) * [misc]approximate: Taking taylor expansion of (* (/ 1 (- n)) PI) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) PI) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) PI) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 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 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 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 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 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 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 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2 2 2 1 1 1) * [misc]approximate: Taking taylor expansion of (* PI (* n 2)) in (n) around 0 * [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]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 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 (* 2 PI) into (* 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 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0)))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 0 0))))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 2) (* 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 (* PI (* (/ 1 n) 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 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 (* (/ 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 (* (/ 1 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 (* (/ 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 (* PI 2) 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 (+ (* PI 0) (* 0 2)) 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 (+ (* PI 0) (+ (* 0 0) (* 0 2))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) 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 (* PI (* (/ 1 (- n)) 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* PI (* (/ 1 (- 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 (* (/ 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 (* (/ 1 (- 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 (* (/ 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 (* PI -2) 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 (+ (* PI 0) (* 0 -2)) 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 (+ (* PI 0) (+ (* 0 0) (* 0 -2))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2)))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2)))))) 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 (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -2))))))) 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 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 3 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 4 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 5 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 6 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 7 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 8 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 9 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 11 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 12 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 13 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 14 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (sqrt k)) (- (* (log n) 1/2) (+ (log (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (log (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (- (log (sqrt 2)) (log (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (100 enodes) * * [misc]simplify: iters left: 3 (300 enodes) * [exit]simplify: Simplified to (+ (+ (log (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (+ (- (log (sqrt 2))) (fma (log n) -1/2 (log (sqrt k))))) (+ (log (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (log (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (exp (+ (+ (log (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (+ (- (log (sqrt 2))) (fma (log n) -1/2 (log (sqrt k))))) (+ (log (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (log (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 15 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (sqrt k)) (- (* (log n) 1/2) (+ (log (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (log (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (log (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * [exit]simplify: Simplified to (- (+ (fma -1/2 (log n) (log (sqrt k))) (log (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (- (log (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (log (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (exp (- (+ (fma -1/2 (log n) (log (sqrt k))) (log (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (- (log (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (log (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 16 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (sqrt k)) (- (* (log n) 1/2) (log (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (- (log (sqrt 2)) (log (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (266 enodes) * [exit]simplify: Simplified to (+ (log (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (+ (log (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (- (log (sqrt k)) (fma (log n) 1/2 (log (sqrt 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (exp (+ (log (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (+ (log (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (- (log (sqrt k)) (fma (log n) 1/2 (log (sqrt 2))))))))) * * * * [misc]progress: [ 17 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (sqrt k)) (- (* (log n) 1/2) (log (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (log (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (213 enodes) * [exit]simplify: Simplified to (+ (log (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (+ (- (fma (log n) -1/2 (log (sqrt k))) (log (sqrt 2))) (log (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (exp (+ (log (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (+ (- (fma (log n) -1/2 (log (sqrt k))) (log (sqrt 2))) (log (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 18 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (sqrt k)) (- (log (pow n 1/2)) (+ (log (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (log (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (- (log (sqrt 2)) (log (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (303 enodes) * [exit]simplify: Simplified to (+ (+ (log (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (log (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (+ (log (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (+ (- (log (sqrt 2))) (fma (log n) -1/2 (log (sqrt k)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (exp (+ (+ (log (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (log (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (+ (log (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (+ (- (log (sqrt 2))) (fma (log n) -1/2 (log (sqrt k))))))))) * * * * [misc]progress: [ 19 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (sqrt k)) (- (log (pow n 1/2)) (+ (log (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (log (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (log (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (230 enodes) * [exit]simplify: Simplified to (- (+ (log (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (fma -1/2 (log n) (log (sqrt k)))) (- (log (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (log (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (exp (- (+ (log (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (fma -1/2 (log n) (log (sqrt k)))) (- (log (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (log (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))))) * * * * [misc]progress: [ 20 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (sqrt k)) (- (log (pow n 1/2)) (log (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (- (log (sqrt 2)) (log (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (268 enodes) * [exit]simplify: Simplified to (+ (log (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (+ (- (log (sqrt k)) (fma 1/2 (log n) (log (sqrt 2)))) (log (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (exp (+ (log (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (+ (- (log (sqrt k)) (fma 1/2 (log n) (log (sqrt 2)))) (log (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))))) * * * * [misc]progress: [ 21 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (sqrt k)) (- (log (pow n 1/2)) (log (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (log (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (216 enodes) * [exit]simplify: Simplified to (+ (+ (log (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (log (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (+ (- (log (sqrt k)) (fma 1/2 (log n) (log (sqrt 2)))) (log (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (exp (+ (+ (log (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (log (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (+ (- (log (sqrt k)) (fma 1/2 (log n) (log (sqrt 2)))) (log (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 22 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (sqrt k)) (log (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (- (log (sqrt 2)) (log (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (181 enodes) * * [misc]simplify: iters left: 2 (464 enodes) * [exit]simplify: Simplified to (+ (+ (log (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (- (- (log (sqrt k)) (log (sqrt 2))) (log (sqrt n)))) (+ (log (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (log (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (exp (+ (+ (log (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (- (- (log (sqrt k)) (log (sqrt 2))) (log (sqrt n)))) (+ (log (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (log (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 23 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (sqrt k)) (log (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (log (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (377 enodes) * [exit]simplify: Simplified to (+ (+ (log (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (log (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (+ (+ (fma (log n) -1/2 (log (sqrt k))) (- (log (sqrt 2)))) (log (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (exp (+ (+ (log (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (log (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (+ (+ (fma (log n) -1/2 (log (sqrt k))) (- (log (sqrt 2)))) (log (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 24 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (- (log (sqrt 2)) (log (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (444 enodes) * [exit]simplify: Simplified to (+ (log (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (+ (log (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (- (log (/ (sqrt k) (sqrt n))) (log (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (exp (+ (log (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (+ (log (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (- (log (/ (sqrt k) (sqrt n))) (log (sqrt 2)))))))) * * * * [misc]progress: [ 25 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (log (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (343 enodes) * [exit]simplify: Simplified to (+ (log (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (+ (- (log (/ (sqrt k) (sqrt n))) (log (sqrt 2))) (log (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (exp (+ (log (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (+ (- (log (/ (sqrt k) (sqrt n))) (log (sqrt 2))) (log (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 26 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 28 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (/ (* (* (pow n 1/2) (pow n 1/2)) (pow n 1/2)) (* (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (160 enodes) * [exit]simplify: Simplified to (* (/ (* (/ k n) (/ (sqrt k) (sqrt n))) (/ 2 (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (pow (* (* n 2) PI) (/ k 2))) (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (* (/ (* (/ k n) (/ (sqrt k) (sqrt n))) (/ 2 (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (pow (* (* n 2) PI) (/ k 2))) (sqrt 2)))))) * * * * [misc]progress: [ 29 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (/ (* (* (pow n 1/2) (pow n 1/2)) (pow n 1/2)) (* (sqrt (pow (* PI (* n 2)) (/ k 2))) (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (* (* (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (186 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (* (/ (* (pow (* (* PI 2) n) (/ k 2)) (/ (* k (sqrt k)) (* (sqrt n) n))) (sqrt 2)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ 2 (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (* (/ (* (pow (* (* PI 2) n) (/ k 2)) (/ (* k (sqrt k)) (* (sqrt n) n))) (sqrt 2)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ 2 (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 30 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (/ (* (* (pow n 1/2) (pow n 1/2)) (pow n 1/2)) (* (* (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (59 enodes) * * [misc]simplify: iters left: 4 (225 enodes) * [exit]simplify: Simplified to (/ (* (* (/ (sqrt k) (* 2 (sqrt 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) k) (* (/ (sqrt n) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ n (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (/ (* (* (/ (sqrt k) (* 2 (sqrt 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) k) (* (/ (sqrt n) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ n (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 31 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (/ (* (* (pow n 1/2) (pow n 1/2)) (pow n 1/2)) (* (* (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (* (* (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (63 enodes) * * [misc]simplify: iters left: 4 (246 enodes) * [exit]simplify: Simplified to (/ (/ (* k (sqrt k)) (/ (pow (sqrt 2) 3) (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (/ n (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt n) (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (/ (/ (* k (sqrt k)) (/ (pow (sqrt 2) 3) (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (/ n (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt n) (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 32 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (54 enodes) * * [misc]simplify: iters left: 4 (185 enodes) * [exit]simplify: Simplified to (/ (/ (* k (sqrt k)) (/ (* (/ (* (sqrt 2) 2) (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ n (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (/ (/ (* k (sqrt k)) (/ (* (/ (* (sqrt 2) 2) (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ n (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 33 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (* (* (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (58 enodes) * * [misc]simplify: iters left: 4 (210 enodes) * [exit]simplify: Simplified to (/ (/ (/ (* k (sqrt k)) (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ 2 (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (/ (/ n (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (/ (/ (/ (* k (sqrt k)) (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ 2 (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (/ (/ n (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))))) * * * * [misc]progress: [ 34 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (136 enodes) * [exit]simplify: Simplified to (* (/ (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (* (sqrt 2) 2) (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (* (/ (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (* (sqrt 2) 2) (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 35 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (* (* (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (53 enodes) * * [misc]simplify: iters left: 4 (180 enodes) * [exit]simplify: Simplified to (pow (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt 2) (/ (sqrt k) (sqrt n))))) 3) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (pow (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt 2) (/ (sqrt k) (sqrt n))))) 3)))) * * * * [misc]progress: [ 36 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 37 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 38 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 39 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 40 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (82 enodes) * * [misc]simplify: iters left: 1 (84 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 41 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 42 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (175 enodes) * * [misc]simplify: iters left: 1 (206 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 43 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (177 enodes) * * [misc]simplify: iters left: 1 (208 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (/ (sqrt n) (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (cbrt (sqrt 2))) (* (cbrt (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (/ (sqrt n) (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (/ (sqrt n) (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (cbrt (sqrt 2))) (* (cbrt (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (/ (sqrt n) (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (sqrt 2))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (/ (sqrt n) (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (cbrt (sqrt 2))) (* (cbrt (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (/ (sqrt n) (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (sqrt 2))))) (/ (cbrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))))) * * * * [misc]progress: [ 44 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (185 enodes) * * [misc]simplify: iters left: 1 (220 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (/ (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt 2)))) (/ (cbrt (sqrt 2)) (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (/ (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt 2)))) (/ (cbrt (sqrt 2)) (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (/ (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt 2)))) (/ (cbrt (sqrt 2)) (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))))) (/ (cbrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 45 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (117 enodes) * * [misc]simplify: iters left: 2 (176 enodes) * * [misc]simplify: iters left: 1 (207 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 46 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (279 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (sqrt 2))) (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (sqrt 2))) (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (sqrt 2)))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (sqrt 2))) (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (sqrt 2)))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 47 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (117 enodes) * * [misc]simplify: iters left: 2 (176 enodes) * * [misc]simplify: iters left: 1 (207 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 48 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (223 enodes) * * [misc]simplify: iters left: 1 (351 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt k) (sqrt n))))) (cbrt (sqrt 2))) (/ (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt k) (sqrt n))))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt k) (sqrt n))))) (cbrt (sqrt 2))) (/ (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt k) (sqrt n))))) (cbrt (sqrt 2)))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt k) (sqrt n))))) (cbrt (sqrt 2))) (/ (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt k) (sqrt n))))) (cbrt (sqrt 2)))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 49 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (299 enodes) * * [misc]simplify: iters left: 1 (411 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2))) (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2))) (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2))) (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2))) (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2))) (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2))) (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 50 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (175 enodes) * * [misc]simplify: iters left: 1 (206 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 51 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (313 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (sqrt 2))) (/ (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (sqrt 2))) (/ (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (sqrt 2)))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (sqrt 2))) (/ (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (sqrt 2)))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 52 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (104 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n))))) (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 53 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (98 enodes) * * [misc]simplify: iters left: 1 (106 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt n) (sqrt k)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (sqrt (sqrt 2))) (* (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt n) (sqrt k)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt n) (sqrt k)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (sqrt (sqrt 2))) (* (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt n) (sqrt k)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt n) (sqrt k)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (sqrt (sqrt 2))) (* (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt n) (sqrt k)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) (/ (cbrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))))) * * * * [misc]progress: [ 54 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (80 enodes) * * [misc]simplify: iters left: 2 (100 enodes) * * [misc]simplify: iters left: 1 (108 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (cbrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 55 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (97 enodes) * * [misc]simplify: iters left: 1 (105 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2))) (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k))))) (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2))) (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k))))) (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2))) (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k))))) (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k))))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 56 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (102 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (sqrt (sqrt 2))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (sqrt (sqrt 2))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (sqrt (sqrt 2))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 57 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (97 enodes) * * [misc]simplify: iters left: 1 (105 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2))) (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k))))) (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2))) (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k))))) (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2))) (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k))))) (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k))))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 58 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (99 enodes) * * [misc]simplify: iters left: 1 (106 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 59 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (144 enodes) * * [misc]simplify: iters left: 1 (177 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (* (/ (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (cbrt (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt n) (sqrt k)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (* (/ (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (cbrt (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt n) (sqrt k)))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (* (/ (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (cbrt (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt n) (sqrt k)))))) (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 60 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (104 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n))))) (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 61 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (87 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (sqrt (sqrt 2))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (sqrt (sqrt 2))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 62 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (80 enodes) * * [misc]simplify: iters left: 2 (111 enodes) * * [misc]simplify: iters left: 1 (187 enodes) * [exit]simplify: Simplified to (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 63 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (273 enodes) * [exit]simplify: Simplified to (* (* (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (sqrt (pow PI (/ k 2))))) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (sqrt (pow PI (/ k 2))))) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (sqrt (pow PI (/ k 2))))) (cbrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))))) * * * * [misc]progress: [ 64 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (115 enodes) * * [misc]simplify: iters left: 1 (176 enodes) * [exit]simplify: Simplified to (* (* (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 65 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (81 enodes) * * [misc]simplify: iters left: 2 (112 enodes) * * [misc]simplify: iters left: 1 (173 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))))) (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 66 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (81 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 67 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (81 enodes) * * [misc]simplify: iters left: 2 (112 enodes) * * [misc]simplify: iters left: 1 (173 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))))) (/ (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 68 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (102 enodes) * * [misc]simplify: iters left: 1 (114 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 69 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * [exit]simplify: Simplified to (* (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 70 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (80 enodes) * * [misc]simplify: iters left: 2 (111 enodes) * * [misc]simplify: iters left: 1 (187 enodes) * [exit]simplify: Simplified to (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 71 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (82 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 72 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) 1) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (110 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (cbrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k))))) (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 73 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (sqrt 2)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (84 enodes) * [exit]simplify: Simplified to (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * * * * [misc]progress: [ 74 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (62 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 75 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 76 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (89 enodes) * * [misc]simplify: iters left: 1 (98 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 77 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (91 enodes) * * [misc]simplify: iters left: 1 (100 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) (/ (sqrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))))) * * * * [misc]progress: [ 78 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (80 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (102 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (sqrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 79 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (90 enodes) * * [misc]simplify: iters left: 1 (99 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 80 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (148 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 81 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (90 enodes) * * [misc]simplify: iters left: 1 (99 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 82 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (129 enodes) * * [misc]simplify: iters left: 1 (155 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 83 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (145 enodes) * * [misc]simplify: iters left: 1 (171 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (* (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (* (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt 2))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (* (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt 2))))) (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 84 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (89 enodes) * * [misc]simplify: iters left: 1 (98 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 85 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (234 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 86 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 87 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) (/ (sqrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))))) * * * * [misc]progress: [ 88 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (71 enodes) * * [misc]simplify: iters left: 1 (73 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (/ (sqrt n) (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (/ (sqrt n) (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (/ (sqrt n) (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (sqrt (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 89 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 90 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (sqrt (sqrt 2))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (sqrt (sqrt 2))) (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 91 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 92 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (80 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (sqrt (sqrt 2))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (sqrt (sqrt 2))) (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 93 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (87 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 94 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 95 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (77 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (sqrt (sqrt 2))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (sqrt (sqrt 2))) (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 96 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (85 enodes) * [exit]simplify: Simplified to (* (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (sqrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (sqrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (sqrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 97 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (* (sqrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2))))) (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))))) * * * * [misc]progress: [ 98 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (82 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (/ (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2)))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (/ (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2)))))) (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 99 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 100 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 101 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (* (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 102 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 103 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (94 enodes) * * [misc]simplify: iters left: 1 (101 enodes) * [exit]simplify: Simplified to (* (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 104 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (85 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (sqrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (sqrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (sqrt (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 105 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (62 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (sqrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 106 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) 1) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (sqrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (/ (sqrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 107 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt 2)) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (sqrt 2)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (sqrt 2)) (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (84 enodes) * [exit]simplify: Simplified to (* (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt n) (sqrt k)))) (sqrt 2)) (* (sqrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * * * * [misc]progress: [ 108 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (256 enodes) * * [misc]simplify: iters left: 1 (317 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 109 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (131 enodes) * * [misc]simplify: iters left: 1 (150 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt k)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 110 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (243 enodes) * [exit]simplify: Simplified to (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 111 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (245 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow PI (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow PI (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow PI (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 112 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (29 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (245 enodes) * [exit]simplify: Simplified to (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 113 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (244 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 114 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (237 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 115 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (244 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 116 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (48 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (219 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 117 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (50 enodes) * * [misc]simplify: iters left: 4 (116 enodes) * * [misc]simplify: iters left: 3 (358 enodes) * [exit]simplify: Simplified to (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 118 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (243 enodes) * [exit]simplify: Simplified to (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 119 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (188 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 120 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (362 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt k)) (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 121 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (364 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 122 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (366 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 123 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (363 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 124 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (357 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (* (sqrt (sqrt 2)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (* (sqrt (sqrt 2)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (* (sqrt (sqrt 2)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 125 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (363 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 126 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (364 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 127 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (213 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (* (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (* (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (* (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 128 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (362 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt k)) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 129 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (358 enodes) * [exit]simplify: Simplified to (/ (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 130 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (189 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 131 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (191 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (sqrt (pow PI (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (sqrt (pow PI (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (sqrt (pow PI (/ k 2)))))) (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 132 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (193 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt k)) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (sqrt k)) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (sqrt k)) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (sqrt k)) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 133 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (189 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 134 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (279 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 135 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (189 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 136 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (301 enodes) * * [misc]simplify: iters left: 1 (441 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 137 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (248 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 138 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (189 enodes) * [exit]simplify: Simplified to (/ (/ (* (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 139 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * * [misc]simplify: iters left: 1 (376 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 140 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) 1) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (291 enodes) * * [misc]simplify: iters left: 1 (371 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 141 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (sqrt 2)) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (129 enodes) * * [misc]simplify: iters left: 1 (146 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (cbrt (sqrt k)))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (159 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (cbrt (sqrt k)))) (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 142 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (131 enodes) * * [misc]simplify: iters left: 1 (150 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 143 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt k)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 144 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (389 enodes) * [exit]simplify: Simplified to (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 145 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (392 enodes) * [exit]simplify: Simplified to (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow PI (/ k 2))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow PI (/ k 2))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow PI (/ k 2))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 146 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (393 enodes) * [exit]simplify: Simplified to (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 147 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (390 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 148 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (125 enodes) * * [misc]simplify: iters left: 2 (344 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 149 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (390 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 150 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (125 enodes) * * [misc]simplify: iters left: 2 (349 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 151 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (243 enodes) * [exit]simplify: Simplified to (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 152 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (389 enodes) * [exit]simplify: Simplified to (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 153 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (344 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 154 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (185 enodes) * * [misc]simplify: iters left: 1 (285 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 155 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (188 enodes) * * [misc]simplify: iters left: 1 (291 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 156 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (190 enodes) * * [misc]simplify: iters left: 1 (285 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 157 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (187 enodes) * * [misc]simplify: iters left: 1 (295 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 158 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (211 enodes) * * [misc]simplify: iters left: 1 (437 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 159 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (187 enodes) * * [misc]simplify: iters left: 1 (295 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 160 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (200 enodes) * * [misc]simplify: iters left: 1 (359 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 161 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (325 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (* (cbrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (* (cbrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (* (cbrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 162 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (185 enodes) * * [misc]simplify: iters left: 1 (285 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 163 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (173 enodes) * * [misc]simplify: iters left: 1 (344 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 164 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (239 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 165 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (244 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow PI (/ k 2))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow PI (/ k 2))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow PI (/ k 2))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 166 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (244 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (sqrt k)) (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (sqrt k)) (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (sqrt k)) (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 167 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (244 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 168 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (161 enodes) * * [misc]simplify: iters left: 1 (211 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 169 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (244 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 170 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (175 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 171 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (422 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt k))) (* (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt k))) (* (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt k))) (* (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 172 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (239 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 173 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (157 enodes) * * [misc]simplify: iters left: 1 (163 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 174 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) 1) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (154 enodes) * * [misc]simplify: iters left: 1 (159 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 175 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt 2)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (73 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (159 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 176 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (223 enodes) * [exit]simplify: Simplified to (/ (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 177 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (163 enodes) * * [misc]simplify: iters left: 2 (363 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 178 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (321 enodes) * [exit]simplify: Simplified to (* (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n)))))))) * * * * [misc]progress: [ 179 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (99 enodes) * * [misc]simplify: iters left: 3 (322 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))))) (cbrt (sqrt (pow PI (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))))) (cbrt (sqrt (pow PI (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))))) (cbrt (sqrt (pow PI (/ k 2))))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) * * * * [misc]progress: [ 180 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (325 enodes) * [exit]simplify: Simplified to (* (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n)))) (cbrt (sqrt (cbrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n)))) (cbrt (sqrt (cbrt (pow (* n (* PI 2)) (/ k 2))))))))) * * * * [misc]progress: [ 181 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (321 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 182 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (236 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 183 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (98 enodes) * * [misc]simplify: iters left: 3 (321 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 184 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (234 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 185 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (47 enodes) * * [misc]simplify: iters left: 4 (122 enodes) * * [misc]simplify: iters left: 3 (446 enodes) * [exit]simplify: Simplified to (* (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n)))))))) * * * * [misc]progress: [ 186 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (321 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt n))))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n)))))))) * * * * [misc]progress: [ 187 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (99 enodes) * * [misc]simplify: iters left: 3 (327 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 188 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (233 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n)))))))) * * * * [misc]progress: [ 189 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (235 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2))))))) (* (* (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) * * * * [misc]progress: [ 190 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (236 enodes) * [exit]simplify: Simplified to (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n)))) (cbrt (sqrt (cbrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n)))) (cbrt (sqrt (cbrt (pow (* n (* PI 2)) (/ k 2))))))))) * * * * [misc]progress: [ 191 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (233 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 192 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (213 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 193 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (233 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 194 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (196 enodes) * [exit]simplify: Simplified to (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 195 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (285 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n)))))))) * * * * [misc]progress: [ 196 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (232 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (sqrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (sqrt (sqrt 2))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (sqrt (sqrt 2))))) (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n)))))))) * * * * [misc]progress: [ 197 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (204 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt 2)) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt 2)) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt 2)) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 198 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (229 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (* (cbrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (* (* (/ (cbrt (sqrt k)) (* (cbrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 199 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (230 enodes) * [exit]simplify: Simplified to (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt 2) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt 2) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))))) * * * * [misc]progress: [ 200 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (231 enodes) * [exit]simplify: Simplified to (* (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2))))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2))))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt 2) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2))))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt 2) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 201 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (229 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (336 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (sqrt 2))))))) * * * * [misc]progress: [ 202 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (198 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt n))))))) * * * * [misc]progress: [ 203 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (229 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (336 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (sqrt 2))))))) * * * * [misc]progress: [ 204 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt n))))))) * * * * [misc]progress: [ 205 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (290 enodes) * [exit]simplify: Simplified to (* (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (* (cbrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (* (/ (cbrt (sqrt k)) (* (cbrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 206 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (* (cbrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))))) (* (* (/ (cbrt (sqrt k)) (* (cbrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 207 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt n))))))) * * * * [misc]progress: [ 208 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) 1) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (184 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n))))) (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt n))))))) * * * * [misc]progress: [ 209 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt 2)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (361 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (sqrt 2) (* (/ (cbrt (sqrt n)) (cbrt (sqrt k))) (/ (cbrt (sqrt n)) (cbrt (sqrt k)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (sqrt 2) (* (/ (cbrt (sqrt n)) (cbrt (sqrt k))) (/ (cbrt (sqrt n)) (cbrt (sqrt k)))))) (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (179 enodes) * * [misc]simplify: iters left: 1 (443 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (cbrt (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (sqrt 2) (* (/ (cbrt (sqrt n)) (cbrt (sqrt k))) (/ (cbrt (sqrt n)) (cbrt (sqrt k)))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (cbrt (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 210 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (316 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 211 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (168 enodes) * * [misc]simplify: iters left: 1 (253 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt k)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt k)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt k)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 212 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (240 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (sqrt (sqrt n)) (cbrt (sqrt k))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (sqrt (sqrt n)) (cbrt (sqrt k))))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (sqrt (sqrt n)) (cbrt (sqrt k))))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n)))))))) * * * * [misc]progress: [ 213 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (241 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (sqrt (sqrt n))) (* (cbrt (sqrt (pow PI (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (sqrt (sqrt n))) (* (cbrt (sqrt (pow PI (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (sqrt (sqrt n))) (* (cbrt (sqrt (pow PI (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) * * * * [misc]progress: [ 214 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (242 enodes) * [exit]simplify: Simplified to (* (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n)))) (cbrt (sqrt (cbrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n)))) (cbrt (sqrt (cbrt (pow (* n (* PI 2)) (/ k 2))))))))) * * * * [misc]progress: [ 215 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (240 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt k))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt k))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt k))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 216 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (235 enodes) * [exit]simplify: Simplified to (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 217 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (85 enodes) * * [misc]simplify: iters left: 3 (240 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt k))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt k))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt k))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 218 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (167 enodes) * [exit]simplify: Simplified to (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 219 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (109 enodes) * * [misc]simplify: iters left: 3 (353 enodes) * [exit]simplify: Simplified to (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n)))))))) * * * * [misc]progress: [ 220 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (238 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n)))))))) * * * * [misc]progress: [ 221 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (189 enodes) * [exit]simplify: Simplified to (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 222 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (390 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt k)) (* (/ (cbrt (sqrt k)) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (* (/ (cbrt (sqrt k)) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (* (/ (cbrt (sqrt k)) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n)))))))) * * * * [misc]progress: [ 223 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (393 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2)))))) (* (* (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) * * * * [misc]progress: [ 224 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (395 enodes) * [exit]simplify: Simplified to (/ (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt (sqrt n)) (cbrt (sqrt k))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt (sqrt n)) (cbrt (sqrt k))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n)))) (cbrt (sqrt (cbrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt (sqrt n)) (cbrt (sqrt k))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n)))) (cbrt (sqrt (cbrt (pow (* n (* PI 2)) (/ k 2))))))))) * * * * [misc]progress: [ 225 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (390 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (/ (sqrt (sqrt n)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (/ (sqrt (sqrt n)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (/ (sqrt (sqrt n)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 226 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (451 enodes) * [exit]simplify: Simplified to (* (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 227 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (390 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (/ (sqrt (sqrt n)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (/ (sqrt (sqrt n)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (/ (sqrt (sqrt n)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 228 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (377 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 229 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (206 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n)))))))) * * * * [misc]progress: [ 230 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (391 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n)))))))) * * * * [misc]progress: [ 231 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (388 enodes) * [exit]simplify: Simplified to (* (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 232 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (486 enodes) * [exit]simplify: Simplified to (* (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (sqrt (sqrt n)))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (* (sqrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (sqrt (sqrt n)))) (* (* (/ (cbrt (sqrt k)) (* (sqrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 233 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * * [misc]simplify: iters left: 2 (488 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (cbrt (sqrt k)) (/ (sqrt (sqrt n)) (cbrt (sqrt k)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (cbrt (sqrt k)) (/ (sqrt (sqrt n)) (cbrt (sqrt k)))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt 2) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (cbrt (sqrt k)) (/ (sqrt (sqrt n)) (cbrt (sqrt k)))))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt 2) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))))) * * * * [misc]progress: [ 234 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (492 enodes) * [exit]simplify: Simplified to (* (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt k))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt k))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt 2) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt k))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (cbrt (sqrt (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt 2) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 235 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (486 enodes) * [exit]simplify: Simplified to (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (336 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (* (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (sqrt 2))))))) * * * * [misc]progress: [ 236 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (125 enodes) * * [misc]simplify: iters left: 2 (363 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n))))))) * * * * [misc]progress: [ 237 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (486 enodes) * [exit]simplify: Simplified to (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (336 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (* (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (sqrt 2))))))) * * * * [misc]progress: [ 238 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (391 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt k)) (/ (sqrt (sqrt n)) (cbrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt k)) (/ (sqrt (sqrt n)) (cbrt (sqrt k))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt k)) (/ (sqrt (sqrt n)) (cbrt (sqrt k))))) (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n))))))) * * * * [misc]progress: [ 239 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (221 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (* (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt n))))) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (* (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt n))))) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (* (sqrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (* (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt n))))) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (* (* (/ (cbrt (sqrt k)) (* (sqrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 240 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (493 enodes) * [exit]simplify: Simplified to (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (* (sqrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (* (/ (cbrt (sqrt k)) (* (sqrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 241 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (281 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n))))))) * * * * [misc]progress: [ 242 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) 1) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (117 enodes) * * [misc]simplify: iters left: 2 (346 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt n)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt n)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt n)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n))))))) * * * * [misc]progress: [ 243 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt 2)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (167 enodes) * * [misc]simplify: iters left: 1 (253 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt k)) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (179 enodes) * * [misc]simplify: iters left: 1 (443 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt n))) (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 244 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (452 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt k))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt k))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt k))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 245 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (230 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 246 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (228 enodes) * [exit]simplify: Simplified to (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 247 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (229 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow PI (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow PI (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (* (sqrt n) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow PI (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (* (sqrt n) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * * * * [misc]progress: [ 248 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (231 enodes) * [exit]simplify: Simplified to (* (cbrt (fabs (cbrt (pow (* (* PI n) 2) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* PI n) 2) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt n) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* PI n) 2) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt n) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 249 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (228 enodes) * [exit]simplify: Simplified to (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt n) (cbrt (sqrt k))) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt n) (cbrt (sqrt k))) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 250 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (153 enodes) * * [misc]simplify: iters left: 2 (443 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 251 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (228 enodes) * [exit]simplify: Simplified to (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt n) (cbrt (sqrt k))) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt n) (cbrt (sqrt k))) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 252 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (478 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 253 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (107 enodes) * * [misc]simplify: iters left: 3 (333 enodes) * [exit]simplify: Simplified to (* (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 254 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (227 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 255 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (204 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 256 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (444 enodes) * [exit]simplify: Simplified to (* (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (sqrt 2)))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (sqrt 2)))) (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 257 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (448 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (* (sqrt n) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (* (sqrt n) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * * * * [misc]progress: [ 258 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (430 enodes) * [exit]simplify: Simplified to (* (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt n) (/ (sqrt (sqrt 2)) (cbrt (sqrt k))))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt n) (/ (sqrt (sqrt 2)) (cbrt (sqrt k))))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 259 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (444 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt n) (cbrt (sqrt k))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt n) (cbrt (sqrt k))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 260 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (347 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 261 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (444 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt n) (cbrt (sqrt k))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt n) (cbrt (sqrt k))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 262 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (285 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 263 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (194 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 264 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 265 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (320 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 266 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (364 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 267 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (372 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (cbrt (sqrt k)) (* (sqrt 2) (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (cbrt (sqrt k)) (* (sqrt 2) (sqrt n)))))))) * * * * [misc]progress: [ 268 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (391 enodes) * [exit]simplify: Simplified to (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2))))) (* (/ (cbrt (sqrt k)) (* (sqrt 2) (sqrt n))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2)))))) (* (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2))))) (* (/ (cbrt (sqrt k)) (* (sqrt 2) (sqrt n))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 269 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (364 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (331 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 270 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (165 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt 2) (sqrt n))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt 2) (sqrt n))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 271 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (364 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (331 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 272 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (277 enodes) * * [misc]simplify: iters left: 1 (399 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt 2) (sqrt n))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt 2) (sqrt n))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 273 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (175 enodes) * [exit]simplify: Simplified to (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 274 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (137 enodes) * * [misc]simplify: iters left: 2 (360 enodes) * [exit]simplify: Simplified to (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 275 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (106 enodes) * * [misc]simplify: iters left: 1 (125 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt 2) (sqrt n))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt 2) (sqrt n))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 276 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) 1) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (118 enodes) * * [misc]simplify: iters left: 1 (137 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt 2) (sqrt n))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt 2) (sqrt n))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 277 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt 2)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (229 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt k)))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (172 enodes) * * [misc]simplify: iters left: 1 (431 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt k)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 278 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (127 enodes) * * [misc]simplify: iters left: 2 (346 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (140 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt n)) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt n)) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 279 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (126 enodes) * * [misc]simplify: iters left: 1 (130 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (140 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (sqrt n)) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (/ (cbrt (sqrt k)) (sqrt n)) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 280 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (188 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 281 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow PI (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow PI (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (321 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow PI (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n))))))))) * * * * [misc]progress: [ 282 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (470 enodes) * [exit]simplify: Simplified to (* (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (321 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 283 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (163 enodes) * * [misc]simplify: iters left: 2 (479 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 284 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (214 enodes) * * [misc]simplify: iters left: 1 (366 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 285 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (163 enodes) * * [misc]simplify: iters left: 2 (479 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 286 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (221 enodes) * * [misc]simplify: iters left: 1 (366 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 287 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (311 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 288 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (163 enodes) * * [misc]simplify: iters left: 2 (479 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k))))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 289 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (205 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (cbrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 290 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (393 enodes) * [exit]simplify: Simplified to (* (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k)))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k)))) (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 291 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (211 enodes) * * [misc]simplify: iters left: 1 (367 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (321 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2))))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n))))))))) * * * * [misc]progress: [ 292 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (392 enodes) * [exit]simplify: Simplified to (* (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k)))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (321 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt k)))) (/ (* (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 293 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (229 enodes) * * [misc]simplify: iters left: 1 (378 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt 2))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt 2))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 294 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (75 enodes) * * [misc]simplify: iters left: 2 (190 enodes) * * [misc]simplify: iters left: 1 (245 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 295 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (229 enodes) * * [misc]simplify: iters left: 1 (378 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt 2))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt 2))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 296 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (164 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 297 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (174 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt 2))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (sqrt 2))))) (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 298 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (229 enodes) * * [misc]simplify: iters left: 1 (378 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 299 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (79 enodes) * * [misc]simplify: iters left: 2 (115 enodes) * * [misc]simplify: iters left: 1 (137 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (sqrt (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 300 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (232 enodes) * * [misc]simplify: iters left: 1 (367 enodes) * [exit]simplify: Simplified to (* (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (316 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 301 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (105 enodes) * * [misc]simplify: iters left: 1 (130 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow PI (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow PI (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (cbrt (sqrt k)) (* (sqrt n) (sqrt 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (cbrt (sqrt (pow PI (/ k 2))))) (* (* (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (cbrt (sqrt k)) (* (sqrt n) (sqrt 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 302 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (119 enodes) * * [misc]simplify: iters left: 2 (232 enodes) * * [misc]simplify: iters left: 1 (339 enodes) * [exit]simplify: Simplified to (* (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (cbrt (sqrt k)) (* (sqrt n) (sqrt 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (* (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (cbrt (sqrt k)) (* (sqrt n) (sqrt 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 303 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (210 enodes) * * [misc]simplify: iters left: 1 (368 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 304 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (99 enodes) * * [misc]simplify: iters left: 1 (105 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (490 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n PI) 2) (/ k 2))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow (* (* n PI) 2) (/ k 2))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt k))))))) * * * * [misc]progress: [ 305 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (210 enodes) * * [misc]simplify: iters left: 1 (368 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 306 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ 1 (cbrt 1))) * * [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 (32 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (61 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (490 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n PI) 2) (/ k 2))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow (* (* n PI) 2) (/ k 2))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt k))))))) * * * * [misc]progress: [ 307 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (353 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (316 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (* (cbrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 308 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (210 enodes) * * [misc]simplify: iters left: 1 (368 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (316 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (sqrt n) (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (sqrt n) (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 309 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (/ 1 1)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (490 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n PI) 2) (/ k 2))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow (* (* n PI) 2) (/ k 2))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt k))))))) * * * * [misc]progress: [ 310 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) 1) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * * [misc]simplify: iters left: 2 (54 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (490 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n PI) 2) (/ k 2))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow (* (* n PI) 2) (/ k 2))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt k))))))) * * * * [misc]progress: [ 311 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) (sqrt 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (102 enodes) * * [misc]simplify: iters left: 1 (106 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt k))) (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (287 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt k))) (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 312 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (127 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (cbrt (sqrt k)) (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (cbrt (sqrt k)) (sqrt n)))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (159 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (cbrt (sqrt k)) (sqrt n)))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 313 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (159 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 314 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (153 enodes) * * [misc]simplify: iters left: 2 (385 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (/ (sqrt n) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (/ (sqrt n) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (/ (sqrt n) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))))) (* (/ (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 315 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (370 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt n)) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt n)) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (315 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt n)) (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * * * * [misc]progress: [ 316 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (386 enodes) * [exit]simplify: Simplified to (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt n)) (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt n)) (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (315 enodes) * [exit]simplify: Simplified to (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt n)) (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2)))))) (* (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * * * * [misc]progress: [ 317 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (384 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (sqrt n) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (sqrt n) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (319 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (sqrt n) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 318 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt n)) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt n)) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 319 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (384 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (sqrt n) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (sqrt n) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (319 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (sqrt n) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 320 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (322 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt n)) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt n)) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 321 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (235 enodes) * [exit]simplify: Simplified to (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt n)) (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt n)) (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt n)) (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (* (/ (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 322 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (384 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (sqrt n) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (sqrt n) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (sqrt n) (/ (cbrt (sqrt k)) (cbrt (sqrt 2))))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (* (/ (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 323 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (155 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (sqrt n))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (/ (/ (cbrt (sqrt k)) (cbrt (sqrt 2))) (sqrt n))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 324 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (283 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt n)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (sqrt n)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (sqrt n)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (* (/ (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 325 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (273 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (/ (sqrt n) (cbrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (/ (sqrt n) (cbrt (sqrt k))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (315 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (/ (sqrt n) (cbrt (sqrt k))))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (cbrt (sqrt k)) (sqrt (sqrt 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * * * * [misc]progress: [ 326 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (286 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt n)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (sqrt n)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (315 enodes) * [exit]simplify: Simplified to (* (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (sqrt n)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2)))))) (* (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * * * * [misc]progress: [ 327 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (293 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (sqrt (sqrt 2)) (sqrt n))) (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (sqrt (sqrt 2)) (sqrt n))) (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (319 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (sqrt (sqrt 2)) (sqrt n))) (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 328 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (79 enodes) * * [misc]simplify: iters left: 2 (177 enodes) * * [misc]simplify: iters left: 1 (290 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (/ (cbrt (sqrt k)) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (/ (cbrt (sqrt k)) (sqrt n))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (/ (cbrt (sqrt k)) (sqrt n))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 329 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (293 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (sqrt (sqrt 2)) (sqrt n))) (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (sqrt (sqrt 2)) (sqrt n))) (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (319 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (sqrt (sqrt 2)) (sqrt n))) (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 330 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (289 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (sqrt n)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (sqrt n)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (sqrt n)) (/ (cbrt (sqrt k)) (sqrt (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 331 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (319 enodes) * [exit]simplify: Simplified to (/ (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n)) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n)) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n)) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (* (/ (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 332 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (181 enodes) * * [misc]simplify: iters left: 1 (293 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (sqrt (sqrt 2)) (sqrt n))) (sqrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (sqrt (sqrt 2)) (sqrt n))) (sqrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (sqrt (sqrt 2)) (sqrt n))) (sqrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (* (/ (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 333 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (150 enodes) * * [misc]simplify: iters left: 1 (280 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (/ (cbrt (sqrt k)) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (/ (cbrt (sqrt k)) (sqrt n))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (sqrt (sqrt 2))) (/ (cbrt (sqrt k)) (sqrt n))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 334 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (208 enodes) * * [misc]simplify: iters left: 1 (488 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt n) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt n) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (326 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt n) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt k))))))) * * * * [misc]progress: [ 335 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (79 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) (cbrt (sqrt (pow PI (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) (cbrt (sqrt (pow PI (/ k 2))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (319 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) (cbrt (sqrt (pow PI (/ k 2))))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 336 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (209 enodes) * * [misc]simplify: iters left: 1 (485 enodes) * [exit]simplify: Simplified to (/ (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt n) (cbrt (sqrt k))) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt n) (cbrt (sqrt k))) (cbrt (sqrt k)))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (319 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt 2)) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt n) (cbrt (sqrt k))) (cbrt (sqrt k)))) (* (/ (cbrt (sqrt (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt 2)) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 337 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (206 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (315 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 338 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (195 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt n))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt k)) (/ (cbrt (sqrt k)) (sqrt n))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 339 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (206 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (315 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt k)))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 340 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (114 enodes) * * [misc]simplify: iters left: 1 (160 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 341 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (346 enodes) * [exit]simplify: Simplified to (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n)) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n)) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (326 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n)) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt k))))))) * * * * [misc]progress: [ 342 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (206 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (326 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt k))))))) * * * * [misc]progress: [ 343 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (/ 1 1)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (87 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n)) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt n)) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 344 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 345 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) (sqrt 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * * [misc]simplify: iters left: 1 (49 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n))) (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (165 enodes) * * [misc]simplify: iters left: 1 (249 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt k)) (sqrt 2)) (/ (cbrt (sqrt k)) (sqrt n))) (* (cbrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * * * * [misc]progress: [ 346 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (82 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 347 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 348 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (278 enodes) * * [misc]simplify: iters left: 1 (484 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (* (/ (cbrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (* (/ (cbrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (* (/ (cbrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 349 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * * [misc]simplify: iters left: 1 (493 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 350 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (28 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (283 enodes) * * [misc]simplify: iters left: 1 (499 enodes) * [exit]simplify: Simplified to (/ (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 351 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (278 enodes) * * [misc]simplify: iters left: 1 (483 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 352 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (231 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 353 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (278 enodes) * * [misc]simplify: iters left: 1 (483 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 354 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (230 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 355 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (88 enodes) * * [misc]simplify: iters left: 3 (203 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (* (* (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (* (* (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (* (* (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 356 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (131 enodes) * * [misc]simplify: iters left: 2 (278 enodes) * * [misc]simplify: iters left: 1 (484 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (* (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (* (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (* (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 357 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * * [misc]simplify: iters left: 2 (440 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (* (cbrt (sqrt 2)) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (* (cbrt (sqrt 2)) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (* (cbrt (sqrt 2)) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 358 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (143 enodes) * * [misc]simplify: iters left: 1 (197 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 359 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (144 enodes) * * [misc]simplify: iters left: 1 (198 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 360 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (147 enodes) * * [misc]simplify: iters left: 1 (201 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 361 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (143 enodes) * * [misc]simplify: iters left: 1 (197 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 362 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (165 enodes) * * [misc]simplify: iters left: 1 (321 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (* (sqrt (sqrt 2)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (* (sqrt (sqrt 2)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (* (sqrt (sqrt 2)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 363 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (143 enodes) * * [misc]simplify: iters left: 1 (197 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 364 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (130 enodes) * * [misc]simplify: iters left: 1 (245 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 365 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (258 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt k)) (/ (* (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (sqrt (sqrt 2)))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (sqrt k)) (/ (* (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (sqrt (sqrt 2)))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (sqrt k)) (/ (* (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (sqrt (sqrt 2)))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 366 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (143 enodes) * * [misc]simplify: iters left: 1 (197 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 367 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (131 enodes) * * [misc]simplify: iters left: 1 (285 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (sqrt (sqrt 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (sqrt (sqrt 2)))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 368 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (157 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 369 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (160 enodes) * * [misc]simplify: iters left: 1 (290 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 370 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (162 enodes) * * [misc]simplify: iters left: 1 (292 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 371 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (158 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt k)) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 372 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (141 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 373 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (158 enodes) * * [misc]simplify: iters left: 1 (310 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt k)) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 374 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (101 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 375 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (331 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (* (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (* (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (* (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 376 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (157 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 377 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 378 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) 1) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 379 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (sqrt 2)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (sqrt 2)) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt 2)) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (159 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt 2)) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 380 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 381 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 382 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (163 enodes) * * [misc]simplify: iters left: 1 (211 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 383 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (164 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 384 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 385 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (163 enodes) * * [misc]simplify: iters left: 1 (211 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 386 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (290 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 387 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (163 enodes) * * [misc]simplify: iters left: 1 (211 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 388 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (158 enodes) * * [misc]simplify: iters left: 1 (314 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 389 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * * [misc]simplify: iters left: 2 (324 enodes) * * [misc]simplify: iters left: 1 (490 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (sqrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (sqrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 390 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (163 enodes) * * [misc]simplify: iters left: 1 (211 enodes) * [exit]simplify: Simplified to (/ (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 391 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (150 enodes) * * [misc]simplify: iters left: 1 (377 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 392 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 393 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 394 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (92 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 395 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 396 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (121 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 397 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 398 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (98 enodes) * * [misc]simplify: iters left: 1 (135 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 399 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (147 enodes) * * [misc]simplify: iters left: 1 (205 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt 2))) (* (sqrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt 2))) (* (sqrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt 2))) (* (sqrt (sqrt k)) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 400 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 401 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (108 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 402 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (94 enodes) * * [misc]simplify: iters left: 1 (150 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 403 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (97 enodes) * * [misc]simplify: iters left: 1 (158 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 404 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (106 enodes) * * [misc]simplify: iters left: 1 (194 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt k))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt k))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt k))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 405 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (155 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt k)) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 406 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (51 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 407 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (155 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt k)) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 408 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (74 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 409 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (185 enodes) * * [misc]simplify: iters left: 1 (456 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (sqrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (sqrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (* (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (sqrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 410 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (94 enodes) * * [misc]simplify: iters left: 1 (150 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 411 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 412 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) 1) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 413 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt 2)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (sqrt 2)) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt 2)) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (159 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt 2)) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))))) * * * * [misc]progress: [ 414 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (271 enodes) * * [misc]simplify: iters left: 1 (463 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 415 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (156 enodes) * * [misc]simplify: iters left: 1 (203 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) (/ (* (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 416 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (224 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n))))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n))))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n)))))))) * * * * [misc]progress: [ 417 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (225 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (sqrt (sqrt k))) (/ (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (sqrt (sqrt k))) (/ (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (sqrt (sqrt k))) (/ (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2)))))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) * * * * [misc]progress: [ 418 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (226 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt n)))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt n)))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n)))) (cbrt (sqrt (cbrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt n)))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))))) (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n)))) (cbrt (sqrt (cbrt (pow (* n (* PI 2)) (/ k 2))))))))) * * * * [misc]progress: [ 419 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (224 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 420 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (83 enodes) * * [misc]simplify: iters left: 3 (221 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (sqrt (sqrt k)))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (sqrt (sqrt k)))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 421 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (224 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 422 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (210 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 423 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (104 enodes) * * [misc]simplify: iters left: 3 (332 enodes) * [exit]simplify: Simplified to (* (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (* (cbrt (sqrt n)) (cbrt (sqrt 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (* (cbrt (sqrt n)) (cbrt (sqrt 2)))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (* (cbrt (sqrt n)) (cbrt (sqrt 2)))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n)))))))) * * * * [misc]progress: [ 424 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (223 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt n))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt n))))) (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt n)))))))) * * * * [misc]progress: [ 425 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt n)))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt n)))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 426 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (366 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n)))))))) * * * * [misc]progress: [ 427 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (366 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (sqrt (pow PI (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (sqrt (pow PI (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (sqrt (pow PI (/ k 2)))))) (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) * * * * [misc]progress: [ 428 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (368 enodes) * [exit]simplify: Simplified to (/ (cbrt (fabs (cbrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n)))) (cbrt (sqrt (cbrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n)))) (cbrt (sqrt (cbrt (pow (* n (* PI 2)) (/ k 2))))))))) * * * * [misc]progress: [ 429 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (366 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 430 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (387 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 431 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (366 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 432 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (127 enodes) * * [misc]simplify: iters left: 2 (313 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (* (cbrt (sqrt n)) (sqrt (sqrt 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (* (cbrt (sqrt n)) (sqrt (sqrt 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (* (cbrt (sqrt n)) (sqrt (sqrt 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 433 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (193 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (sqrt (sqrt 2)) (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (sqrt (sqrt 2)) (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (sqrt (sqrt 2)) (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n)))))))) * * * * [misc]progress: [ 434 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (366 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (* (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (* (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (* (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt n)))))))) * * * * [misc]progress: [ 435 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt n))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 436 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (422 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 437 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (425 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt 2) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2))))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt 2) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))))) * * * * [misc]progress: [ 438 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (152 enodes) * * [misc]simplify: iters left: 2 (426 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt 2) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (cbrt (sqrt (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt 2) (/ (sqrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 439 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (422 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (336 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (* (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (sqrt 2))))))) * * * * [misc]progress: [ 440 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (253 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt n)))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt n)))) (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt n))))))) * * * * [misc]progress: [ 441 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (422 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (336 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (* (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (sqrt 2))))))) * * * * [misc]progress: [ 442 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (112 enodes) * * [misc]simplify: iters left: 2 (268 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt n)) (/ (cbrt (sqrt n)) (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt n)) (/ (cbrt (sqrt n)) (sqrt (sqrt k))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt n)) (/ (cbrt (sqrt n)) (sqrt (sqrt k))))) (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt n))))))) * * * * [misc]progress: [ 443 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (200 enodes) * [exit]simplify: Simplified to (* (* (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))))) (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 444 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (149 enodes) * * [misc]simplify: iters left: 2 (423 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt n))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt n))))) (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 445 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (202 enodes) * * [misc]simplify: iters left: 1 (398 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt n))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt n))))))) * * * * [misc]progress: [ 446 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) 1) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (211 enodes) * * [misc]simplify: iters left: 1 (433 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (* (cbrt (sqrt n)) (cbrt (sqrt n))) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (* (cbrt (sqrt n)) (cbrt (sqrt n))) (sqrt (sqrt k)))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (* (cbrt (sqrt n)) (cbrt (sqrt n))) (sqrt (sqrt k)))) (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt n))))))) * * * * [misc]progress: [ 447 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt 2)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (155 enodes) * * [misc]simplify: iters left: 1 (203 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (sqrt 2)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (sqrt 2)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (179 enodes) * * [misc]simplify: iters left: 1 (443 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (cbrt (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (sqrt 2)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (cbrt (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 448 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (140 enodes) * * [misc]simplify: iters left: 1 (205 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 449 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 450 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (174 enodes) * * [misc]simplify: iters left: 2 (425 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n)))))))) * * * * [misc]progress: [ 451 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (176 enodes) * * [misc]simplify: iters left: 2 (428 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow PI (/ k 2)))))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) * * * * [misc]progress: [ 452 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (178 enodes) * * [misc]simplify: iters left: 2 (434 enodes) * [exit]simplify: Simplified to (* (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n)))) (cbrt (sqrt (cbrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))))) (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n)))) (cbrt (sqrt (cbrt (pow (* n (* PI 2)) (/ k 2))))))))) * * * * [misc]progress: [ 453 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (174 enodes) * * [misc]simplify: iters left: 2 (425 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 454 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (74 enodes) * * [misc]simplify: iters left: 3 (177 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 455 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (174 enodes) * * [misc]simplify: iters left: 2 (425 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 456 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (120 enodes) * * [misc]simplify: iters left: 2 (342 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 457 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (95 enodes) * * [misc]simplify: iters left: 3 (274 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n)))))))) * * * * [misc]progress: [ 458 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (174 enodes) * * [misc]simplify: iters left: 2 (424 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (sqrt n)))))))) * * * * [misc]progress: [ 459 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (127 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 460 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n)))))))) * * * * [misc]progress: [ 461 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow PI (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow PI (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow PI (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) * * * * [misc]progress: [ 462 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (198 enodes) * * [misc]simplify: iters left: 1 (336 enodes) * [exit]simplify: Simplified to (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n)))) (cbrt (sqrt (cbrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n)))) (cbrt (sqrt (cbrt (pow (* n (* PI 2)) (/ k 2))))))))) * * * * [misc]progress: [ 463 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 464 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (398 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 465 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 466 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (170 enodes) * * [misc]simplify: iters left: 1 (354 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 467 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (343 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n)))))))) * * * * [misc]progress: [ 468 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (335 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n))))) (* (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n)))))))) * * * * [misc]progress: [ 469 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (163 enodes) * * [misc]simplify: iters left: 1 (377 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n)))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (sqrt n)))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 470 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (* (sqrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (* (* (/ (sqrt (sqrt k)) (* (sqrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 471 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (218 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt 2) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n))))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt 2) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))))) * * * * [misc]progress: [ 472 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (220 enodes) * [exit]simplify: Simplified to (* (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (sqrt n)) (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (sqrt n)) (sqrt (sqrt k))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt 2) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (sqrt n)) (sqrt (sqrt k))))) (/ (cbrt (sqrt (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt 2) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 473 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (336 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (sqrt 2))))))) * * * * [misc]progress: [ 474 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (85 enodes) * * [misc]simplify: iters left: 2 (165 enodes) * * [misc]simplify: iters left: 1 (291 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n))))))) * * * * [misc]progress: [ 475 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (111 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (336 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (sqrt 2))))))) * * * * [misc]progress: [ 476 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (144 enodes) * * [misc]simplify: iters left: 1 (277 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n))))))) * * * * [misc]progress: [ 477 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (412 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (sqrt n)) (sqrt (sqrt k)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (sqrt n)) (sqrt (sqrt k)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (* (sqrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (sqrt n)) (sqrt (sqrt k)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (* (* (/ (sqrt (sqrt k)) (* (sqrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 478 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (* (sqrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (* (* (/ (sqrt (sqrt k)) (* (sqrt (sqrt n)) (sqrt 2))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 479 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (106 enodes) * * [misc]simplify: iters left: 1 (188 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt (sqrt n)) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt (sqrt n)) (sqrt (sqrt k)))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (sqrt (sqrt n)) (sqrt (sqrt k)))) (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n))))))) * * * * [misc]progress: [ 480 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) 1) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (118 enodes) * * [misc]simplify: iters left: 1 (184 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (214 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt n)))) (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n))))))) * * * * [misc]progress: [ 481 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt 2)) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (sqrt 2))) (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (179 enodes) * * [misc]simplify: iters left: 1 (443 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (sqrt 2))) (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 482 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (189 enodes) * * [misc]simplify: iters left: 1 (401 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (sqrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (sqrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (sqrt (sqrt k)) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 483 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (73 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (145 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 484 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (462 enodes) * [exit]simplify: Simplified to (* (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt 2))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt 2))))) (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 485 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (174 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (* (sqrt n) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (* (sqrt n) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * * * * [misc]progress: [ 486 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (176 enodes) * * [misc]simplify: iters left: 2 (485 enodes) * [exit]simplify: Simplified to (/ (cbrt (fabs (cbrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt n) (/ (cbrt (sqrt 2)) (sqrt (sqrt k))))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt n) (/ (cbrt (sqrt 2)) (sqrt (sqrt k))))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 487 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (462 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt n) (sqrt (sqrt k))) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt n) (sqrt (sqrt k))) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 488 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 489 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (173 enodes) * * [misc]simplify: iters left: 2 (462 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt n) (sqrt (sqrt k))) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt n) (sqrt (sqrt k))) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 490 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * * [misc]simplify: iters left: 2 (468 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 491 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (266 enodes) * [exit]simplify: Simplified to (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 492 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (172 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt 2)) (/ (cbrt (sqrt 2)) (sqrt (sqrt k))))) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt 2)) (/ (cbrt (sqrt 2)) (sqrt (sqrt k))))) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt 2)) (/ (cbrt (sqrt 2)) (sqrt (sqrt k))))) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 493 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (401 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 494 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (113 enodes) * * [misc]simplify: iters left: 2 (243 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k)))) (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 495 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (251 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (cbrt (sqrt (pow PI (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (cbrt (sqrt (pow PI (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (* (sqrt n) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (cbrt (sqrt (pow PI (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k))))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (* (sqrt n) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * * * * [misc]progress: [ 496 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (217 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt n) (/ (sqrt (sqrt 2)) (sqrt (sqrt k))))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt n) (/ (sqrt (sqrt 2)) (sqrt (sqrt k))))) (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 497 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (113 enodes) * * [misc]simplify: iters left: 2 (243 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt n) (sqrt (sqrt k))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt n) (sqrt (sqrt k))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 498 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (170 enodes) * * [misc]simplify: iters left: 1 (352 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 499 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (113 enodes) * * [misc]simplify: iters left: 2 (243 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt n) (sqrt (sqrt k))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (/ (sqrt n) (sqrt (sqrt k))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 500 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (135 enodes) * * [misc]simplify: iters left: 1 (220 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 501 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (146 enodes) * * [misc]simplify: iters left: 2 (382 enodes) * [exit]simplify: Simplified to (* (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 502 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (112 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 503 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (147 enodes) * * [misc]simplify: iters left: 1 (244 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 504 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (135 enodes) * * [misc]simplify: iters left: 1 (243 enodes) * [exit]simplify: Simplified to (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (* (sqrt 2) (sqrt n)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (* (sqrt 2) (sqrt n)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 505 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (138 enodes) * * [misc]simplify: iters left: 1 (231 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt k)))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (sqrt (sqrt k)) (* (sqrt 2) (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (sqrt (sqrt k)) (* (sqrt 2) (sqrt n)))))))) * * * * [misc]progress: [ 506 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (207 enodes) * [exit]simplify: Simplified to (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2))))) (* (/ (sqrt (sqrt k)) (* (sqrt 2) (sqrt n))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (* (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2))))) (* (/ (sqrt (sqrt k)) (* (sqrt 2) (sqrt n))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 507 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (135 enodes) * * [misc]simplify: iters left: 1 (239 enodes) * [exit]simplify: Simplified to (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (331 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (* (sqrt 2) (sqrt n)) (sqrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (* (sqrt 2) (sqrt n)) (sqrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 508 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt 2) (sqrt n))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt 2) (sqrt n))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 509 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (135 enodes) * * [misc]simplify: iters left: 1 (239 enodes) * [exit]simplify: Simplified to (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (331 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (* (sqrt 2) (sqrt n)) (sqrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (* (sqrt 2) (sqrt n)) (sqrt (sqrt k)))) (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 510 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (71 enodes) * * [misc]simplify: iters left: 1 (85 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt 2) (sqrt n))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt 2) (sqrt n))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 511 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (124 enodes) * * [misc]simplify: iters left: 2 (216 enodes) * * [misc]simplify: iters left: 1 (458 enodes) * [exit]simplify: Simplified to (* (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k))) (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k))) (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (* (sqrt 2) (sqrt n)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (sqrt k))) (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (* (sqrt 2) (sqrt n)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 512 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (132 enodes) * * [misc]simplify: iters left: 1 (225 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (* (sqrt 2) (sqrt n)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (* (sqrt 2) (sqrt n)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 513 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt 2) (sqrt n))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt 2) (sqrt n))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 514 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) 1) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt 2) (sqrt n))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (sqrt 2) (sqrt n))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 515 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt 2)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (129 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (172 enodes) * * [misc]simplify: iters left: 1 (431 enodes) * [exit]simplify: Simplified to (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt 2))) (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 516 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (140 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt n)) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt n)) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 517 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (140 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt (sqrt k)) (sqrt n)) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (/ (* (/ (sqrt (sqrt k)) (sqrt n)) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 518 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (174 enodes) * * [misc]simplify: iters left: 1 (378 enodes) * [exit]simplify: Simplified to (* (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))) (* (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 519 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (179 enodes) * * [misc]simplify: iters left: 1 (410 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (sqrt k)))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (321 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n))))))))) * * * * [misc]progress: [ 520 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (189 enodes) * * [misc]simplify: iters left: 1 (428 enodes) * [exit]simplify: Simplified to (* (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (321 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2)))) (/ (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 521 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (417 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 522 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (112 enodes) * * [misc]simplify: iters left: 1 (148 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 523 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (417 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 524 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (105 enodes) * * [misc]simplify: iters left: 1 (129 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 525 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (185 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt (sqrt k)) (cbrt (sqrt 2)))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (* (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 526 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (417 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (* (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 527 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (88 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (cbrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 528 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (110 enodes) * [exit]simplify: Simplified to (* (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 529 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (100 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (321 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2))))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n))))))))) * * * * [misc]progress: [ 530 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (* (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (321 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (/ (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 531 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt 2))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt 2))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 532 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * * [misc]simplify: iters left: 2 (35 enodes) * * [misc]simplify: iters left: 1 (49 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 533 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt 2))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (* (/ (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt 2))) (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))))) * * * * [misc]progress: [ 534 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * * [misc]simplify: iters left: 1 (48 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 535 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (176 enodes) * * [misc]simplify: iters left: 1 (425 enodes) * [exit]simplify: Simplified to (* (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 536 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 537 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (54 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n)))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 538 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt k)) (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt k)) (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (316 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt k)) (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 539 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt k)) (cbrt (sqrt (pow PI (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow PI (/ k 2))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (sqrt (sqrt k)) (* (sqrt n) (sqrt 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt k)) (cbrt (sqrt (pow PI (/ k 2))))) (* (* (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (sqrt (sqrt k)) (* (sqrt n) (sqrt 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 540 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt k)) (cbrt (fabs (cbrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt k)) (cbrt (fabs (cbrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt (sqrt k)) (* (sqrt n) (sqrt 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (sqrt k)) (cbrt (fabs (cbrt (pow (* (* PI n) 2) (/ k 2)))))) (* (* (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (sqrt (sqrt k)) (* (sqrt n) (sqrt 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 541 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (sqrt (sqrt k))) (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 542 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * * [misc]simplify: iters left: 2 (28 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt k)) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (490 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n PI) 2) (/ k 2))) (/ (* (sqrt n) (sqrt 2)) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt k)) (/ (sqrt (pow (* (* n PI) 2) (/ k 2))) (/ (* (sqrt n) (sqrt 2)) (sqrt (sqrt k))))))) * * * * [misc]progress: [ 543 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (sqrt (sqrt k))) (* (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 544 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt k)) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (490 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n PI) 2) (/ k 2))) (/ (* (sqrt n) (sqrt 2)) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt k)) (/ (sqrt (pow (* (* n PI) 2) (/ k 2))) (/ (* (sqrt n) (sqrt 2)) (sqrt (sqrt k))))))) * * * * [misc]progress: [ 545 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (* (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt k))) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt k))) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (316 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt k))) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 546 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (sqrt (sqrt k))) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (316 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (sqrt n) (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (sqrt (sqrt k))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (sqrt n) (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 547 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (/ 1 1)) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt k)) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (490 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n PI) 2) (/ k 2))) (/ (* (sqrt n) (sqrt 2)) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt k)) (/ (sqrt (pow (* (* n PI) 2) (/ k 2))) (/ (* (sqrt n) (sqrt 2)) (sqrt (sqrt k))))))) * * * * [misc]progress: [ 548 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) 1) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (8 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt k)) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * * [misc]simplify: iters left: 1 (490 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n PI) 2) (/ k 2))) (/ (* (sqrt n) (sqrt 2)) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (sqrt k)) (/ (sqrt (pow (* (* n PI) 2) (/ k 2))) (/ (* (sqrt n) (sqrt 2)) (sqrt (sqrt k))))))) * * * * [misc]progress: [ 549 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) 1) (sqrt 2)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt 2)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt 2)) (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (287 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt 2)) (* (* (/ (sqrt (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 550 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (sqrt n)) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt n)) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (159 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt n)) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 551 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (sqrt n)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt n)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (159 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt n)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 552 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (158 enodes) * * [misc]simplify: iters left: 1 (206 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (* (/ (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 553 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (143 enodes) * * [misc]simplify: iters left: 1 (190 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n)))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (315 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (sqrt 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (sqrt 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * * * * [misc]progress: [ 554 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (160 enodes) * * [misc]simplify: iters left: 1 (208 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (315 enodes) * [exit]simplify: Simplified to (* (* (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (* (* (* (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * * * * [misc]progress: [ 555 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (158 enodes) * * [misc]simplify: iters left: 1 (205 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (319 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 556 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (270 enodes) * * [misc]simplify: iters left: 1 (446 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 557 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (158 enodes) * * [misc]simplify: iters left: 1 (205 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (319 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 558 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (135 enodes) * * [misc]simplify: iters left: 1 (247 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 559 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (160 enodes) * * [misc]simplify: iters left: 2 (321 enodes) * * [misc]simplify: iters left: 1 (493 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt n))) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt n))) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt (sqrt k)) (sqrt n))) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (* (/ (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 560 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (158 enodes) * * [misc]simplify: iters left: 1 (205 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (* (/ (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (cbrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 561 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (126 enodes) * * [misc]simplify: iters left: 1 (264 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 562 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (71 enodes) * * [misc]simplify: iters left: 1 (86 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n)))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (/ (sqrt (sqrt k)) (sqrt n)))) (* (/ (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 563 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt n)) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt n)) (sqrt (sqrt 2)))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (315 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt n)) (sqrt (sqrt 2)))) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* n 2) (/ k 2)))) (/ (sqrt (sqrt k)) (sqrt (sqrt 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * * * * [misc]progress: [ 564 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (* (sqrt (sqrt 2)) (sqrt n))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (* (sqrt (sqrt 2)) (sqrt n))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (315 enodes) * [exit]simplify: Simplified to (* (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (* (sqrt (sqrt 2)) (sqrt n))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))))) (* (* (* (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) * * * * [misc]progress: [ 565 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (85 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (sqrt (sqrt k)) (* (sqrt (sqrt 2)) (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (sqrt (sqrt k)) (* (sqrt (sqrt 2)) (sqrt n)))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (319 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (sqrt (sqrt k)) (* (sqrt (sqrt 2)) (sqrt n)))) (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 566 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (81 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt n)) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt n)) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 567 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (85 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (sqrt (sqrt k)) (* (sqrt (sqrt 2)) (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (sqrt (sqrt k)) (* (sqrt (sqrt 2)) (sqrt n)))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (319 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (sqrt (sqrt k)) (* (sqrt (sqrt 2)) (sqrt n)))) (/ (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (sqrt (sqrt k)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 568 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt n)) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (sqrt k)) (sqrt (sqrt 2))) (sqrt n)) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 569 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (143 enodes) * * [misc]simplify: iters left: 1 (201 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt (sqrt k)) (sqrt n)) (sqrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (sqrt n)) (sqrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt (sqrt k)) (sqrt n)) (sqrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (* (/ (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 570 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (85 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (sqrt (sqrt k)) (* (sqrt (sqrt 2)) (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (sqrt (sqrt k)) (* (sqrt (sqrt 2)) (sqrt n)))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (sqrt (sqrt k)) (* (sqrt (sqrt 2)) (sqrt n)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (sqrt (sqrt 2)) (sqrt (sqrt k)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 571 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (77 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (* (sqrt n) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (* (sqrt n) (sqrt (sqrt 2)))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (130 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (* (sqrt n) (sqrt (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 572 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (82 enodes) * * [misc]simplify: iters left: 1 (129 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt n)) (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt n)) (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (326 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt 2) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt n)) (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt 2) (sqrt (sqrt k))))))) * * * * [misc]progress: [ 573 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (67 enodes) * * [misc]simplify: iters left: 1 (110 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (/ k 2)))) (/ (sqrt n) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (/ (sqrt n) (sqrt (sqrt k)))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (319 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (/ (sqrt n) (sqrt (sqrt k)))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 574 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (84 enodes) * * [misc]simplify: iters left: 1 (137 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt n)) (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt n)) (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (319 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt 2)) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt (sqrt k)) (sqrt n)) (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) (* (/ (cbrt (sqrt (cbrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt 2)) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 575 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (82 enodes) * * [misc]simplify: iters left: 1 (132 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt n))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (315 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt n))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 576 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ 1 (cbrt (sqrt 1)))) * * [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) * * [misc]simplify: iters left: 2 (27 enodes) * * [misc]simplify: iters left: 1 (33 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt n)) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt n)) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 577 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (82 enodes) * * [misc]simplify: iters left: 1 (132 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt n))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (315 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt n))) (/ (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 578 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ 1 (cbrt 1))) * * [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 (26 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * * [misc]simplify: iters left: 1 (50 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt n)) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt n)) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 579 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (169 enodes) * * [misc]simplify: iters left: 1 (391 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt (sqrt k)) (sqrt n)) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (sqrt (sqrt k)) (sqrt n)) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (326 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt 2) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (sqrt (sqrt k)) (sqrt n)) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt 2) (sqrt (sqrt k))))))) * * * * [misc]progress: [ 580 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (82 enodes) * * [misc]simplify: iters left: 1 (132 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt n))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (326 enodes) * [exit]simplify: Simplified to (/ (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt 2) (sqrt (sqrt k)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt n))) (/ (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt 2) (sqrt (sqrt k))))))) * * * * [misc]progress: [ 581 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (/ 1 1)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt n)) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt n)) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 582 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * * [misc]simplify: iters left: 2 (23 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt n)) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (248 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (sqrt n)) (* (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (* (/ (sqrt (sqrt k)) (sqrt 2)) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * * * * [misc]progress: [ 583 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (pow n 1/2)) (sqrt 2)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (* (sqrt 2) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (* (sqrt 2) (sqrt n))) (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (165 enodes) * * [misc]simplify: iters left: 1 (249 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (sqrt k)) (* (sqrt 2) (sqrt n))) (* (sqrt (sqrt k)) (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * * * * [misc]progress: [ 584 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (80 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ 1 (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt k) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ 1 (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt k) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 585 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ 1 (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt k) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ 1 (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (/ (sqrt k) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 586 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 587 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (sqrt 2)))) (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))))) * * * * [misc]progress: [ 588 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (27 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (327 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (sqrt 2)))) (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))))) * * * * [misc]progress: [ 589 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (313 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (sqrt 2)))) (/ (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 590 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (357 enodes) * [exit]simplify: Simplified to (* (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 591 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (313 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (sqrt 2)))) (/ (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 592 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (305 enodes) * * [misc]simplify: iters left: 1 (477 enodes) * [exit]simplify: Simplified to (* (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 593 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (89 enodes) * * [misc]simplify: iters left: 3 (206 enodes) * [exit]simplify: Simplified to (/ (/ (* (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (* (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 594 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (314 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 595 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (388 enodes) * [exit]simplify: Simplified to (* (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ 1 (cbrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 596 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (171 enodes) * * [misc]simplify: iters left: 1 (437 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (sqrt 2)))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (sqrt 2)))) (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 597 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (425 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt 2))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))))) * * * * [misc]progress: [ 598 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (169 enodes) * * [misc]simplify: iters left: 1 (449 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt 2))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt 2))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt (sqrt 2))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))))) (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))))) * * * * [misc]progress: [ 599 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (172 enodes) * * [misc]simplify: iters left: 1 (438 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 600 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (83 enodes) * * [misc]simplify: iters left: 2 (135 enodes) * * [misc]simplify: iters left: 1 (158 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ 1 (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ 1 (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 601 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (172 enodes) * * [misc]simplify: iters left: 1 (438 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 602 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (83 enodes) * * [misc]simplify: iters left: 2 (102 enodes) * * [misc]simplify: iters left: 1 (118 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (sqrt 2)))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 603 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (sqrt 2)))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (sqrt 2)))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (sqrt 2)))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 604 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (171 enodes) * * [misc]simplify: iters left: 1 (437 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (sqrt 2)))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (sqrt 2)))) (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 605 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (95 enodes) * * [misc]simplify: iters left: 1 (112 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (sqrt (sqrt 2)))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (sqrt (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt 2)))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 606 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (221 enodes) * * [misc]simplify: iters left: 1 (271 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt 2) (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt 2) (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 607 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (221 enodes) * * [misc]simplify: iters left: 1 (254 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (sqrt k) (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (sqrt k) (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 608 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (224 enodes) * * [misc]simplify: iters left: 1 (261 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (* (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt 2))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 609 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (213 enodes) * * [misc]simplify: iters left: 1 (373 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) (/ (* (/ (sqrt k) (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 610 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (83 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt 2) (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) (/ (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt 2) (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 611 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (213 enodes) * * [misc]simplify: iters left: 1 (373 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) (/ (* (/ (sqrt k) (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 612 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * * [misc]simplify: iters left: 1 (74 enodes) * [exit]simplify: Simplified to (* (/ 1 (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ 1 (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ 1 (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ 1 (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt 2) (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ 1 (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ 1 (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt 2) (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 613 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (338 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt 2) (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) (/ (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt 2) (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 614 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (221 enodes) * * [misc]simplify: iters left: 1 (271 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt 2) (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt 2) (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 615 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt 2) (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt 2) (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 616 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) 1) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt 2) (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt 2) (sqrt k))) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 617 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) (sqrt 2)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (54 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt 2)) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt 2)) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (92 enodes) * * [misc]simplify: iters left: 1 (151 enodes) * [exit]simplify: Simplified to (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt 2)) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 618 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * [exit]simplify: Simplified to (/ (/ 1 (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt k) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (/ (sqrt k) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 619 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt k) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (sqrt k) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 620 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (198 enodes) * * [misc]simplify: iters left: 1 (460 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 621 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (200 enodes) * * [misc]simplify: iters left: 1 (458 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))))) * * * * [misc]progress: [ 622 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (202 enodes) * * [misc]simplify: iters left: 1 (465 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))))) * * * * [misc]progress: [ 623 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (199 enodes) * * [misc]simplify: iters left: 1 (450 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 624 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (250 enodes) * * [misc]simplify: iters left: 1 (357 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ 1 (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ 1 (cbrt (sqrt 2))) (cbrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 625 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (199 enodes) * * [misc]simplify: iters left: 1 (450 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 626 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (252 enodes) * * [misc]simplify: iters left: 1 (381 enodes) * [exit]simplify: Simplified to (/ (* (/ 1 (cbrt (sqrt 2))) (/ 1 (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ 1 (cbrt (sqrt 2))) (/ 1 (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ 1 (cbrt (sqrt 2))) (/ 1 (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 627 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (166 enodes) * * [misc]simplify: iters left: 2 (442 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 628 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (198 enodes) * * [misc]simplify: iters left: 1 (460 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (* (/ (sqrt k) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 629 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (255 enodes) * * [misc]simplify: iters left: 1 (438 enodes) * [exit]simplify: Simplified to (/ (* (/ 1 (cbrt (sqrt 2))) (/ 1 (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ 1 (cbrt (sqrt 2))) (/ 1 (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ 1 (cbrt (sqrt 2))) (/ 1 (cbrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 630 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 631 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (87 enodes) * * [misc]simplify: iters left: 1 (141 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))))) * * * * [misc]progress: [ 632 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (89 enodes) * * [misc]simplify: iters left: 1 (143 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (91 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (fabs (cbrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))))) * * * * [misc]progress: [ 633 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 634 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (84 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 635 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 636 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (83 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 637 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (93 enodes) * * [misc]simplify: iters left: 2 (201 enodes) * * [misc]simplify: iters left: 1 (464 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 638 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (sqrt (sqrt 2))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 639 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt 2)))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 640 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (119 enodes) * * [misc]simplify: iters left: 1 (129 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt 2) (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt 2) (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 641 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (132 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (sqrt k) (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (sqrt k) (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 642 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (80 enodes) * * [misc]simplify: iters left: 2 (126 enodes) * * [misc]simplify: iters left: 1 (134 enodes) * [exit]simplify: Simplified to (/ (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (64 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (90 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (* (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt 2))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 643 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (133 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (* (/ (sqrt k) (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 644 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt 2) (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt 2) (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 645 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (122 enodes) * * [misc]simplify: iters left: 1 (133 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (* (/ (sqrt k) (sqrt 2)) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 646 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (49 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt 2) (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt 2) (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 647 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (199 enodes) * * [misc]simplify: iters left: 1 (269 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt 2) (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt 2) (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 648 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (119 enodes) * * [misc]simplify: iters left: 1 (129 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt 2) (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt 2) (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 649 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt 2) (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt 2) (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 650 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) 1) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt 2) (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt 2) (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))))) * * * * [misc]progress: [ 651 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (sqrt 2)) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt 2)) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt 2)) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (92 enodes) * * [misc]simplify: iters left: 1 (151 enodes) * [exit]simplify: Simplified to (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt 2)) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 652 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (400 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))))) (/ (* (/ (sqrt k) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))))) * * * * [misc]progress: [ 653 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (236 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) (/ (* (/ (sqrt k) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))))) * * * * [misc]progress: [ 654 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (234 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 655 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (235 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (/ (* (cbrt (sqrt n)) (cbrt (sqrt 2))) (sqrt k)) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (/ (* (cbrt (sqrt n)) (cbrt (sqrt 2))) (sqrt k)) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))))) * * * * [misc]progress: [ 656 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (44 enodes) * * [misc]simplify: iters left: 4 (84 enodes) * * [misc]simplify: iters left: 3 (237 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (* (cbrt (sqrt n)) (cbrt (sqrt 2))) (sqrt k))) (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (* (cbrt (sqrt n)) (cbrt (sqrt 2))) (sqrt k))) (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 657 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (234 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (cbrt (sqrt n)) (/ (cbrt (sqrt 2)) (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (cbrt (sqrt n)) (/ (cbrt (sqrt 2)) (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 658 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (229 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n))))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt n))))))) * * * * [misc]progress: [ 659 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (234 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (cbrt (sqrt n)) (/ (cbrt (sqrt 2)) (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (cbrt (sqrt n)) (/ (cbrt (sqrt 2)) (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 660 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (216 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt n))))))) * * * * [misc]progress: [ 661 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (45 enodes) * * [misc]simplify: iters left: 4 (105 enodes) * * [misc]simplify: iters left: 3 (346 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (cbrt (sqrt 2)))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (cbrt (sqrt 2)))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (cbrt (sqrt 2)))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (sqrt 2)))) (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 662 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (233 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 663 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (79 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (448 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt n)) (cbrt (sqrt n))))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt n))))))) * * * * [misc]progress: [ 664 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (497 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (* (cbrt (sqrt n)) (* (sqrt (sqrt 2)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (* (cbrt (sqrt n)) (* (sqrt (sqrt 2)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (* (cbrt (sqrt n)) (* (sqrt (sqrt 2)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 665 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * * [misc]simplify: iters left: 2 (482 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (* (sqrt (sqrt 2)) (cbrt (sqrt n))) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (* (sqrt (sqrt 2)) (cbrt (sqrt n))) (cbrt (sqrt n))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (/ (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (sqrt k)) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (* (sqrt (sqrt 2)) (cbrt (sqrt n))) (cbrt (sqrt n))))) (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (/ (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (sqrt k)) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))))) * * * * [misc]progress: [ 666 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (161 enodes) * [exit]simplify: Simplified to (/ (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (sqrt k))) (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (sqrt k))) (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 667 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (465 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (cbrt (sqrt n)) (/ (sqrt (sqrt 2)) (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (cbrt (sqrt n)) (/ (sqrt (sqrt 2)) (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 668 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (268 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (sqrt (sqrt 2)))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (sqrt (sqrt 2)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt n))))))) * * * * [misc]progress: [ 669 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * * [misc]simplify: iters left: 2 (465 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (cbrt (sqrt n)) (/ (sqrt (sqrt 2)) (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (cbrt (sqrt n)) (/ (sqrt (sqrt 2)) (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 670 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (274 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n)))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt n))))))) * * * * [misc]progress: [ 671 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (76 enodes) * * [misc]simplify: iters left: 3 (202 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (cbrt (sqrt n))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 672 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (483 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 673 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (113 enodes) * * [misc]simplify: iters left: 2 (247 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n)))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (* (cbrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt n)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt n))))))) * * * * [misc]progress: [ 674 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (485 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (* (cbrt (sqrt n)) (cbrt (sqrt n))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (* (cbrt (sqrt n)) (cbrt (sqrt n))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (cbrt (sqrt n)) (/ (sqrt k) (sqrt 2))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (* (cbrt (sqrt n)) (cbrt (sqrt n))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (cbrt (sqrt n)) (/ (sqrt k) (sqrt 2))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 675 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (495 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (/ (sqrt k) (sqrt 2)) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (/ (sqrt k) (sqrt 2)) (cbrt (sqrt n)))))))) * * * * [misc]progress: [ 676 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (145 enodes) * * [misc]simplify: iters left: 2 (470 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (cbrt (pow (* (* PI n) 2) (/ k 2))))) (* (/ (/ (sqrt k) (sqrt 2)) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2)))))) (* (cbrt (sqrt (cbrt (pow (* (* PI n) 2) (/ k 2))))) (* (/ (/ (sqrt k) (sqrt 2)) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 677 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (481 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (331 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (* (cbrt (sqrt n)) (/ (sqrt 2) (sqrt k))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (* (cbrt (sqrt n)) (/ (sqrt 2) (sqrt k))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 678 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (202 enodes) * * [misc]simplify: iters left: 1 (266 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt 2)) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt 2)) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt n)))))))) * * * * [misc]progress: [ 679 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (481 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (331 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (* (cbrt (sqrt n)) (/ (sqrt 2) (sqrt k))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (* (cbrt (sqrt n)) (/ (sqrt 2) (sqrt k))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 680 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (86 enodes) * * [misc]simplify: iters left: 2 (206 enodes) * * [misc]simplify: iters left: 1 (377 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt 2)) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt 2)) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt n)))))))) * * * * [misc]progress: [ 681 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (176 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt n))) (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (cbrt (sqrt n)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt n))) (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (cbrt (sqrt n)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (cbrt (sqrt n)) (/ (sqrt k) (sqrt 2))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (cbrt (sqrt n))) (/ (cbrt (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (cbrt (sqrt n)) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))))) (/ (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (cbrt (sqrt n)) (/ (sqrt k) (sqrt 2))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 682 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (465 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (cbrt (sqrt n)) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (cbrt (sqrt n)) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (cbrt (sqrt n)) (/ (sqrt k) (sqrt 2))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (cbrt (sqrt n)) (cbrt (sqrt n))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (cbrt (sqrt n)) (/ (sqrt k) (sqrt 2))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 683 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (188 enodes) * * [misc]simplify: iters left: 1 (368 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt 2)) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt 2)) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt n)))))))) * * * * [misc]progress: [ 684 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) 1) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt 2)) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt 2)) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt k) (cbrt (sqrt n)))))))) * * * * [misc]progress: [ 685 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt 2)) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (232 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt n)) (* (cbrt (sqrt n)) (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt n)) (* (cbrt (sqrt n)) (sqrt 2)))) (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (178 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (cbrt (sqrt n)) (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (* (cbrt (sqrt n)) (* (cbrt (sqrt n)) (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (cbrt (sqrt n)) (sqrt k)))))) * * * * [misc]progress: [ 686 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (101 enodes) * * [misc]simplify: iters left: 2 (207 enodes) * [exit]simplify: Simplified to (/ (/ (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt n))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt n))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt n))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (/ (* (/ (sqrt k) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))))) * * * * [misc]progress: [ 687 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (112 enodes) * * [misc]simplify: iters left: 1 (195 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt (sqrt n))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt (sqrt n))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt (sqrt n))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (* (/ (sqrt k) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))))) * * * * [misc]progress: [ 688 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (184 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 689 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (185 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (/ (* (sqrt (sqrt n)) (cbrt (sqrt 2))) (sqrt k)) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (/ (* (sqrt (sqrt n)) (cbrt (sqrt 2))) (sqrt k)) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))))) * * * * [misc]progress: [ 690 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (25 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * [exit]simplify: Simplified to (* (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (* (sqrt (sqrt n)) (cbrt (sqrt 2))) (sqrt k))) (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (* (sqrt (sqrt n)) (cbrt (sqrt 2))) (sqrt k))) (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 691 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (184 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (sqrt (sqrt n)) (/ (cbrt (sqrt 2)) (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (sqrt (sqrt n)) (/ (cbrt (sqrt 2)) (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 692 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (68 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (326 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (* (cbrt (sqrt 2)) (sqrt (sqrt n))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (* (cbrt (sqrt 2)) (sqrt (sqrt n))) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (* (cbrt (sqrt 2)) (sqrt (sqrt n))) (cbrt (sqrt 2)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt n))))))) * * * * [misc]progress: [ 693 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (184 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (sqrt (sqrt n)) (/ (cbrt (sqrt 2)) (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (sqrt (sqrt n)) (/ (cbrt (sqrt 2)) (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 694 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (330 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) (sqrt (sqrt n))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) (sqrt (sqrt n))))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt n))))))) * * * * [misc]progress: [ 695 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (285 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (cbrt (sqrt 2)) (* (sqrt (sqrt n)) (cbrt (sqrt 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (cbrt (sqrt 2)) (* (sqrt (sqrt n)) (cbrt (sqrt 2))))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (cbrt (sqrt 2)) (* (sqrt (sqrt n)) (cbrt (sqrt 2))))))) (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 696 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (183 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 697 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (158 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) (sqrt (sqrt n))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) (sqrt (sqrt n))))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt n))))))) * * * * [misc]progress: [ 698 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (282 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt (sqrt n))) (sqrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt (sqrt n))) (sqrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt (sqrt n))) (sqrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 699 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (280 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (/ (* (sqrt (sqrt n)) (sqrt (sqrt 2))) (sqrt k)) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (/ (* (sqrt (sqrt n)) (sqrt (sqrt 2))) (sqrt k)) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))))) * * * * [misc]progress: [ 700 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (289 enodes) * [exit]simplify: Simplified to (/ (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))) (/ (* (sqrt (sqrt 2)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))) (/ (* (sqrt (sqrt 2)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (194 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (* (sqrt (sqrt n)) (sqrt (sqrt 2))) (sqrt k))) (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* n (* PI 2)) (/ k 2))))) (/ (* (sqrt (sqrt 2)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (* (sqrt (sqrt n)) (sqrt (sqrt 2))) (sqrt k))) (cbrt (sqrt (cbrt (pow (* (* 2 PI) n) (/ k 2))))))))) * * * * [misc]progress: [ 701 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (277 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (sqrt (sqrt n)) (/ (sqrt (sqrt 2)) (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (sqrt (sqrt n)) (/ (sqrt (sqrt 2)) (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 702 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (244 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt n))))))) * * * * [misc]progress: [ 703 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (277 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (sqrt (sqrt n)) (/ (sqrt (sqrt 2)) (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (* (sqrt (sqrt n)) (/ (sqrt (sqrt 2)) (sqrt k))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 704 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (147 enodes) * * [misc]simplify: iters left: 1 (211 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (sqrt (sqrt n)) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (sqrt (sqrt n)) (sqrt (sqrt 2)))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (sqrt (sqrt n)) (sqrt (sqrt 2)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt n))))))) * * * * [misc]progress: [ 705 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (* (sqrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (* (sqrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (* (sqrt (sqrt n)) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 706 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (278 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (sqrt (sqrt n)) (sqrt (sqrt 2)))) (sqrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (sqrt (sqrt n)) (sqrt (sqrt 2)))) (sqrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (332 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (sqrt (sqrt n)) (sqrt (sqrt 2)))) (sqrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (sqrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 707 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (83 enodes) * * [misc]simplify: iters left: 2 (124 enodes) * * [misc]simplify: iters left: 1 (195 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (137 enodes) * * [misc]simplify: iters left: 1 (213 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (* (sqrt (sqrt 2)) (sqrt (sqrt n)))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt n))))))) * * * * [misc]progress: [ 708 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (* (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n)))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (sqrt (sqrt n)) (/ (sqrt k) (sqrt 2))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n)))) (/ (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (sqrt (sqrt n)) (/ (sqrt k) (sqrt 2))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 709 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (273 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt n)) (cbrt (sqrt (pow PI (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt n)) (cbrt (sqrt (pow PI (/ k 2)))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (/ (sqrt k) (sqrt 2)) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt n)) (cbrt (sqrt (pow PI (/ k 2)))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (/ (sqrt k) (sqrt 2)) (sqrt (sqrt n)))))))) * * * * [misc]progress: [ 710 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (273 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt n))) (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt n))) (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2)))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (cbrt (pow (* (* PI n) 2) (/ k 2))))) (* (/ (/ (sqrt k) (sqrt 2)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt n))) (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2)))))) (* (cbrt (sqrt (cbrt (pow (* (* PI n) 2) (/ k 2))))) (* (/ (/ (sqrt k) (sqrt 2)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 711 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (272 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (331 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (* (sqrt (sqrt n)) (/ (sqrt 2) (sqrt k))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (* (sqrt (sqrt n)) (/ (sqrt 2) (sqrt k))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 712 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (119 enodes) * * [misc]simplify: iters left: 1 (140 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt 2)) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt n))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt 2)) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt n)))))))) * * * * [misc]progress: [ 713 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (115 enodes) * * [misc]simplify: iters left: 2 (272 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (331 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (* (sqrt (sqrt n)) (/ (sqrt 2) (sqrt k))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (* (sqrt (sqrt n)) (/ (sqrt 2) (sqrt k))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))))) * * * * [misc]progress: [ 714 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (94 enodes) * * [misc]simplify: iters left: 1 (112 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt n))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt 2)) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt n))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt 2)) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt n)))))))) * * * * [misc]progress: [ 715 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (400 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (sqrt (sqrt n)) (/ (sqrt k) (sqrt 2))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (/ (sqrt (sqrt n)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (sqrt (sqrt n)) (/ (sqrt k) (sqrt 2))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 716 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (268 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt n)))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (sqrt (sqrt n)) (/ (sqrt k) (sqrt 2))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt n)))) (/ (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (sqrt (sqrt n)) (/ (sqrt k) (sqrt 2))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 717 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt n))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt 2)) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt (sqrt n))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt 2)) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt n)))))))) * * * * [misc]progress: [ 718 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) 1) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (57 enodes) * * [misc]simplify: iters left: 2 (90 enodes) * * [misc]simplify: iters left: 1 (104 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt 2)) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt n))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n))) (* (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt 2)) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (/ (sqrt k) (sqrt (sqrt n)))))))) * * * * [misc]progress: [ 719 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt 2)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (109 enodes) * * [misc]simplify: iters left: 1 (196 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (sqrt (sqrt n)) (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (sqrt (sqrt n)) (sqrt 2))) (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (178 enodes) * * [misc]simplify: iters left: 1 (445 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (sqrt (sqrt n)) (sqrt k))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (* (sqrt (sqrt n)) (sqrt 2))) (/ (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (sqrt (sqrt n)) (sqrt k)))))) * * * * [misc]progress: [ 720 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (163 enodes) * * [misc]simplify: iters left: 1 (279 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 721 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (104 enodes) * * [misc]simplify: iters left: 1 (132 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (94 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt n))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt n))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 722 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (150 enodes) * * [misc]simplify: iters left: 2 (393 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 723 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (363 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2)))))))) * * * * [misc]progress: [ 724 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (363 enodes) * [exit]simplify: Simplified to (* (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (* (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2)))))))) * * * * [misc]progress: [ 725 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (365 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2)))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2)))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 726 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (350 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt n))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt n))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 727 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (365 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2)))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2)))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 728 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (169 enodes) * * [misc]simplify: iters left: 1 (277 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt n))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt n))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 729 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (82 enodes) * * [misc]simplify: iters left: 3 (215 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt 2)))) (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 730 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (361 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (cbrt (sqrt 2)) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 731 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (187 enodes) * * [misc]simplify: iters left: 1 (308 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt n))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt n))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 732 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (179 enodes) * * [misc]simplify: iters left: 1 (423 enodes) * [exit]simplify: Simplified to (* (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt 2)))) (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 733 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (84 enodes) * * [misc]simplify: iters left: 2 (154 enodes) * * [misc]simplify: iters left: 1 (395 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2)))))))) * * * * [misc]progress: [ 734 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (153 enodes) * * [misc]simplify: iters left: 1 (376 enodes) * [exit]simplify: Simplified to (* (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt 2)))) (* (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2)))))))) * * * * [misc]progress: [ 735 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (83 enodes) * * [misc]simplify: iters left: 2 (153 enodes) * * [misc]simplify: iters left: 1 (391 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2)))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2)))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 736 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt n))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt 2))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt n))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 737 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (83 enodes) * * [misc]simplify: iters left: 2 (153 enodes) * * [misc]simplify: iters left: 1 (391 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (328 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2)))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2)))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 738 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (85 enodes) * * [misc]simplify: iters left: 1 (96 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt n))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt 2))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt n))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 739 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (267 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 740 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (152 enodes) * * [misc]simplify: iters left: 1 (390 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 741 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (78 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (88 enodes) * * [misc]simplify: iters left: 2 (136 enodes) * * [misc]simplify: iters left: 1 (212 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt n))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (sqrt (sqrt 2))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt k) (sqrt n))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 742 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (115 enodes) * [exit]simplify: Simplified to (* (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (190 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt k) (sqrt 2)) (sqrt n))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt k) (sqrt 2)) (sqrt n))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 743 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (98 enodes) * * [misc]simplify: iters left: 1 (101 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt 2) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow PI (/ k 2)))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt 2) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))))) * * * * [misc]progress: [ 744 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (99 enodes) * * [misc]simplify: iters left: 1 (102 enodes) * [exit]simplify: Simplified to (* (cbrt (fabs (cbrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2))) (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2))) (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 745 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (94 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (/ (sqrt 2) (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (/ (sqrt 2) (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 746 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (135 enodes) * * [misc]simplify: iters left: 1 (210 enodes) * [exit]simplify: Simplified to (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 747 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (68 enodes) * * [misc]simplify: iters left: 2 (94 enodes) * * [misc]simplify: iters left: 1 (97 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (191 enodes) * * [misc]simplify: iters left: 1 (333 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (/ (sqrt 2) (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (/ (sqrt 2) (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 748 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (135 enodes) * * [misc]simplify: iters left: 1 (210 enodes) * [exit]simplify: Simplified to (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 749 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [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 (149 enodes) * * [misc]simplify: iters left: 1 (255 enodes) * [exit]simplify: Simplified to (* (* (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (190 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt k) (sqrt 2)) (sqrt n))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (* (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt k) (sqrt 2)) (sqrt n))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 750 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (92 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (190 enodes) * * [misc]simplify: iters left: 1 (329 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt k) (sqrt 2)) (sqrt n))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (/ (sqrt k) (sqrt 2)) (sqrt n))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 751 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 1)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (135 enodes) * * [misc]simplify: iters left: 1 (210 enodes) * [exit]simplify: Simplified to (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 752 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) 1) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (135 enodes) * * [misc]simplify: iters left: 1 (210 enodes) * [exit]simplify: Simplified to (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 753 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (sqrt 2)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (73 enodes) * * [misc]simplify: iters left: 1 (95 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (sqrt 2)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (sqrt 2)) (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (172 enodes) * * [misc]simplify: iters left: 1 (403 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (sqrt 2)) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt k) (sqrt n)))))) * * * * [misc]progress: [ 754 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (86 enodes) * * [misc]simplify: iters left: 2 (141 enodes) * * [misc]simplify: iters left: 1 (211 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt n)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt n)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 755 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (86 enodes) * * [misc]simplify: iters left: 2 (141 enodes) * * [misc]simplify: iters left: 1 (211 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt n)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt n)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 756 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (112 enodes) * * [misc]simplify: iters left: 1 (221 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 757 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (92 enodes) * * [misc]simplify: iters left: 1 (198 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (sqrt n) (/ (sqrt k) (cbrt (sqrt 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (sqrt n) (/ (sqrt k) (cbrt (sqrt 2))))))))) * * * * [misc]progress: [ 758 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (67 enodes) * * [misc]simplify: iters left: 2 (111 enodes) * * [misc]simplify: iters left: 1 (221 enodes) * [exit]simplify: Simplified to (/ (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (/ (sqrt k) (cbrt (sqrt 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (/ (sqrt k) (cbrt (sqrt 2))))))))) * * * * [misc]progress: [ 759 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (106 enodes) * * [misc]simplify: iters left: 1 (204 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)))))) * * * * [misc]progress: [ 760 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt 2))) (cbrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (489 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 761 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (106 enodes) * * [misc]simplify: iters left: 1 (204 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)))))) * * * * [misc]progress: [ 762 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt 2))) (cbrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (489 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 763 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (173 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2)))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 764 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (106 enodes) * * [misc]simplify: iters left: 1 (204 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 765 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * [exit]simplify: Simplified to (* (/ 1 (cbrt (sqrt 2))) (/ 1 (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ 1 (cbrt (sqrt 2))) (/ 1 (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (489 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ 1 (cbrt (sqrt 2))) (/ 1 (cbrt (sqrt 2)))) (* (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 766 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (54 enodes) * * [misc]simplify: iters left: 1 (72 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (sqrt (sqrt 2))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 767 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * * [misc]simplify: iters left: 1 (54 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (sqrt n) (/ (sqrt k) (sqrt (sqrt 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt 2))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (sqrt n) (/ (sqrt k) (sqrt (sqrt 2))))))))) * * * * [misc]progress: [ 768 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (73 enodes) * [exit]simplify: Simplified to (/ (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (/ (sqrt k) (sqrt (sqrt 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt 2))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (/ (sqrt k) (sqrt (sqrt 2))))))))) * * * * [misc]progress: [ 769 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt 2))) (* (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)))))) * * * * [misc]progress: [ 770 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (489 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (sqrt 2))) (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 771 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt 2))) (* (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)))))) * * * * [misc]progress: [ 772 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (489 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (sqrt 2))) (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 773 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (71 enodes) * * [misc]simplify: iters left: 1 (102 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 774 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt 2))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 775 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (489 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (sqrt 2))) (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 776 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * * [misc]simplify: iters left: 1 (40 enodes) * [exit]simplify: Simplified to (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (322 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (/ (sqrt 2) (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (/ (sqrt 2) (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 777 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (pow PI (/ k 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (sqrt k) (sqrt 2)) (sqrt n))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (sqrt k) (sqrt 2)) (sqrt n))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))))) * * * * [misc]progress: [ 778 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * * [misc]simplify: iters left: 1 (41 enodes) * [exit]simplify: Simplified to (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2))))) (* (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 779 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * * [misc]simplify: iters left: 1 (39 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 780 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (127 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2))))))) * * * * [misc]progress: [ 781 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * * [misc]simplify: iters left: 1 (39 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 782 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (9 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (127 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2))))))) * * * * [misc]progress: [ 783 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (322 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (/ (sqrt 2) (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (/ (sqrt 2) (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 784 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * * [misc]simplify: iters left: 1 (39 enodes) * [exit]simplify: Simplified to (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (322 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (/ (sqrt 2) (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (/ (sqrt 2) (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 785 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (/ 1 1)) * * [misc]simplify: iters left: 4 (3 enodes) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (127 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2))))))) * * * * [misc]progress: [ 786 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) 1) * * [misc]simplify: iters left: 4 (3 enodes) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (127 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2))))))) * * * * [misc]progress: [ 787 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (sqrt 2)) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt 2)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt 2)) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (285 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt 2)) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 788 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt n)) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt n)) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (162 enodes) * * [misc]simplify: iters left: 1 (237 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt n)) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))))) * * * * [misc]progress: [ 789 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt n)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt n)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (162 enodes) * * [misc]simplify: iters left: 1 (237 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt n)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))))) * * * * [misc]progress: [ 790 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (99 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (453 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (sqrt n) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (sqrt n) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (312 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (* (sqrt n) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (* (/ (sqrt k) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))))) * * * * [misc]progress: [ 791 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (83 enodes) * * [misc]simplify: iters left: 2 (179 enodes) * * [misc]simplify: iters left: 1 (434 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) (sqrt n)))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt k) (/ (cbrt (sqrt (pow (* n 2) (/ k 2)))) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt 2)) (* (cbrt (sqrt 2)) (sqrt n)))) (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt k) (/ (cbrt (sqrt (pow (* n 2) (/ k 2)))) (cbrt (sqrt 2)))))))) * * * * [misc]progress: [ 792 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (100 enodes) * * [misc]simplify: iters left: 2 (197 enodes) * * [misc]simplify: iters left: 1 (450 enodes) * [exit]simplify: Simplified to (/ (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt n))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt n))) (* (/ (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 793 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (447 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt 2)) (* (sqrt n) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt 2)) (* (sqrt n) (cbrt (sqrt 2))))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (312 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (sqrt k) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt 2)) (* (sqrt n) (cbrt (sqrt 2))))) (/ (* (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (sqrt k) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 794 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (82 enodes) * * [misc]simplify: iters left: 2 (228 enodes) * * [misc]simplify: iters left: 1 (344 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt n)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ 1 (sqrt n)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (246 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ 1 (sqrt n)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))))) * * * * [misc]progress: [ 795 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (447 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt 2)) (* (sqrt n) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt 2)) (* (sqrt n) (cbrt (sqrt 2))))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (312 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (sqrt k) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt 2)) (* (sqrt n) (cbrt (sqrt 2))))) (/ (* (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (sqrt k) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 796 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (91 enodes) * * [misc]simplify: iters left: 2 (219 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (sqrt n)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ 1 (sqrt n)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (246 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ 1 (sqrt n)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))))) * * * * [misc]progress: [ 797 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (77 enodes) * * [misc]simplify: iters left: 3 (162 enodes) * * [misc]simplify: iters left: 2 (437 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (sqrt n) (cbrt (sqrt 2)))) (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (sqrt n) (cbrt (sqrt 2)))) (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (312 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (sqrt n) (cbrt (sqrt 2)))) (/ (cbrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt 2)))) (* (/ (sqrt k) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))))) * * * * [misc]progress: [ 798 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (193 enodes) * * [misc]simplify: iters left: 1 (447 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt 2)) (* (sqrt n) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt 2)) (* (sqrt n) (cbrt (sqrt 2))))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (312 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (cbrt (sqrt 2))) (* (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt 2)) (* (sqrt n) (cbrt (sqrt 2))))) (* (/ (sqrt k) (cbrt (sqrt 2))) (* (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))))) * * * * [misc]progress: [ 799 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (104 enodes) * * [misc]simplify: iters left: 1 (133 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt 2))) (* (sqrt n) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (sqrt 2))) (* (sqrt n) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (246 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (sqrt 2))) (* (sqrt n) (cbrt (sqrt 2)))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (cbrt (sqrt 2)) (sqrt k))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))))) * * * * [misc]progress: [ 800 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (82 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (* (sqrt n) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (* (sqrt n) (sqrt (sqrt 2)))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (312 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (sqrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (* (sqrt n) (sqrt (sqrt 2)))) (* (/ (sqrt k) (sqrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))))) * * * * [misc]progress: [ 801 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (118 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (sqrt n) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (sqrt n) (sqrt (sqrt 2)))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt k) (/ (cbrt (sqrt (pow (* n 2) (/ k 2)))) (sqrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (sqrt n) (sqrt (sqrt 2)))) (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt k) (/ (cbrt (sqrt (pow (* n 2) (/ k 2)))) (sqrt (sqrt 2)))))))) * * * * [misc]progress: [ 802 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (83 enodes) * * [misc]simplify: iters left: 1 (141 enodes) * [exit]simplify: Simplified to (/ (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt n) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt n) (sqrt (sqrt 2)))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt n) (sqrt (sqrt 2)))) (* (/ (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 803 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (81 enodes) * * [misc]simplify: iters left: 1 (137 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt n) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt n) (sqrt (sqrt 2)))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (312 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (sqrt k) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt n) (sqrt (sqrt 2)))) (/ (* (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (sqrt k) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 804 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (50 enodes) * * [misc]simplify: iters left: 1 (55 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt n)) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt n)) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (246 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt n)) (sqrt (sqrt 2))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))))) * * * * [misc]progress: [ 805 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (81 enodes) * * [misc]simplify: iters left: 1 (137 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt n) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt n) (sqrt (sqrt 2)))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (312 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (sqrt k) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt n) (sqrt (sqrt 2)))) (/ (* (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (sqrt k) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 806 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (54 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt n)) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt n)) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (246 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt n)) (sqrt (sqrt 2))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))))) * * * * [misc]progress: [ 807 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (89 enodes) * * [misc]simplify: iters left: 2 (197 enodes) * * [misc]simplify: iters left: 1 (465 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt n)) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt n)) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (312 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (sqrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt n)) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) (* (/ (sqrt k) (sqrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))))) * * * * [misc]progress: [ 808 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (81 enodes) * * [misc]simplify: iters left: 1 (137 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt n) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt n) (sqrt (sqrt 2)))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (312 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (sqrt (sqrt 2))) (* (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (sqrt n) (sqrt (sqrt 2)))) (* (/ (sqrt k) (sqrt (sqrt 2))) (* (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))))) * * * * [misc]progress: [ 809 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * * [misc]simplify: iters left: 1 (41 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt n)) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt n)) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (129 enodes) * * [misc]simplify: iters left: 2 (246 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (sqrt n)) (sqrt (sqrt 2))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt (sqrt 2)) (sqrt k))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))))) * * * * [misc]progress: [ 810 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (109 enodes) * * [misc]simplify: iters left: 1 (113 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (sqrt n)) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (320 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt 2)) (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (sqrt n)) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt 2)) (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))))) * * * * [misc]progress: [ 811 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (95 enodes) * * [misc]simplify: iters left: 1 (99 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt n)) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (312 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (sqrt k) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt n)) (/ (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (sqrt k) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 812 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (110 enodes) * * [misc]simplify: iters left: 1 (115 enodes) * [exit]simplify: Simplified to (/ (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt n)) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (312 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (cbrt (pow (* (* PI n) 2) (/ k 2))))) (* (sqrt k) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt n)) (/ (* (cbrt (sqrt (cbrt (pow (* (* PI n) 2) (/ k 2))))) (* (sqrt k) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 813 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (112 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt n)) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (312 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt n)) (/ (* (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 814 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt n)) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt k) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt n)) (* (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt k) (sqrt 2))))))) * * * * [misc]progress: [ 815 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (112 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt n)) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (142 enodes) * * [misc]simplify: iters left: 2 (312 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt n)) (/ (* (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (sqrt k))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 816 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * * [misc]simplify: iters left: 1 (22 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt n)) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt k) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt n)) (* (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt k) (sqrt 2))))))) * * * * [misc]progress: [ 817 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (154 enodes) * * [misc]simplify: iters left: 1 (225 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt n) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt n) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (320 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt 2)) (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (/ (sqrt n) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt 2)) (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))))) * * * * [misc]progress: [ 818 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (65 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (112 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt n)) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (320 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt 2)) (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (sqrt n)) (* (/ (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (sqrt 2)) (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))))) * * * * [misc]progress: [ 819 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (/ 1 1)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (13 enodes) * * [misc]simplify: iters left: 2 (17 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt n)) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt k) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt n)) (* (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt k) (sqrt 2))))))) * * * * [misc]progress: [ 820 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) 1) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt n)) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (245 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt k) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt n)) (* (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (/ (sqrt k) (sqrt 2))))))) * * * * [misc]progress: [ 821 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow n 1/2)) (sqrt 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * [exit]simplify: Simplified to (/ 1 (* (sqrt n) (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (* (sqrt n) (sqrt 2))) (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (167 enodes) * * [misc]simplify: iters left: 1 (251 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* 2 (* PI n)) (/ k 2))) (sqrt k)) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (* (sqrt n) (sqrt 2))) (* (sqrt (pow (* 2 (* PI n)) (/ k 2))) (sqrt k))))) * * * * [misc]progress: [ 822 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* 2 n)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* 2 n)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* 2 n)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* 2 n)) (/ k 2))))))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (86 enodes) * * [misc]simplify: iters left: 2 (141 enodes) * * [misc]simplify: iters left: 1 (211 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt n)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt n)))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 823 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* 2 n)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* 2 n)) (/ k 2))))))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (86 enodes) * * [misc]simplify: iters left: 2 (141 enodes) * * [misc]simplify: iters left: 1 (211 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt n)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (sqrt n)))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 824 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (100 enodes) * * [misc]simplify: iters left: 1 (187 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 825 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (177 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (sqrt n) (/ (sqrt k) (cbrt (sqrt 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (sqrt n) (/ (sqrt k) (cbrt (sqrt 2))))))))) * * * * [misc]progress: [ 826 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (63 enodes) * * [misc]simplify: iters left: 2 (104 enodes) * * [misc]simplify: iters left: 1 (196 enodes) * [exit]simplify: Simplified to (/ (cbrt (fabs (cbrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (/ (sqrt k) (cbrt (sqrt 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* PI n) 2) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (/ (sqrt k) (cbrt (sqrt 2))))))))) * * * * [misc]progress: [ 827 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (101 enodes) * * [misc]simplify: iters left: 1 (191 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)))))) * * * * [misc]progress: [ 828 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt 2))) (cbrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (489 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ 1 (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 829 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (101 enodes) * * [misc]simplify: iters left: 1 (191 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)))))) * * * * [misc]progress: [ 830 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (30 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (59 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (489 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 831 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (77 enodes) * * [misc]simplify: iters left: 2 (177 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2))) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2)))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 832 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (101 enodes) * * [misc]simplify: iters left: 1 (191 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 833 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * [exit]simplify: Simplified to (* (/ 1 (cbrt (sqrt 2))) (/ 1 (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ 1 (cbrt (sqrt 2))) (/ 1 (cbrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (489 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (* (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 834 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (sqrt (sqrt 2))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 835 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * * [misc]simplify: iters left: 2 (35 enodes) * * [misc]simplify: iters left: 1 (48 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (sqrt n) (/ (sqrt k) (sqrt (sqrt 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (sqrt (sqrt 2))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (pow (* 2 n) (/ k 2)))) (/ (sqrt n) (/ (sqrt k) (sqrt (sqrt 2))))))))) * * * * [misc]progress: [ 836 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (66 enodes) * [exit]simplify: Simplified to (/ (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * * [misc]simplify: iters left: 2 (323 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (/ (sqrt k) (sqrt (sqrt 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (sqrt (sqrt 2))) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (/ (sqrt k) (sqrt (sqrt 2))))))))) * * * * [misc]progress: [ 837 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (sqrt 2))) (* (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)))))) * * * * [misc]progress: [ 838 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (489 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (sqrt 2))) (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 839 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (sqrt 2))) (* (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)))))) * * * * [misc]progress: [ 840 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (489 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (sqrt 2))) (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 841 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (76 enodes) * * [misc]simplify: iters left: 1 (127 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt 2)))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 842 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt (sqrt 2))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 843 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (sqrt 2))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (128 enodes) * * [misc]simplify: iters left: 2 (263 enodes) * * [misc]simplify: iters left: 1 (489 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt (sqrt 2))) (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * * * * [misc]progress: [ 844 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (322 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (/ (sqrt 2) (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (/ (sqrt 2) (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 845 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (15 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (pow PI (/ k 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (sqrt k) (sqrt 2)) (sqrt n))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (pow PI (/ k 2)))) (* (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (sqrt k) (sqrt 2)) (sqrt n))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))))) * * * * [misc]progress: [ 846 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (140 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (* (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (fabs (cbrt (pow (* (* 2 PI) n) (/ k 2))))) (* (/ (* (sqrt k) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 847 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 848 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (127 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2))))))) * * * * [misc]progress: [ 849 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (139 enodes) * * [misc]simplify: iters left: 2 (317 enodes) * [exit]simplify: Simplified to (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (* (sqrt k) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 850 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 5 (4 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (127 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2))))))) * * * * [misc]progress: [ 851 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [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 (39 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * [exit]simplify: Simplified to (* (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (322 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (/ (sqrt 2) (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (/ (sqrt 2) (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 852 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (61 enodes) * * [misc]simplify: iters left: 3 (138 enodes) * * [misc]simplify: iters left: 2 (322 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (/ (sqrt 2) (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (/ (sqrt 2) (sqrt k)) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 853 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 1)) * * [misc]simplify: iters left: 4 (3 enodes) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to 1 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (127 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2))))))) * * * * [misc]progress: [ 854 / 1019 ] 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) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (127 enodes) * * [misc]simplify: iters left: 2 (259 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* 1 (* (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (sqrt 2))))))) * * * * [misc]progress: [ 855 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt 2)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt 2)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt 2)) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (285 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ 1 (sqrt 2)) (* (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 856 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* 2 (* PI n)) (/ k 2)))))))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (189 enodes) * * [misc]simplify: iters left: 1 (468 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))))) * * * * [misc]progress: [ 857 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (189 enodes) * * [misc]simplify: iters left: 1 (468 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))))) * * * * [misc]progress: [ 858 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (398 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (* (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2))))))) * * * * [misc]progress: [ 859 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * * [misc]simplify: iters left: 1 (48 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (sqrt k) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (sqrt k) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (404 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 860 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt k) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (404 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt k) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (fabs (cbrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 861 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt k) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt k) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (404 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 862 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * * [misc]simplify: iters left: 2 (93 enodes) * * [misc]simplify: iters left: 1 (152 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (343 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt n) (cbrt (sqrt 2)))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt n) (cbrt (sqrt 2)))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * * * * [misc]progress: [ 863 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt k) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt k) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (404 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (cbrt (sqrt 2))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 864 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * * [misc]simplify: iters left: 2 (77 enodes) * * [misc]simplify: iters left: 1 (105 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (343 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt n) (cbrt (sqrt 2)))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt n) (cbrt (sqrt 2)))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * * * * [misc]progress: [ 865 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (78 enodes) * * [misc]simplify: iters left: 2 (108 enodes) * * [misc]simplify: iters left: 1 (132 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt k))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (398 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (* (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2))))))) * * * * [misc]progress: [ 866 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt k) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (sqrt k) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (398 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (* (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt 2))))))) * * * * [misc]progress: [ 867 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (343 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt n) (cbrt (sqrt 2)))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt n) (cbrt (sqrt 2)))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * * * * [misc]progress: [ 868 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (17 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 (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (sqrt k) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) (/ (sqrt k) (sqrt (sqrt 2)))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (398 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (* (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2))))))) * * * * [misc]progress: [ 869 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (sqrt k) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (pow PI (/ k 2)))) (/ (sqrt k) (sqrt (sqrt 2)))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (404 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) (* (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 870 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (136 enodes) * * [misc]simplify: iters left: 2 (404 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (fabs (cbrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (cbrt (sqrt (cbrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))))))) * * * * [misc]progress: [ 871 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 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 k) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (404 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 872 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt (sqrt 2))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (343 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt n) (sqrt (sqrt 2)))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt (sqrt 2))) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt n) (sqrt (sqrt 2)))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * * * * [misc]progress: [ 873 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 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 k) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (404 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt (sqrt 2))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 874 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt (sqrt 2))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (343 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt n) (sqrt (sqrt 2)))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt (sqrt 2))) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt n) (sqrt (sqrt 2)))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * * * * [misc]progress: [ 875 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (54 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (sqrt k)) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) (/ (/ (sqrt (sqrt 2)) (sqrt k)) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (398 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (* (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (/ (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2))))))) * * * * [misc]progress: [ 876 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 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 k) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt k) (sqrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (398 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (* (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (/ (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt (sqrt 2))))))) * * * * [misc]progress: [ 877 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt (sqrt 2))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (343 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt n) (sqrt (sqrt 2)))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt (sqrt 2))) (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (* (sqrt n) (sqrt (sqrt 2)))) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * * * * [misc]progress: [ 878 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * * [misc]simplify: iters left: 1 (52 enodes) * [exit]simplify: Simplified to (* (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (sqrt k)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (sqrt k)) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) (sqrt k)) (* (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 879 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * * [misc]simplify: iters left: 2 (30 enodes) * * [misc]simplify: iters left: 1 (35 enodes) * [exit]simplify: Simplified to (* (sqrt k) (cbrt (sqrt (pow PI (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt k) (cbrt (sqrt (pow PI (/ k 2))))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (404 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt (pow (* 2 n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt k) (cbrt (sqrt (pow PI (/ k 2))))) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (* (sqrt 2) (sqrt n)) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))))))) * * * * [misc]progress: [ 880 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * * [misc]simplify: iters left: 1 (53 enodes) * [exit]simplify: Simplified to (* (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt k)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt k)) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (22 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (135 enodes) * * [misc]simplify: iters left: 2 (404 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* 2 (* PI n)) (/ k 2))))) (sqrt k)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (sqrt (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (sqrt n) (sqrt 2)) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))))) * * * * [misc]progress: [ 881 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (50 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt k)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt k)) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (398 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt k)) (* (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt 2)))))) * * * * [misc]progress: [ 882 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (sqrt k) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt k) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (343 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (sqrt n) (sqrt 2))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt k) (* (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (sqrt n) (sqrt 2))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) * * * * [misc]progress: [ 883 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (50 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt k)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt k)) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (134 enodes) * * [misc]simplify: iters left: 2 (398 enodes) * [exit]simplify: Simplified to (* (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt k)) (* (/ (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt n)) (/ (cbrt (sqrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt 2)))))) * * * * [misc]progress: [ 884 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * [exit]simplify: Simplified to (sqrt k) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt k) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (343 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (sqrt n) (sqrt 2))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt k) (* (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (sqrt n) (sqrt 2))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) * * * * [misc]progress: [ 885 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (* (sqrt k) (* (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt k) (* (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt k) (* (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))) (* (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt 2)) (cbrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 886 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (50 enodes) * [exit]simplify: Simplified to (* (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt k)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt k)) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (397 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt n))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (sqrt k)) (* (* (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt 2)) (sqrt (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (sqrt n)))))) * * * * [misc]progress: [ 887 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ 1 1)) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (sqrt k) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt k) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (343 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (sqrt n) (sqrt 2))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt k) (* (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (sqrt n) (sqrt 2))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) * * * * [misc]progress: [ 888 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) 1) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * * [misc]simplify: iters left: 1 (8 enodes) * [exit]simplify: Simplified to (sqrt k) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt k) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (343 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (sqrt n) (sqrt 2))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (sqrt k) (* (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (* (sqrt n) (sqrt 2))) (* (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))))))) * * * * [misc]progress: [ 889 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt 2)) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt 2)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt 2)) (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (147 enodes) * * [misc]simplify: iters left: 2 (436 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt 2)) (/ (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (sqrt n) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))))) * * * * [misc]progress: [ 890 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt k) (sqrt n)) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (sqrt n)) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (sqrt n)) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 891 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt k) (sqrt n)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (sqrt n)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (sqrt n)) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))))) * * * * [misc]progress: [ 892 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (158 enodes) * * [misc]simplify: iters left: 1 (205 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 893 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (81 enodes) * * [misc]simplify: iters left: 2 (142 enodes) * * [misc]simplify: iters left: 1 (189 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt k) (cbrt (sqrt 2))) (* (sqrt n) (cbrt (sqrt 2)))) (cbrt (sqrt (pow PI (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt k) (cbrt (sqrt 2))) (* (sqrt n) (cbrt (sqrt 2)))) (cbrt (sqrt (pow PI (/ k 2))))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt k) (cbrt (sqrt 2))) (* (sqrt n) (cbrt (sqrt 2)))) (cbrt (sqrt (pow PI (/ k 2))))) (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * * * * [misc]progress: [ 894 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (97 enodes) * * [misc]simplify: iters left: 2 (158 enodes) * * [misc]simplify: iters left: 1 (206 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt k) (cbrt (sqrt 2))) (* (sqrt n) (cbrt (sqrt 2)))) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt k) (cbrt (sqrt 2))) (* (sqrt n) (cbrt (sqrt 2)))) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (/ (sqrt k) (cbrt (sqrt 2))) (* (sqrt n) (cbrt (sqrt 2)))) (cbrt (fabs (cbrt (pow (* (* PI 2) n) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 895 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (157 enodes) * * [misc]simplify: iters left: 1 (205 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt k) (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt k) (sqrt n)))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt k) (sqrt n)))) (* (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * * * * [misc]progress: [ 896 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (135 enodes) * * [misc]simplify: iters left: 1 (225 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt 2)))))) * * * * [misc]progress: [ 897 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (157 enodes) * * [misc]simplify: iters left: 1 (205 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt k) (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt k) (sqrt n)))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt k) (sqrt n)))) (* (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * * * * [misc]progress: [ 898 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (134 enodes) * * [misc]simplify: iters left: 1 (240 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (/ (sqrt k) (sqrt n)) (cbrt (sqrt 2))) (cbrt (sqrt 2))) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt 2)))))) * * * * [misc]progress: [ 899 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (157 enodes) * * [misc]simplify: iters left: 2 (318 enodes) * * [misc]simplify: iters left: 1 (486 enodes) * [exit]simplify: Simplified to (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt k) (sqrt n))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt k) (sqrt n))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt k) (sqrt n))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 900 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (157 enodes) * * [misc]simplify: iters left: 1 (205 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt k) (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt k) (sqrt n)))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ (sqrt k) (sqrt n)))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 901 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (265 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt k) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (sqrt n))) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (sqrt 2)))))) * * * * [misc]progress: [ 902 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (85 enodes) * [exit]simplify: Simplified to (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (* (/ (sqrt n) (sqrt k)) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (* (/ (sqrt n) (sqrt k)) (sqrt (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (* (/ (sqrt n) (sqrt k)) (sqrt (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 903 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (/ (sqrt n) (sqrt k)) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (/ (sqrt n) (sqrt k)) (sqrt (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (* (/ (sqrt n) (sqrt k)) (sqrt (sqrt 2)))) (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))))) * * * * [misc]progress: [ 904 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (72 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (* (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (fabs (cbrt (pow (* 2 (* n PI)) (/ k 2))))) (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2)))) (/ (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (/ (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (cbrt (pow (* (* PI 2) n) (/ k 2)))))))))) * * * * [misc]progress: [ 905 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (85 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (sqrt n) (sqrt k)) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (sqrt n) (sqrt k)) (sqrt (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (sqrt n) (sqrt k)) (sqrt (sqrt 2)))) (* (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * * * * [misc]progress: [ 906 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (69 enodes) * * [misc]simplify: iters left: 1 (88 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt 2)))))) * * * * [misc]progress: [ 907 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (85 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (sqrt n) (sqrt k)) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (sqrt n) (sqrt k)) (sqrt (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (sqrt n) (sqrt k)) (sqrt (sqrt 2)))) (* (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * * * * [misc]progress: [ 908 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (sqrt (sqrt 2)) (cbrt 1))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (68 enodes) * * [misc]simplify: iters left: 1 (87 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt 2)))))) * * * * [misc]progress: [ 909 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (52 enodes) * * [misc]simplify: iters left: 3 (86 enodes) * * [misc]simplify: iters left: 2 (141 enodes) * * [misc]simplify: iters left: 1 (201 enodes) * [exit]simplify: Simplified to (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (sqrt n) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (sqrt n) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (* (/ (sqrt k) (sqrt (sqrt 2))) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))) (/ (sqrt n) (cbrt (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 910 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (85 enodes) * [exit]simplify: Simplified to (/ (sqrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (sqrt n) (sqrt k)) (sqrt (sqrt 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (sqrt n) (sqrt k)) (sqrt (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2))))) (* (/ (sqrt n) (sqrt k)) (sqrt (sqrt 2)))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 911 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ (sqrt (sqrt 2)) 1)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (76 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (sqrt n)) (sqrt (sqrt 2))) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt (sqrt 2)))))) * * * * [misc]progress: [ 912 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (60 enodes) * * [misc]simplify: iters left: 2 (82 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt k) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt k) (sqrt n))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (cbrt (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (sqrt k) (sqrt n))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 913 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (66 enodes) * * [misc]simplify: iters left: 1 (122 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow PI (/ k 2)))) (/ (sqrt n) (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (/ (sqrt n) (sqrt k))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (cbrt (sqrt (pow PI (/ k 2)))) (/ (sqrt n) (sqrt k))) (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * * * * [misc]progress: [ 914 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (83 enodes) * * [misc]simplify: iters left: 1 (131 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (sqrt n)) (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt k) (sqrt n)) (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (70 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt k) (sqrt n)) (cbrt (fabs (cbrt (pow (* (* n 2) PI) (/ k 2)))))) (* (* (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt 2)) (cbrt (sqrt (cbrt (pow (* (* 2 n) PI) (/ k 2)))))) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))))) * * * * [misc]progress: [ 915 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (81 enodes) * * [misc]simplify: iters left: 1 (127 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt 2)))))) * * * * [misc]progress: [ 916 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ 1 (cbrt (sqrt 1)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * * [misc]simplify: iters left: 1 (56 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (43 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt 2)) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt 2))))) * * * * [misc]progress: [ 917 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (81 enodes) * * [misc]simplify: iters left: 1 (127 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (63 enodes) * * [misc]simplify: iters left: 1 (69 enodes) * [exit]simplify: Simplified to (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (* (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (sqrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt 2)))))) * * * * [misc]progress: [ 918 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ 1 (cbrt 1))) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (22 enodes) * * [misc]simplify: iters left: 1 (25 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (43 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt 2)) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt 2))))) * * * * [misc]progress: [ 919 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (55 enodes) * * [misc]simplify: iters left: 3 (83 enodes) * * [misc]simplify: iters left: 2 (166 enodes) * * [misc]simplify: iters left: 1 (367 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (sqrt n)) (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt k) (sqrt n)) (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt k) (sqrt n)) (* (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 920 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (59 enodes) * * [misc]simplify: iters left: 2 (81 enodes) * * [misc]simplify: iters left: 1 (127 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (sqrt n)) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt k) (sqrt n)) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (* (/ (sqrt k) (sqrt n)) (sqrt (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))) (/ (* (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) (sqrt (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))))) * * * * [misc]progress: [ 921 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (/ 1 1)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * * [misc]simplify: iters left: 2 (22 enodes) * * [misc]simplify: iters left: 1 (23 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (43 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt 2)) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt 2))))) * * * * [misc]progress: [ 922 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) 1) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * * [misc]simplify: iters left: 1 (22 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (43 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt 2)) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (/ (sqrt (pow (* (* 2 n) PI) (/ k 2))) (sqrt 2))))) * * * * [misc]progress: [ 923 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt k) (pow n 1/2)) (sqrt 2)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (15 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (* (sqrt 2) (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (* (sqrt 2) (sqrt n))) (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * [enter]simplify: Simplifying (/ (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (75 enodes) * * [misc]simplify: iters left: 1 (110 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (/ k 2))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (sqrt k) (* (sqrt 2) (sqrt n))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))))) * * * * [misc]progress: [ 924 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 925 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 926 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 927 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (* (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 928 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 929 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 930 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (pow PI (/ k 2)))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))))) * * * * [misc]progress: [ 931 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 932 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 933 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt 1)))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 934 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 935 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (cbrt 1))) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 936 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (cbrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 937 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (cbrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 938 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) 1)) (/ (cbrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 939 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 940 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow PI (/ k 2)))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* n 2) (/ k 2)))))))) * * * * [misc]progress: [ 941 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 942 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 943 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt 1)))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 944 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 945 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (cbrt 1))) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 946 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt (sqrt 2)) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 947 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 948 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt (sqrt 2)) 1)) (/ (sqrt (sqrt 2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 949 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 950 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 2) (cbrt (sqrt (pow (* n 2) (/ k 2))))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (cbrt (sqrt (pow (* 2 n) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (pow PI (/ k 2)))))) (/ (sqrt 2) (cbrt (sqrt (pow (* 2 n) (/ k 2)))))))) * * * * [misc]progress: [ 951 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (* (cbrt (pow (* PI (* n 2)) (/ k 2))) (cbrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (sqrt (cbrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 952 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 953 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt 1)))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))) * * * * [misc]progress: [ 954 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt (sqrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 955 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (cbrt 1))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))) * * * * [misc]progress: [ 956 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (* (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (/ (sqrt 2) (cbrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 957 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 (sqrt (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (sqrt (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))))))) * * * * [misc]progress: [ 958 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ 1 1)) (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))) * * * * [misc]progress: [ 959 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) 1) (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))) * * * * [misc]progress: [ 960 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ 1 (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt 2)) (/ 1 (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * * * * [misc]progress: [ 961 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (48 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (58 enodes) * [exit]simplify: Simplified to (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (* (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2))))))) (cbrt (* (/ (sqrt k) (sqrt n)) (* (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (cbrt (sqrt (pow (* 2 (* n PI)) (/ k 2)))))))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (cbrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))))) * * * * [misc]progress: [ 962 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (47 enodes) * * [misc]simplify: iters left: 2 (55 enodes) * * [misc]simplify: iters left: 1 (57 enodes) * [exit]simplify: Simplified to (sqrt (* (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt (* (* (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (sqrt k) (sqrt n))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (sqrt (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))))) * * * * [misc]progress: [ 963 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (* (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))))))) (/ (cbrt (sqrt k)) (cbrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))))))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))))) * * * * [misc]progress: [ 964 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))))) * * * * [misc]progress: [ 965 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (151 enodes) * * [misc]simplify: iters left: 1 (182 enodes) * [exit]simplify: Simplified to (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (* (* (/ (cbrt (sqrt k)) (cbrt (sqrt n))) (/ (cbrt (sqrt k)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* (* n 2) PI) (/ k 2))))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 966 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (71 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt n)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (* (/ (cbrt (sqrt k)) (/ (sqrt (sqrt n)) (cbrt (sqrt k)))) (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2))))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 967 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (78 enodes) * * [misc]simplify: iters left: 1 (138 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 968 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * * [misc]simplify: iters left: 2 (23 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt k)) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))))) * * * * [misc]progress: [ 969 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n 1/2)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (14 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (* (/ (cbrt (sqrt k)) (sqrt n)) (cbrt (sqrt k))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (cbrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))))) * * * * [misc]progress: [ 970 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (* (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))))))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))))) * * * * [misc]progress: [ 971 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2)))))))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))))) * * * * [misc]progress: [ 972 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (* (/ (sqrt (sqrt k)) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (cbrt (sqrt (pow (* n (* 2 PI)) (/ k 2))))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 973 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (* (/ (sqrt (sqrt k)) (sqrt (sqrt n))) (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2))))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 974 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (50 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (sqrt (sqrt k))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (* (cbrt (sqrt (pow (* (* 2 PI) n) (/ k 2)))) (sqrt (sqrt k))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 975 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) 1) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * * [misc]simplify: iters left: 2 (9 enodes) * [exit]simplify: Simplified to (sqrt (sqrt k)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt (sqrt k)) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))))) * * * * [misc]progress: [ 976 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (sqrt k)) (pow n 1/2)) * * [misc]simplify: iters left: 4 (7 enodes) * * [misc]simplify: iters left: 3 (8 enodes) * [exit]simplify: Simplified to (/ (sqrt (sqrt k)) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt (sqrt k)) (sqrt n)) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt (sqrt k)) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))))) * * * * [misc]progress: [ 977 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (/ 1 (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (cbrt (/ (/ (sqrt n) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2))))))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt k) (cbrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))))) * * * * [misc]progress: [ 978 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ 1 (sqrt (/ (sqrt n) (* (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))) (cbrt (sqrt (pow (* (* PI 2) n) (/ k 2)))))))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt k) (sqrt (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))))) * * * * [misc]progress: [ 979 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (* (cbrt (pow n 1/2)) (cbrt (pow n 1/2))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (100 enodes) * * [misc]simplify: iters left: 1 (182 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt n)) (cbrt (sqrt n)))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt k) (/ (cbrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 980 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * * [misc]simplify: iters left: 2 (53 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (cbrt (sqrt (pow (* n (* PI 2)) (/ k 2)))) (sqrt (sqrt n))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt k) (/ (sqrt (pow n 1/2)) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 981 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (/ 1 (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (cbrt (sqrt (pow (* (* n PI) 2) (/ k 2)))) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt k) (/ (pow n 1/2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 982 / 1019 ] 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) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ 1 (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))))) * * * * [misc]progress: [ 983 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (pow n 1/2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (8 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ 1 (sqrt n)) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (sqrt k) (/ 1 (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))))) * * * * [misc]progress: [ 984 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 985 / 1019 ] 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 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ 1 (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))))) * * * * [misc]progress: [ 986 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow n 1/2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt n)) * [misc]simplify: Simplified (2 2 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (sqrt n)) (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))))) * * * * [misc]progress: [ 987 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [misc]simplify: Simplified (2 2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (* (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (sqrt 2)) (cbrt (sqrt (pow (* (* 2 n) PI) (/ k 2))))))) * * * * [misc]progress: [ 988 / 1019 ] 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 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (sqrt k) (* (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))))) * * * * [misc]progress: [ 989 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 990 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 991 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 992 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 993 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 994 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 995 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 996 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 997 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 998 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 999 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 1000 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 1001 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 1002 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 1003 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 1004 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 1005 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 1006 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 1007 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 1008 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 1009 / 1019 ] simplifiying candidate # * * * * [misc]progress: [ 1010 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) * * [misc]simplify: iters left: 6 (26 enodes) * * [misc]simplify: iters left: 5 (43 enodes) * * [misc]simplify: iters left: 4 (92 enodes) * * [misc]simplify: iters left: 3 (300 enodes) * [exit]simplify: Simplified to (* (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* 2 n)) (/ k 2))))) (cbrt (sqrt (pow (* PI (* 2 n)) (/ k 2))))) (/ (/ (sqrt PI) (sqrt (pow (* PI (* 2 n)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* PI (* 2 n)) (/ k 2))))))) * [misc]simplify: Simplified (2) to (λ (k n) (* (/ (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* 2 n)) (/ k 2))))) (cbrt (sqrt (pow (* PI (* 2 n)) (/ k 2))))) (/ (/ (sqrt PI) (sqrt (pow (* PI (* 2 n)) (/ k 2)))) (* (/ (sqrt k) (sqrt n)) (cbrt (sqrt (pow (* PI (* 2 n)) (/ k 2)))))))) * * * * [misc]progress: [ 1011 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ k (sqrt 2))) (- (+ (* +nan.0 (/ (* (log n) (pow k 2)) (sqrt 2))) (- (+ (* +nan.0 (/ (* n k) (sqrt 2))) (- (+ (* +nan.0 (/ (pow k 2) (sqrt 2))) (- (* +nan.0 (/ (* (pow k 2) (log (* 2 PI))) (sqrt 2)))))))))))) * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) +nan.0)) * * * * [misc]progress: [ 1012 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) (* n k)))) (- (+ (* +nan.0 (/ (pow (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) 2) (* (sqrt 2) (pow n 2)))) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* 2 PI)) (log (/ 1 n))) k))) (* (sqrt 2) n)))))))) * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) +nan.0)) * * * * [misc]progress: [ 1013 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (/ 1 (* (sqrt 2) n)) (sqrt (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))))) (- (+ (* +nan.0 (* (/ 1 (* (sqrt 2) k)) (sqrt (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k)))))) (- (* +nan.0 (* (/ 1 (sqrt 2)) (sqrt (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) k))))))))))) * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) +nan.0)) * * * * [misc]progress: [ 1014 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [misc]simplify: Simplified (2 1 2 1 1 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 1015 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [misc]simplify: Simplified (2 1 2 1 1 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 1016 / 1019 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [misc]simplify: Simplified (2 1 2 1 1 2) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))))))) * * * * [misc]progress: [ 1017 / 1019 ] 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 2 2 1 1 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))) * * * * [misc]progress: [ 1018 / 1019 ] 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 2 2 1 1 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))) * * * * [misc]progress: [ 1019 / 1019 ] 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 2 2 1 1 1) to (λ (k n) (/ (/ (sqrt PI) (sqrt (pow (* 2 (* n PI)) (/ k 2)))) (/ (/ (sqrt k) (/ (pow n 1/2) (* (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2)))) (cbrt (sqrt (pow (* PI (* n 2)) (/ k 2))))))) (/ (sqrt 2) (cbrt (sqrt (pow (* (* PI n) 2) (/ k 2)))))))) * * * [misc]progress: adding candidates to table * [misc]progress: [Phase 3 of 3] Extracting. * * [misc]regime: Finding splitpoints for: (# # # # # #) * * * [misc]regime-changes: Trying 2 branch expressions: (n k) * * * * [misc]regimes: Trying to branch on n from (# # # # # #) * * * * [misc]regimes: Trying to branch on k from (# # # # # #) * * * [misc]regime: Found split indices: #