* [misc]progress: [Phase 1 of 3] Setting up. * * * [misc]progress: [1/2] Preparing points * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 * * * * [misc]points: Computing exacts on every 16 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Setting MPFR precision to 576 * * * * [misc]points: Computing exacts on every 8 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Setting MPFR precision to 576 * * * * [misc]points: Computing exacts on every 4 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Setting MPFR precision to 576 * * * * [misc]points: Setting MPFR precision to 832 * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 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 216 additional inputs, on iter 1 have 40 / 256 * * * * [misc]points: Computing exacts on every 13 of 216 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 216 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 216 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 216 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 166 additional inputs, on iter 2 have 90 / 256 * * * * [misc]points: Computing exacts on every 10 of 166 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 166 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 166 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 166 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 133 additional inputs, on iter 3 have 123 / 256 * * * * [misc]points: Computing exacts on every 8 of 133 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 133 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 133 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 133 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 111 additional inputs, on iter 4 have 145 / 256 * * * * [misc]points: Computing exacts on every 6 of 111 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 111 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 111 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 95 additional inputs, on iter 5 have 161 / 256 * * * * [misc]points: Computing exacts on every 5 of 95 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 95 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 95 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 74 additional inputs, on iter 6 have 182 / 256 * * * * [misc]points: Computing exacts on every 4 of 74 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 74 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 74 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 59 additional inputs, on iter 7 have 197 / 256 * * * * [misc]points: Computing exacts on every 3 of 59 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 59 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 50 additional inputs, on iter 8 have 206 / 256 * * * * [misc]points: Computing exacts on every 3 of 50 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 50 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 42 additional inputs, on iter 9 have 214 / 256 * * * * [misc]points: Computing exacts on every 2 of 42 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 42 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 33 additional inputs, on iter 10 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 25 additional inputs, on iter 11 have 231 / 256 * * * * [misc]points: Computing exacts for 25 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 20 additional inputs, on iter 12 have 236 / 256 * * * * [misc]points: Computing exacts for 20 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 14 additional inputs, on iter 13 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 12 additional inputs, on iter 14 have 244 / 256 * * * * [misc]points: Computing exacts for 12 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 11 additional inputs, on iter 15 have 245 / 256 * * * * [misc]points: Computing exacts for 11 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 9 additional inputs, on iter 16 have 247 / 256 * * * * [misc]points: Computing exacts for 9 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 9 additional inputs, on iter 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 4 additional inputs, on iter 20 have 252 / 256 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 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 253 / 256 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 24 have 255 / 256 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [exit]points: Sampled 256 points with exact outputs * * * [misc]progress: [2/2] Setting up program. * [misc]progress: [Phase 2 of 3] Improving. * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) * * [misc]progress: iteration 1 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1 1) * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (pow (* (* n PI) 2) (/ (- 1 k) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* n PI) 2) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n PI) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n PI) 2))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* n PI) 2)) in k * [misc]taylor: Taking taylor expansion of (* (* n PI) 2) in k * [misc]taylor: Taking taylor expansion of (* n PI) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (* n PI) 2) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ 1 k) into (+ k 1) * [misc]backup-simplify: Simplify (/ (+ k 1) 2) into (* 1/2 (+ k 1)) * [misc]taylor: Taking taylor expansion of (log (* (* n PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* n PI) 2) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [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 (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ k 1)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1)))) into (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1)))) * [misc]taylor: Taking taylor expansion of (pow (* (* n PI) 2) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ 1 k) into (+ k 1) * [misc]backup-simplify: Simplify (/ (+ k 1) 2) into (* 1/2 (+ k 1)) * [misc]taylor: Taking taylor expansion of (log (* (* n PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* n PI) 2) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [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 (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ k 1)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1)))) into (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1))) 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 1)) 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 1) in k * [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 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 1 into 1 * [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]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 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 PI)) 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 (+ (log n) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (/ 0 n) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [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)))) (* 1/2 (+ (log (* 2 PI)) (log n)))) into (* 1/2 (* (+ (log (* 2 PI)) (log n)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ (log (* 2 PI)) (log n)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (* 1/2 (* (+ (log (* 2 PI)) (log n)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI))) 2) 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 (+ (log n) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow n 2))) (/ 0 n)) 2) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (pow (* 1/2 (+ (log (* 2 PI)) (log n))) 2) 2)) into (* 1/8 (* (pow (+ (log (* 2 PI)) (log n)) 2) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* 1/8 (* (pow (+ (log (* 2 PI)) (log n)) 2) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (* 1/8 (* (pow (+ (log (* 2 PI)) (log n)) 2) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* (* 1/8 (* (pow (+ (log (* 2 PI)) (log n)) 2) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (pow k 2)) (+ (* (* 1/2 (* (+ (log (* 2 PI)) (log n)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) k) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (+ (* 1/2 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))) (+ (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)))) (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))) (* 1/2 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))))))))) * [misc]approximate: Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in k * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) PI) 2) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) PI) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [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 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [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 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify 1 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)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI))) 2) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow (* 2 PI) 3))) (+ (* -3 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))) 6) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 k)) 1) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (+ k 1) (- (log (* 2 PI)) (log (/ 1 n)))))) * [misc]approximate: Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in k * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) PI) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n * [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 into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (* 2 (* -1 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n * [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 into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (* 2 (* -1 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (log n)) into (+ (log n) (log (* -2 PI))) * [misc]backup-simplify: Simplify (+ (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 n) (log (* -2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* -2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* -2 PI) 2))) (/ 0 (* -2 PI))) 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)) 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 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow (* -2 PI) 3))) (+ (* -3 (/ 0 (pow (* -2 PI) 2))) (/ 0 (* -2 PI)))) 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)) 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 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1 1) * [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 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 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 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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 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 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 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 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 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 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 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [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 0 into 0 * [misc]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 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 0 into 0 * [misc]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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) * * * * [misc]progress: [ 3 / 3 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (pow (* (* n PI) 2) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n PI) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n PI) 2))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* n PI) 2)) in k * [misc]taylor: Taking taylor expansion of (* (* n PI) 2) in k * [misc]taylor: Taking taylor expansion of (* n PI) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 1 0) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* n PI)) 1/2) +nan.0) into (* +nan.0 (sqrt (* PI (* n 2)))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (pow (* (* n PI) 2) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ 1 k) into (+ k 1) * [misc]backup-simplify: Simplify (/ (+ k 1) 2) into (* 1/2 (+ k 1)) * [misc]taylor: Taking taylor expansion of (log (* (* n PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* n PI) 2) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [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 (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ k 1)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1)))) into (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1)))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1)))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (pow (* (* n PI) 2) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* n PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* n PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ 1 k) into (+ k 1) * [misc]backup-simplify: Simplify (/ (+ k 1) 2) into (* 1/2 (+ k 1)) * [misc]taylor: Taking taylor expansion of (log (* (* n PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* n PI) 2) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [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 (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ k 1)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1)))) into (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1)))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1)))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1))))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1))))) 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 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 1 0) into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1))) 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 1)) 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 1) in k * [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 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 1 into 1 * [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]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 PI)) 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 (+ (log n) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt k)) (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1))))) (/ 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 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (/ 0 n) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [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)))) (* 1/2 (+ (log (* 2 PI)) (log n)))) into (* 1/2 (* (+ (log (* 2 PI)) (log n)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI))) 2) 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 (+ (log n) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt k)) (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1))))) (/ 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 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow n 2))) (/ 0 n)) 2) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (pow (* 1/2 (+ (log (* 2 PI)) (log n))) 2) 2)) into (* 1/8 (* (pow (+ (log (* 2 PI)) (log n)) 2) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (pow +nan.0 2) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify (+ (* +nan.0 (* 1/2 (* (+ (log (* 2 PI)) (log n)) (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) (* (* +nan.0 (pow +nan.0 2)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow (* 2 PI) 3))) (+ (* -3 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))) 6) 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 (+ (log n) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt k)) (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (+ k 1))))) (/ 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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow (* 2 PI) 3))) (+ (* -3 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow n 3))) (+ (* -3 (/ 0 (pow n 2))) (/ 0 n))) 6) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (pow (* 1/2 (+ (log (* 2 PI)) (log n))) 3) 6)) into (* 1/48 (* (pow (+ (log (* 2 PI)) (log n)) 3) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (* 2 (* +nan.0 (* +nan.0 (pow +nan.0 2)))) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify (+ (* +nan.0 (* 1/8 (* (pow (+ (log (* 2 PI)) (log n)) 2) (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) (+ (* (* +nan.0 (pow +nan.0 2)) (* 1/2 (* (+ (log (* 2 PI)) (log n)) (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) (* (* +nan.0 (pow +nan.0 2)) (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) (pow k 2)) (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))))) k) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) into (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* k (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)))) (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (* (pow k 2) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in k * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) PI) 2) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) PI) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 1 0) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [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 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]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 k) 1) (- (log (* 2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* (/ 1 n) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [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 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]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 k) 1) (- (log (* 2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify 1 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)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking 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 0) into +nan.0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt (/ 1 k))) (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 k) 1) (- (log (* 2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI))) 2) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [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 (+ (/ 0 (sqrt (/ 1 k))) (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 0 into 0 * [misc]backup-simplify: Simplify (/ (pow +nan.0 2) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) (* +nan.0 (pow +nan.0 2))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) (pow +nan.0 2))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) (pow +nan.0 2))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) (pow +nan.0 2))) * [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 (pow (* 2 PI) 3))) (+ (* -3 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))) 6) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [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 (+ (/ 0 (sqrt (/ 1 k))) (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (* 2 (* +nan.0 (* +nan.0 (pow +nan.0 2)))) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) (* +nan.0 (pow +nan.0 2))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) (pow +nan.0 2))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) (pow +nan.0 2))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* 2 PI)) (log n))))) (pow +nan.0 2))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 k)) 1) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow +nan.0 2))) (pow (/ 1 k) 3)) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 k)) 1) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow +nan.0 2))) (pow (/ 1 k) 2)) (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 k)) 1) (- (log (* 2 PI)) (log (/ 1 n))))))) (/ 1 k)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ k 1) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ k 1) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ k 1) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2)))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in k * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) PI) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ -1 0) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -2 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -2 (/ PI n))))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n * [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 into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (* 2 (* -1 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (sqrt k) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* (/ 1 (- n)) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n * [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 into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (* 2 (* -1 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (sqrt k) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) * [misc]taylor: Taking taylor expansion of (* (sqrt k) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) 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 0 into 0 * [misc]backup-simplify: Simplify (/ 1 0) into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (log n)) into (+ (log n) (log (* -2 PI))) * [misc]backup-simplify: Simplify (+ (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 n) (log (* -2 PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* -2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt (/ 1 k))) (* (* (sqrt k) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ 0 (sqrt (/ 1 k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [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 (pow (* -2 PI) 2))) (/ 0 (* -2 PI))) 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)) 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 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 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)) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt (/ 1 k))) (* (* (sqrt k) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ 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 (/ (pow +nan.0 2) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify (* (* +nan.0 (pow +nan.0 2)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (* +nan.0 (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [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 (pow (* -2 PI) 3))) (+ (* -3 (/ 0 (pow (* -2 PI) 2))) (/ 0 (* -2 PI)))) 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)) 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 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 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)) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt (/ 1 k))) (* (* (sqrt k) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ 0 (sqrt (/ 1 k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (* 2 (* +nan.0 (* +nan.0 (pow +nan.0 2)))) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify (* (* +nan.0 (pow +nan.0 2)) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (* +nan.0 (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (/ 1 (- k)) 3)) (+ (* (* +nan.0 (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (/ 1 (- k)) 2)) (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (/ 1 (- k))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) (pow k 3)))))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (pow (* (* n PI) 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (expm1 (pow (* (* PI n) 2) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (expm1 (pow (* (* PI n) 2) (/ (- 1 k) 2))) * * * * [misc]progress: [ 2 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (pow (* (* n PI) 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (log1p (pow (* (* PI n) 2) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (log1p (pow (* (* PI n) 2) (/ (- 1 k) 2))) * * * * [misc]progress: [ 3 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* n PI) 2)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * [exit]simplify: Simplified to (/ (log (* (* PI n) 2)) (/ 2 (- 1 k))) * [exit]simplify: Simplified to (/ (log (* (* PI n) 2)) (/ 2 (- 1 k))) * * * * [misc]progress: [ 4 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* n PI) 2)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (144 enodes) * [exit]simplify: Simplified to (/ (log (* (* PI n) 2)) (/ 2 (- 1 k))) * [exit]simplify: Simplified to (/ (log (* (* PI n) 2)) (/ 2 (- 1 k))) * * * * [misc]progress: [ 5 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (117 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [exit]simplify: Simplified to (/ (- 1 k) 2) * * * * [misc]progress: [ 6 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* n PI) 2) (/ 1 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (22 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ 1 2)) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ 1 2)) * [enter]simplify: Simplifying (pow (* (* n PI) 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 (* (* PI n) 2) (/ k 2)) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ k 2)) * * * * [misc]progress: [ 7 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* n PI) 2) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 8 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* n PI) 2) (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 9 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* n PI) 2) 1) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * [exit]simplify: Simplified to (* (* PI n) 2) * [exit]simplify: Simplified to (* (* PI n) 2) * * * * [misc]progress: [ 10 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* n PI) 2) (- 1 k)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (25 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- 1 k)) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- 1 k)) * * * * [misc]progress: [ 11 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n PI) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (22 enodes) * [exit]simplify: Simplified to (pow (* PI n) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* PI n) (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow 2 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (pow 2 (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow 2 (/ (- 1 k) 2)) * * * * [misc]progress: [ 12 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 13 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (* (* n PI) 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (246 enodes) * [exit]simplify: Simplified to (/ (log (* (* PI n) 2)) (/ 2 (- 1 k))) * [exit]simplify: Simplified to (/ (log (* (* PI n) 2)) (/ 2 (- 1 k))) * * * * [misc]progress: [ 14 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (* (* n PI) 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (exp (pow (* (* PI n) 2) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (* (* PI n) 2) (/ (- 1 k) 2))) * * * * [misc]progress: [ 15 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) * * * * [misc]progress: [ 16 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (* (* n PI) 2) (/ (- 1 k) 2)) (pow (* (* n PI) 2) (/ (- 1 k) 2))) (pow (* (* n PI) 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (pow (pow (* (* PI n) 2) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (* (* PI n) 2) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 17 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) * * * * [misc]progress: [ 18 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 19 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (expm1 (* PI n)) * [exit]simplify: Simplified to (expm1 (* PI n)) * * * * [misc]progress: [ 20 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (log1p (* PI n)) * [exit]simplify: Simplified to (log1p (* PI n)) * * * * [misc]progress: [ 21 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 22 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (8 enodes) * * [misc]simplify: iters left: 1 (9 enodes) * [exit]simplify: Simplified to (log (* PI n)) * [exit]simplify: Simplified to (log (* PI n)) * * * * [misc]progress: [ 23 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (exp (* PI n)) * [exit]simplify: Simplified to (exp (* PI n)) * * * * [misc]progress: [ 24 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n PI)) (cbrt (* n PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (6 enodes) * [exit]simplify: Simplified to (* (cbrt (* PI n)) (cbrt (* PI n))) * [exit]simplify: Simplified to (* (cbrt (* PI n)) (cbrt (* PI n))) * [enter]simplify: Simplifying (cbrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (cbrt (* PI n)) * [exit]simplify: Simplified to (cbrt (* PI n)) * * * * [misc]progress: [ 25 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n PI) (* n PI)) (* n PI)) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (pow (* PI n) 3) * [exit]simplify: Simplified to (pow (* PI n) 3) * * * * [misc]progress: [ 26 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * [enter]simplify: Simplifying (sqrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * * * * [misc]progress: [ 27 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 28 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 29 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (expm1 (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (expm1 (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 30 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (log1p (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (log1p (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 31 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 32 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* (* n PI) 2)) (/ (- 1 k) 2)) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 33 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* (* n PI) 2)) (/ (- 1 k) 2)) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (66 enodes) * * [misc]simplify: iters left: 3 (165 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 34 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* (* n PI) 2) (/ (- 1 k) 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (302 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* (* PI n) 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (log (* (* PI n) 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 35 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (139 enodes) * * [misc]simplify: iters left: 1 (418 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 36 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (exp (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (exp (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 37 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (* (* n PI) 2) (/ (- 1 k) 2)) (pow (* (* n PI) 2) (/ (- 1 k) 2))) (pow (* (* n PI) 2) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (71 enodes) * * [misc]simplify: iters left: 3 (123 enodes) * * [misc]simplify: iters left: 2 (192 enodes) * * [misc]simplify: iters left: 1 (302 enodes) * [exit]simplify: Simplified to (* (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (* k (sqrt k))) (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (* k (sqrt k))) (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 38 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (cbrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 39 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (86 enodes) * * [misc]simplify: iters left: 2 (121 enodes) * * [misc]simplify: iters left: 1 (152 enodes) * [exit]simplify: Simplified to (/ (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow (* (* PI n) 2) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow (* (* PI n) 2) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* PI n) 2) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 40 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) * [enter]simplify: Simplifying (sqrt (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 41 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (- (pow (* (* n PI) 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (- (pow (* (* PI n) 2) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (- (pow (* (* PI n) 2) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (- (sqrt k)) * * [misc]simplify: iters left: 3 (3 enodes) * [exit]simplify: Simplified to (- (sqrt k)) * [exit]simplify: Simplified to (- (sqrt k)) * * * * [misc]progress: [ 42 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (pow (* PI n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow (* PI n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k))) * * * * [misc]progress: [ 43 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 44 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n PI) (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (pow (* PI n) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* PI n) (/ (- 1 k) 2)) * [enter]simplify: Simplifying (/ (pow 2 (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 45 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (61 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 46 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 47 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) 1) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (/ (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 48 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 49 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 50 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (/ (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 51 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (cbrt (sqrt k))) * * * * [misc]progress: [ 52 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 53 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [exit]simplify: Simplified to 1 * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 54 / 73 ] simplifiying candidate # * * * * [misc]progress: [ 55 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 56 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow (* (* n PI) 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 57 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 58 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 59 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ (- 1 k) 2)) * * * * [misc]progress: [ 60 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow 2 (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow 2 (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow 2 (/ (- 1 k) 2))) * * * * [misc]progress: [ 61 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* PI (* 2 n)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* PI (* 2 n)) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 62 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (pow (* (* n PI) 2) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* PI (* 2 n)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* PI (* 2 n)) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 63 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow (* (* n PI) 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 64 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt k) (pow (* (* n PI) 2) (/ k 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (* (pow (* n (* PI 2)) (/ k 2)) (sqrt k)) * [exit]simplify: Simplified to (* (pow (* n (* PI 2)) (/ k 2)) (sqrt k)) * * * * [misc]progress: [ 65 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (+ (* 1/2 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))) (+ (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)))) (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))) (* 1/2 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))))))))) (sqrt k)) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (105 enodes) * * [misc]simplify: iters left: 4 (351 enodes) * [exit]simplify: Simplified to (/ (+ (fma (* (log n) (* k 1/2)) (* (pow (* 2 PI) 1/2) (pow n 1/2)) (* (pow (* 2 PI) 1/2) (pow n 1/2))) (fma 1/8 (* (* (pow (* 2 PI) 1/2) (* (pow n 1/2) (* k k))) (+ (* (log (* 2 PI)) (log (* 2 PI))) (* (log n) (log n)))) (fma (* (* (log n) (log (* 2 PI))) (* (pow (* 2 PI) 1/2) (* (pow n 1/2) (* k k)))) 1/4 (* (* (pow (* 2 PI) 1/2) (pow n 1/2)) (* (log (* 2 PI)) (* k 1/2)))))) (sqrt k)) * * * * [misc]progress: [ 66 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (* (+ k 1) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (261 enodes) * [exit]simplify: Simplified to (/ (* (pow n (fma k 1/2 1/2)) (pow (* PI 2) (fma k 1/2 1/2))) (sqrt k)) * * * * [misc]progress: [ 67 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) (sqrt k)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (316 enodes) * [exit]simplify: Simplified to (/ (pow (exp (* 1/2 (- 1 k))) (- (log (* PI -2)) (log (/ -1 n)))) (sqrt k)) * * * * [misc]progress: [ 68 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 69 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 70 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 71 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* k (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)))) (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (* (pow k 2) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))))))))))))))))))))) * * * * [misc]progress: [ 72 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ k 1) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (+ k 1) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (+ k 1) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2)))))))) * * * * [misc]progress: [ 73 / 73 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1 k)))) (pow k 3)))))))) * * * [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 2 1 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 1 1 1) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1 1) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 2 1 1) * [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 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 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 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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 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 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 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 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 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 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 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [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 0 into 0 * [misc]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 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 0 into 0 * [misc]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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 1 1 1) * [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 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 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 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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 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 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 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 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 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 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 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [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 0 into 0 * [misc]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 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 0 into 0 * [misc]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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) * * * * [misc]progress: [ 3 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* (* n PI) 2) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n PI) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (* n PI) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* n PI) 2)) in k * [misc]taylor: Taking taylor expansion of (* (* n PI) 2) in k * [misc]taylor: Taking taylor expansion of (* n PI) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (* n PI) 2) (/ k 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* (* n PI) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* (* n PI) 2))) in k * [misc]taylor: Taking taylor expansion of (/ k 2) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* n PI) 2)) in k * [misc]taylor: Taking taylor expansion of (* (* n PI) 2) in k * [misc]taylor: Taking taylor expansion of (* n PI) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (pow (* 2 (* n PI)) 1/2) 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 0 into 0 * [misc]backup-simplify: Simplify (/ 1 0) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* n PI)) 1/2) +nan.0) into (* +nan.0 (sqrt (* PI (* n 2)))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (* n PI) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (* n PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* n PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* n PI) 2) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [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 (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (* n PI) 2) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* (* n PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* (* n PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ k 2) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ k 2) into (* 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (* n PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* n PI) 2) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [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 (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt k)) into (* (sqrt (/ 1 k)) (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (* n PI) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (* n PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* n PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* n PI) 2) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [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 (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (* n PI) 2) (/ k 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ k 2) (log (* (* n PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ k 2) (log (* (* n PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ k 2) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ k 2) into (* 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (* n PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* n PI) 2) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [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 (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt k)) into (* (sqrt (/ 1 k)) (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) in k * [misc]taylor: Taking taylor expansion of (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 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 1 0) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* k (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (/ 0 n) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [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 1 into 1 * [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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt k)) (* (* (sqrt (/ 1 k)) (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (/ 0 (sqrt k)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (/ 0 n) 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 (* 1/2 (+ (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)))) (* 1/2 (+ (log (* 2 PI)) (log n)))) into (* 1/2 (* (+ (log (* 2 PI)) (log n)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI))) 2) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI))) 2) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt k)) (* (* (sqrt (/ 1 k)) (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (/ 0 (sqrt k)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow n 2))) (/ 0 n)) 2) 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 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow n 2))) (/ 0 n)) 2) 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 (/ (pow (* 1/2 (+ (log (* 2 PI)) (log n))) 2) 2) into (* 1/8 (pow (+ (log (* 2 PI)) (log n)) 2)) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* 1/8 (pow (+ (log (* 2 PI)) (log n)) 2))) (* (* 1/2 (* (+ (log (* 2 PI)) (log n)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (* 1/2 (+ (log (* 2 PI)) (log n))))) into (+ (* 3/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (+ (* 3/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (* 3/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (pow +nan.0 2) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify (+ (* +nan.0 (* 1/2 (* (+ (log (* 2 PI)) (log n)) (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) (* (* +nan.0 (pow +nan.0 2)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow (* 2 PI) 3))) (+ (* -3 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))) 6) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow (* 2 PI) 3))) (+ (* -3 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))) 6) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (/ 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt k)) (* (* (sqrt (/ 1 k)) (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) (/ 0 (sqrt k)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow (* 2 PI) 3))) (+ (* -3 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow n 3))) (+ (* -3 (/ 0 (pow n 2))) (/ 0 n))) 6) 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 (/ (+ (* 2 (/ 0 (pow (* 2 PI) 3))) (+ (* -3 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow n 3))) (+ (* -3 (/ 0 (pow n 2))) (/ 0 n))) 6) 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 (/ (pow (* 1/2 (+ (log (* 2 PI)) (log n))) 3) 6) into (* 1/48 (pow (+ (log (* 2 PI)) (log n)) 3)) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* 1/48 (pow (+ (log (* 2 PI)) (log n)) 3))) (+ (* (* 1/2 (* (+ (log (* 2 PI)) (log n)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (* 1/8 (pow (+ (log (* 2 PI)) (log n)) 2))) (* (+ (* 3/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (+ (* 3/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (* 3/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (+ (* 13/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 13/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (+ (* 13/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (* 13/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2))))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (* 2 (* +nan.0 (* +nan.0 (pow +nan.0 2)))) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify (+ (* +nan.0 (+ (* 3/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (+ (* 3/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (* 3/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))) (+ (* (* +nan.0 (pow +nan.0 2)) (* 1/2 (* (+ (log (* 2 PI)) (log n)) (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) (* (* +nan.0 (pow +nan.0 2)) (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) (pow k 2)) (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))))))) k) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) into (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* k (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)))) (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (* (pow k 2) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (/ (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) PI) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) PI) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in k * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) PI) 2) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) PI) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) * [misc]backup-simplify: Simplify (* 2 (/ PI 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 (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) PI) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) PI) 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 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in k * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) PI) 2) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) PI) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) * [misc]backup-simplify: Simplify (* 2 (/ PI 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 (* (* (/ 1 n) PI) 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 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 1 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 (* (* (/ 1 n) PI) 2) (/ 1 2)) (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [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 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [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 (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 (* (sqrt k) (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [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 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ (/ 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 k) 2) (log (* (* (/ 1 n) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [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 (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 (* (sqrt k) (/ (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) (/ (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 (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 0 into 0 * [misc]backup-simplify: Simplify (/ 1 0) into +nan.0 * [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)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt (/ 1 k))) (* (* (sqrt k) (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (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 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (/ 0 n) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (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 (* +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 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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI))) 2) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI))) 2) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt (/ 1 k))) (* (* (sqrt k) (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow n 2))) (/ 0 n)) 2) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (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 (/ (pow +nan.0 2) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify (* (* +nan.0 (pow +nan.0 2)) (/ (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)))) (pow +nan.0 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* +nan.0 (/ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow +nan.0 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* +nan.0 (/ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow +nan.0 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) 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 (pow (* 2 PI) 3))) (+ (* -3 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))) 6) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow (* 2 PI) 3))) (+ (* -3 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))) 6) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt (/ 1 k))) (* (* (sqrt k) (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow (* 2 PI) 3))) (+ (* -3 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow n 3))) (+ (* -3 (/ 0 (pow n 2))) (/ 0 n))) 6) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (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 (/ (* 2 (* +nan.0 (* +nan.0 (pow +nan.0 2)))) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify (* (* +nan.0 (pow +nan.0 2)) (/ (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)))) (pow +nan.0 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* +nan.0 (/ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow +nan.0 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* +nan.0 (/ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow +nan.0 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (/ (* (exp (* 1/2 (+ (log (* 2 PI)) (log (/ 1 n))))) (pow +nan.0 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))))) (pow (/ 1 k) 3)) (+ (* (* +nan.0 (/ (* (exp (* 1/2 (+ (log (* 2 PI)) (log (/ 1 n))))) (pow +nan.0 2)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k)))))) (pow (/ 1 k) 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)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (+ (log (/ 1 n)) (log (* 2 PI))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (+ (log (/ 1 n)) (log (* 2 PI))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (+ (log (/ 1 n)) (log (* 2 PI))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in k * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) PI) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) * [misc]backup-simplify: Simplify (* 2 (/ PI 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 (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) PI) 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 into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in k * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) PI) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) * [misc]backup-simplify: Simplify (* 2 (/ PI 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 (* (* (/ 1 (- n)) PI) 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 into -1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ -1 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) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) (sqrt (/ PI n)))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n * [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 into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (* 2 (* -1 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n * [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 into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (* 2 (* -1 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* -2 PI)) (log n))) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ 1 k))) into (* (sqrt k) (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]taylor: Taking taylor expansion of (/ (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (/ (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n * [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 into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (* 2 (* -1 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ (/ 1 (- k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (/ 1 (- k)) 2) (log (* (* (/ 1 (- n)) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ (/ 1 (- k)) 2) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ (/ 1 k) 2) into (/ 1/2 k) * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n * [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 into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (* 2 (* -1 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* -2 PI)) (log n))) into (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (sqrt (/ 1 k))) into (* (sqrt k) (/ (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) (/ (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 (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 0 into 0 * [misc]backup-simplify: Simplify (/ 1 0) into +nan.0 * [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 n) (log (* -2 PI))) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* -2 PI)))) 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 n) (log (* -2 PI))))) * [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 n) (log (* -2 PI))) * [misc]backup-simplify: Simplify (+ (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 n) (log (* -2 PI)))) * [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 n) (log (* -2 PI))))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (+ (log (* -2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify 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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* -2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [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 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt (/ 1 k))) (* (* (sqrt k) (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (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 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* -2 PI)) into 0 * [misc]backup-simplify: Simplify (/ 0 n) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (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 (* +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 n) (log (* -2 PI))))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* 1/2 (+ (log n) (log (* -2 PI))))) (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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* -2 PI) 2))) (/ 0 (* -2 PI))) 2) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* -2 PI) 2))) (/ 0 (* -2 PI))) 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)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify 0 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)) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt (/ 1 k))) (* (* (sqrt k) (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* -2 PI) 2))) (/ 0 (* -2 PI))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow n 2))) (/ 0 n)) 2) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (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 (/ (pow +nan.0 2) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify (* (* +nan.0 (pow +nan.0 2)) (/ (exp (* 1/2 (+ (log (* -2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ (* (exp (* 1/2 (+ (log n) (log (* -2 PI))))) (pow +nan.0 2)) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* +nan.0 (/ (* (exp (* 1/2 (+ (log n) (log (* -2 PI))))) (pow +nan.0 2)) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ (* (pow +nan.0 2) (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 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [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 (pow (* -2 PI) 3))) (+ (* -3 (/ 0 (pow (* -2 PI) 2))) (/ 0 (* -2 PI)))) 6) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow (* -2 PI) 3))) (+ (* -3 (/ 0 (pow (* -2 PI) 2))) (/ 0 (* -2 PI)))) 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)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify 0 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)) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt (/ 1 k))) (* (* (sqrt k) (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow (* -2 PI) 3))) (+ (* -3 (/ 0 (pow (* -2 PI) 2))) (/ 0 (* -2 PI)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow n 3))) (+ (* -3 (/ 0 (pow n 2))) (/ 0 n))) 6) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (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 (/ (* 2 (* +nan.0 (* +nan.0 (pow +nan.0 2)))) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify (* (* +nan.0 (pow +nan.0 2)) (/ (exp (* 1/2 (+ (log (* -2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ (* (exp (* 1/2 (+ (log n) (log (* -2 PI))))) (pow +nan.0 2)) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* +nan.0 (/ (* (exp (* 1/2 (+ (log n) (log (* -2 PI))))) (pow +nan.0 2)) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ (* (pow +nan.0 2) (exp (* 1/2 (+ (log (* -2 PI)) (log n))))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (/ (* (pow +nan.0 2) (exp (* 1/2 (+ (log (* -2 PI)) (log (/ 1 (- n))))))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))) (pow (/ 1 (- k)) 3)) (+ (* (* +nan.0 (/ (* (pow +nan.0 2) (exp (* 1/2 (+ (log (* -2 PI)) (log (/ 1 (- n))))))) (exp (* 1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))) (pow (/ 1 (- k)) 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))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (+ (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* -1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (+ (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* -1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (+ (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* -1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 3))))))))) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 1 1) * [misc]approximate: Taking taylor expansion of (pow (* (* n PI) 2) (/ 1 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* n PI) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (* n PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* n PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* n PI) 2) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [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 (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (* n PI) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (* n PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (* n PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* n PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* n PI) 2) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [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 (* 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 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI))) 2) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow (* 2 PI) 3))) (+ (* -3 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))) 6) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ 0 (pow (* 2 PI) 4))) (+ (* 12 (/ 0 (pow (* 2 PI) 3))) (+ (* -3 (/ 0 (pow (* 2 PI) 2))) (+ (* -4 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))))) 24) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ 0 (pow (* 2 PI) 5))) (+ (* -60 (/ 0 (pow (* 2 PI) 4))) (+ (* 30 (/ 0 (pow (* 2 PI) 3))) (+ (* 20 (/ 0 (pow (* 2 PI) 3))) (+ (* -10 (/ 0 (pow (* 2 PI) 2))) (+ (* -5 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))))))) 120) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ 0 (pow (* 2 PI) 6))) (+ (* 360 (/ 0 (pow (* 2 PI) 5))) (+ (* -270 (/ 0 (pow (* 2 PI) 4))) (+ (* -120 (/ 0 (pow (* 2 PI) 4))) (+ (* 30 (/ 0 (pow (* 2 PI) 3))) (+ (* 120 (/ 0 (pow (* 2 PI) 3))) (+ (* 30 (/ 0 (pow (* 2 PI) 3))) (+ (* -10 (/ 0 (pow (* 2 PI) 2))) (+ (* -15 (/ 0 (pow (* 2 PI) 2))) (+ (* -6 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))))))))))) 720) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]approximate: Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [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 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 n) PI) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 n) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 n) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 n) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 n) PI) 2) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [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 (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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI))) 2) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow (* 2 PI) 3))) (+ (* -3 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))) 6) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ 0 (pow (* 2 PI) 4))) (+ (* 12 (/ 0 (pow (* 2 PI) 3))) (+ (* -3 (/ 0 (pow (* 2 PI) 2))) (+ (* -4 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))))) 24) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ 0 (pow (* 2 PI) 5))) (+ (* -60 (/ 0 (pow (* 2 PI) 4))) (+ (* 30 (/ 0 (pow (* 2 PI) 3))) (+ (* 20 (/ 0 (pow (* 2 PI) 3))) (+ (* -10 (/ 0 (pow (* 2 PI) 2))) (+ (* -5 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))))))) 120) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ 0 (pow (* 2 PI) 6))) (+ (* 360 (/ 0 (pow (* 2 PI) 5))) (+ (* -270 (/ 0 (pow (* 2 PI) 4))) (+ (* -120 (/ 0 (pow (* 2 PI) 4))) (+ (* 30 (/ 0 (pow (* 2 PI) 3))) (+ (* 120 (/ 0 (pow (* 2 PI) 3))) (+ (* 30 (/ 0 (pow (* 2 PI) 3))) (+ (* -10 (/ 0 (pow (* 2 PI) 2))) (+ (* -15 (/ 0 (pow (* 2 PI) 2))) (+ (* -6 (/ 0 (pow (* 2 PI) 2))) (/ 0 (* 2 PI)))))))))))) 720) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) * [misc]approximate: Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n * [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 into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (* 2 (* -1 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (* (/ 1 (- n)) PI) 2) (/ 1 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2)))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 2) (log (* (* (/ 1 (- n)) PI) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* (/ 1 (- n)) PI) 2)) in n * [misc]taylor: Taking taylor expansion of (* (* (/ 1 (- n)) PI) 2) in n * [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 into -1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (* 2 (* -1 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [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 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* -2 PI) 2))) (/ 0 (* -2 PI))) 2) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow (* -2 PI) 3))) (+ (* -3 (/ 0 (pow (* -2 PI) 2))) (/ 0 (* -2 PI)))) 6) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ 0 (pow (* -2 PI) 4))) (+ (* 12 (/ 0 (pow (* -2 PI) 3))) (+ (* -3 (/ 0 (pow (* -2 PI) 2))) (+ (* -4 (/ 0 (pow (* -2 PI) 2))) (/ 0 (* -2 PI)))))) 24) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ 0 (pow (* -2 PI) 5))) (+ (* -60 (/ 0 (pow (* -2 PI) 4))) (+ (* 30 (/ 0 (pow (* -2 PI) 3))) (+ (* 20 (/ 0 (pow (* -2 PI) 3))) (+ (* -10 (/ 0 (pow (* -2 PI) 2))) (+ (* -5 (/ 0 (pow (* -2 PI) 2))) (/ 0 (* -2 PI)))))))) 120) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ 0 (pow (* -2 PI) 6))) (+ (* 360 (/ 0 (pow (* -2 PI) 5))) (+ (* -270 (/ 0 (pow (* -2 PI) 4))) (+ (* -120 (/ 0 (pow (* -2 PI) 4))) (+ (* 30 (/ 0 (pow (* -2 PI) 3))) (+ (* 120 (/ 0 (pow (* -2 PI) 3))) (+ (* 30 (/ 0 (pow (* -2 PI) 3))) (+ (* -10 (/ 0 (pow (* -2 PI) 2))) (+ (* -15 (/ 0 (pow (* -2 PI) 2))) (+ (* -6 (/ 0 (pow (* -2 PI) 2))) (/ 0 (* -2 PI)))))))))))) 720) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (expm1 (* PI n)) * [exit]simplify: Simplified to (expm1 (* PI n)) * * * * [misc]progress: [ 2 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (log1p (* PI n)) * [exit]simplify: Simplified to (log1p (* PI n)) * * * * [misc]progress: [ 3 / 157 ] simplifiying candidate # * * * * [misc]progress: [ 4 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (8 enodes) * * [misc]simplify: iters left: 1 (9 enodes) * [exit]simplify: Simplified to (log (* PI n)) * [exit]simplify: Simplified to (log (* PI n)) * * * * [misc]progress: [ 5 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (exp (* PI n)) * [exit]simplify: Simplified to (exp (* PI n)) * * * * [misc]progress: [ 6 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n PI)) (cbrt (* n PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (6 enodes) * [exit]simplify: Simplified to (* (cbrt (* PI n)) (cbrt (* PI n))) * [exit]simplify: Simplified to (* (cbrt (* PI n)) (cbrt (* PI n))) * [enter]simplify: Simplifying (cbrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (cbrt (* PI n)) * [exit]simplify: Simplified to (cbrt (* PI n)) * * * * [misc]progress: [ 7 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n PI) (* n PI)) (* n PI)) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (pow (* PI n) 3) * [exit]simplify: Simplified to (pow (* PI n) 3) * * * * [misc]progress: [ 8 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * [enter]simplify: Simplifying (sqrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * * * * [misc]progress: [ 9 / 157 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 157 ] simplifiying candidate # * * * * [misc]progress: [ 11 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (expm1 (* PI n)) * [exit]simplify: Simplified to (expm1 (* PI n)) * * * * [misc]progress: [ 12 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (log1p (* PI n)) * [exit]simplify: Simplified to (log1p (* PI n)) * * * * [misc]progress: [ 13 / 157 ] simplifiying candidate # * * * * [misc]progress: [ 14 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (8 enodes) * * [misc]simplify: iters left: 1 (9 enodes) * [exit]simplify: Simplified to (log (* PI n)) * [exit]simplify: Simplified to (log (* PI n)) * * * * [misc]progress: [ 15 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (exp (* PI n)) * [exit]simplify: Simplified to (exp (* PI n)) * * * * [misc]progress: [ 16 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n PI)) (cbrt (* n PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (6 enodes) * [exit]simplify: Simplified to (* (cbrt (* PI n)) (cbrt (* PI n))) * [exit]simplify: Simplified to (* (cbrt (* PI n)) (cbrt (* PI n))) * [enter]simplify: Simplifying (cbrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (cbrt (* PI n)) * [exit]simplify: Simplified to (cbrt (* PI n)) * * * * [misc]progress: [ 17 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n PI) (* n PI)) (* n PI)) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (pow (* PI n) 3) * [exit]simplify: Simplified to (pow (* PI n) 3) * * * * [misc]progress: [ 18 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * [enter]simplify: Simplifying (sqrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * * * * [misc]progress: [ 19 / 157 ] simplifiying candidate # * * * * [misc]progress: [ 20 / 157 ] simplifiying candidate # * * * * [misc]progress: [ 21 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (expm1 (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) * [exit]simplify: Simplified to (expm1 (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 22 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (log1p (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) * [exit]simplify: Simplified to (log1p (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 23 / 157 ] simplifiying candidate # * * * * [misc]progress: [ 24 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (303 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 25 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (303 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 26 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (log (pow (* (* n PI) 2) (/ k 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 27 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (303 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 28 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (303 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 29 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (* (log (* (* n PI) 2)) (/ 1 2)) (log (pow (* (* n PI) 2) (/ k 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (87 enodes) * * [misc]simplify: iters left: 3 (286 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 30 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (pow (* (* n PI) 2) (/ 1 2))) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (263 enodes) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 31 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (pow (* (* n PI) 2) (/ 1 2))) (* (log (* (* n PI) 2)) (/ k 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (90 enodes) * * [misc]simplify: iters left: 3 (263 enodes) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 32 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (- (- (log (pow (* (* n PI) 2) (/ 1 2))) (log (pow (* (* n PI) 2) (/ k 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (205 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 33 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (285 enodes) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 34 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (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 (55 enodes) * * [misc]simplify: iters left: 2 (103 enodes) * * [misc]simplify: iters left: 1 (295 enodes) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 35 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (exp (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) * [exit]simplify: Simplified to (exp (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 36 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (* (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ 1 2))) (* (* (pow (* (* n PI) 2) (/ k 2)) (pow (* (* n PI) 2) (/ k 2))) (pow (* (* n PI) 2) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (113 enodes) * * [misc]simplify: iters left: 3 (389 enodes) * [exit]simplify: Simplified to (/ (* (/ (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) k) (/ (pow (* (* PI n) 2) (/ k 2)) (pow (* (* PI n) 2) (/ 1 2))))) * [exit]simplify: Simplified to (/ (* (/ (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) k) (/ (pow (* (* PI n) 2) (/ k 2)) (pow (* (* PI n) 2) (/ 1 2))))) * * * * [misc]progress: [ 37 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (96 enodes) * * [misc]simplify: iters left: 3 (267 enodes) * [exit]simplify: Simplified to (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (sqrt k) k)) (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (sqrt k) k)) (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))) * * * * [misc]progress: [ 38 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))) (cbrt (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) (cbrt (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) (cbrt (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (cbrt (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 39 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))) (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (201 enodes) * [exit]simplify: Simplified to (/ (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k))) (/ (* k (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))) * [exit]simplify: Simplified to (/ (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k))) (/ (* k (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))))) * * * * [misc]progress: [ 40 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) * [enter]simplify: Simplifying (sqrt (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) * * * * [misc]progress: [ 41 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (- (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) * * [misc]simplify: iters left: 6 (13 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 (- (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (- (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) * [enter]simplify: Simplifying (- (sqrt k)) * * [misc]simplify: iters left: 3 (3 enodes) * [exit]simplify: Simplified to (- (sqrt k)) * [exit]simplify: Simplified to (- (sqrt k)) * * * * [misc]progress: [ 42 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ 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 (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k))) * * [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 (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 43 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (* (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))) * [exit]simplify: Simplified to (/ (* (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))) * [enter]simplify: Simplifying (/ (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) * * [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 (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 44 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (52 enodes) * [exit]simplify: Simplified to (* (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))))) * [exit]simplify: Simplified to (* (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))))) * [enter]simplify: Simplifying (/ (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (sqrt k)) * * [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 (28 enodes) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (cbrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 45 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [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 (32 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k))) * * [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 (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))) * * * * [misc]progress: [ 46 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) * * [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 (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) * * [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 (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt (sqrt k))) * * * * [misc]progress: [ 47 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) * [enter]simplify: Simplifying (/ (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2)))) (sqrt k)) * * [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 (28 enodes) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2)))) (sqrt k)) * * * * [misc]progress: [ 48 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (pow (* n PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [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 (33 enodes) * * [misc]simplify: iters left: 2 (34 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (pow (* PI n) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (pow (* PI n) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))) (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 2 (/ 1 2)) (pow 2 (/ k 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 49 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (pow (* n PI) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (pow (* PI n) (/ k 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (pow (* PI n) (/ k 2))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))) (sqrt (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 2 (/ 1 2)) (pow 2 (/ k 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 50 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (pow (* n PI) (/ k 2))) 1) * * [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 (24 enodes) * * [misc]simplify: iters left: 2 (25 enodes) * [exit]simplify: Simplified to (/ (pow (* PI n) (/ 1 2)) (pow (* PI n) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (* PI n) (/ 1 2)) (pow (* PI n) (/ k 2))) * [enter]simplify: Simplifying (/ (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2))) (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 (/ (pow 2 (/ 1 2)) (* (sqrt k) (pow 2 (/ k 2)))) * [exit]simplify: Simplified to (/ (pow 2 (/ 1 2)) (* (sqrt k) (pow 2 (/ k 2)))) * * * * [misc]progress: [ 51 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 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 (/ (/ (/ (/ (pow (* PI n) (/ 1 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (/ (/ (pow (* PI n) (/ 1 2)) (cbrt (sqrt k))) (cbrt (sqrt k))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow 2 (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 52 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (sqrt (sqrt k))) (* (cbrt (pow (* (* 2 PI) n) (/ k 2))) (cbrt (pow (* (* 2 PI) n) (/ k 2))))) * [exit]simplify: Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (sqrt (sqrt k))) (* (cbrt (pow (* (* 2 PI) n) (/ k 2))) (cbrt (pow (* (* 2 PI) n) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (pow 2 (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 53 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (cbrt (pow (* PI (* 2 n)) (/ k 2)))) (cbrt (pow (* PI (* 2 n)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (cbrt (pow (* PI (* 2 n)) (/ k 2)))) (cbrt (pow (* PI (* 2 n)) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow 2 (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 54 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* 2 PI) n) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* 2 PI) n) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow 2 (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 55 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* PI n) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow 2 (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 56 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n PI) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * [exit]simplify: Simplified to (/ (pow (* PI n) (/ 1 2)) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (* PI n) (/ 1 2)) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow 2 (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 57 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n PI) (/ 1 2)) 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [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 (37 enodes) * [exit]simplify: Simplified to (/ (pow (* PI n) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow (* PI n) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow 2 (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (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 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (cbrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (cbrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 58 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n PI) (/ 1 2)) 1) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * [exit]simplify: Simplified to (/ (pow (* PI n) (/ 1 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* PI n) (/ 1 2)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (pow 2 (/ 1 2)) (pow (* (* n PI) 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 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 59 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* n PI) (/ 1 2)) 1) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (12 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * [exit]simplify: Simplified to (pow (* PI n) (/ 1 2)) * [exit]simplify: Simplified to (pow (* PI n) (/ 1 2)) * [enter]simplify: Simplifying (/ (/ (pow 2 (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (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 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow 2 (/ 1 2)) (sqrt k)) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 60 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (pow (* n PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (50 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (144 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) (* (pow (* PI n) (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) (* (pow (* PI n) (/ k 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow 2 (/ k 2)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow 2 (/ k 2)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 61 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (pow (* n PI) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (56 enodes) * * [misc]simplify: iters left: 2 (64 enodes) * * [misc]simplify: iters left: 1 (67 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) (* (pow (* PI n) (/ k 2)) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) (* (pow (* PI n) (/ k 2)) (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow 2 (/ k 2)) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow 2 (/ k 2)) (sqrt (sqrt k)))) * * * * [misc]progress: [ 62 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (pow (* n PI) (/ k 2))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (165 enodes) * * [misc]simplify: iters left: 1 (244 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* PI n) (/ k 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* PI n) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt k) (pow 2 (/ k 2)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt k) (pow 2 (/ k 2)))) * * * * [misc]progress: [ 63 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (143 enodes) * * [misc]simplify: iters left: 2 (250 enodes) * * [misc]simplify: iters left: 1 (309 enodes) * [exit]simplify: Simplified to (* (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))) (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k))) (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (sqrt k)))) * * * * [misc]progress: [ 64 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (126 enodes) * * [misc]simplify: iters left: 1 (144 enodes) * [exit]simplify: Simplified to (/ (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k)))) * * * * [misc]progress: [ 65 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (95 enodes) * * [misc]simplify: iters left: 2 (303 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 66 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (51 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (126 enodes) * * [misc]simplify: iters left: 1 (147 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2))))) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (sqrt k)))) * * * * [misc]progress: [ 67 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) * * [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 (57 enodes) * * [misc]simplify: iters left: 2 (65 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2))))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k)))) * * * * [misc]progress: [ 68 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) (sqrt (pow (* (* n PI) 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 (65 enodes) * * [misc]simplify: iters left: 2 (156 enodes) * * [misc]simplify: iters left: 1 (273 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 69 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) 1) (* (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 (56 enodes) * * [misc]simplify: iters left: 3 (103 enodes) * * [misc]simplify: iters left: 2 (244 enodes) * * [misc]simplify: iters left: 1 (272 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow (* (* PI n) 2) (/ k 2)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow (* (* PI n) 2) (/ k 2)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 70 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) 1) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (133 enodes) * * [misc]simplify: iters left: 1 (136 enodes) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow (* (* PI n) 2) (/ k 2)) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow (* (* PI n) 2) (/ k 2)) (sqrt (sqrt k)))) * * * * [misc]progress: [ 71 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) 1) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) * [enter]simplify: Simplifying (/ (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 72 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* n PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (* (pow (* PI n) (/ k 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (* (pow (* PI n) (/ k 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow 2 (/ k 2)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow 2 (/ k 2)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 73 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* n PI) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow (* PI n) (/ k 2)) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow (* PI n) (/ k 2)) (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow 2 (/ k 2)) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow 2 (/ k 2)) (sqrt (sqrt k)))) * * * * [misc]progress: [ 74 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* n PI) (/ k 2))) 1) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* PI n) (/ k 2))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (pow (* PI n) (/ k 2))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow 2 (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt k) (pow 2 (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt k) (pow 2 (/ k 2)))) * * * * [misc]progress: [ 75 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (47 enodes) * * [misc]simplify: iters left: 3 (62 enodes) * * [misc]simplify: iters left: 2 (74 enodes) * * [misc]simplify: iters left: 1 (77 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (sqrt k)))) * * * * [misc]progress: [ 76 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (pow (* (* PI n) 2) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k)))) * * * * [misc]progress: [ 77 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 2) (/ k 2))))) 1) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (37 enodes) * * [misc]simplify: iters left: 3 (43 enodes) * * [misc]simplify: iters left: 2 (48 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 78 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (46 enodes) * * [misc]simplify: iters left: 2 (47 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (cbrt (sqrt k)))) * * * * [misc]progress: [ 79 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt (pow (* (* PI n) 2) (/ k 2))) (sqrt (sqrt k)))) * * * * [misc]progress: [ 80 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) 1) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 81 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) 1) (* (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 (39 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow (* (* PI n) 2) (/ k 2)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow (* (* PI n) 2) (/ k 2)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 82 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) 1) (sqrt (sqrt k))) * * [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 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow (* (* PI n) 2) (/ k 2)) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (pow (* (* PI n) 2) (/ k 2)) (sqrt (sqrt k)))) * * * * [misc]progress: [ 83 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) 1) 1) * * [misc]simplify: iters left: 6 (11 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 (pow (* (* PI n) 2) (/ 1 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2))) * [enter]simplify: Simplifying (/ (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (* (sqrt k) (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 84 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow (* n PI) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [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 (31 enodes) * * [misc]simplify: iters left: 2 (32 enodes) * [exit]simplify: Simplified to (/ (/ 1 (pow (* PI n) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (pow (* PI n) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow 2 (/ k 2))) (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 (33 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (* (cbrt (sqrt k)) (pow 2 (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (* (cbrt (sqrt k)) (pow 2 (/ k 2)))) * * * * [misc]progress: [ 85 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow (* n PI) (/ k 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * [exit]simplify: Simplified to (/ (/ 1 (pow (* PI n) (/ k 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ 1 (pow (* PI n) (/ k 2))) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow 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 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow 2 (/ k 2)))) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (* (sqrt (sqrt k)) (pow 2 (/ k 2)))) * * * * [misc]progress: [ 86 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (pow (* n 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 (/ 1 (pow (* PI n) (/ k 2))) * [exit]simplify: Simplified to (/ 1 (pow (* PI n) (/ k 2))) * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow 2 (/ k 2))) (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 (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow 2 (/ k 2)) (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (* (pow 2 (/ k 2)) (sqrt k))) * * * * [misc]progress: [ 87 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 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 (58 enodes) * * [misc]simplify: iters left: 2 (70 enodes) * * [misc]simplify: iters left: 1 (73 enodes) * [exit]simplify: Simplified to (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (pow (* PI (* 2 n)) (/ k 2)))) (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (pow (* PI (* 2 n)) (/ k 2)))) (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (cbrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 88 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 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 (cbrt (pow (* PI (* 2 n)) (/ k 2)))) (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (pow (* PI (* 2 n)) (/ k 2)))) (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (sqrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 89 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (* (cbrt (pow (* (* n PI) 2) (/ k 2))) (cbrt (pow (* (* n PI) 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 (* (* 2 n) PI) (/ k 2))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))) * [exit]simplify: Simplified to (/ 1 (* (cbrt (pow (* (* 2 n) PI) (/ k 2))) (cbrt (pow (* (* 2 n) PI) (/ k 2))))) * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (cbrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (cbrt (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 90 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (pow (* (* n PI) 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 n) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (cbrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 91 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (pow (* (* n PI) 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 (* PI (* 2 n)) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (sqrt (pow (* PI (* 2 n)) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 92 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 (sqrt (pow (* (* n PI) 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 (* (* 2 n) PI) (/ k 2)))) * [exit]simplify: Simplified to (/ 1 (sqrt (pow (* (* 2 n) PI) (/ k 2)))) * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (sqrt (pow (* (* n PI) 2) (/ k 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) (sqrt (pow (* (* PI n) 2) (/ k 2)))) * * * * [misc]progress: [ 93 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (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 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (cbrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (cbrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 94 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (6 enodes) * * [misc]simplify: iters left: 3 (8 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 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 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 95 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ 1 1) 1) * * [misc]simplify: iters left: 4 (3 enodes) * * [misc]simplify: iters left: 3 (5 enodes) * [exit]simplify: Simplified to 1 * [exit]simplify: Simplified to 1 * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (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 (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 96 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (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 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (cbrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (cbrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 97 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 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 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 98 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [exit]simplify: Simplified to 1 * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (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 (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 99 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (/ 1 (pow (* (* n PI) 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 (* (* 2 PI) n) (/ k 2))) * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ k 2))) * * * * [misc]progress: [ 100 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (/ 1 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 (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (/ 1 (pow (* (* n PI) 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 (* (* 2 PI) n) (/ k 2))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ k 2))) * * * * [misc]progress: [ 101 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* (* n PI) 2) (/ 1 2)) 1) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ 1 2)) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ 1 2)) * [enter]simplify: Simplifying (/ (/ 1 (pow (* (* n PI) 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 (* (* 2 n) PI) (/ k 2))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt k)) (pow (* (* 2 n) PI) (/ k 2))) * * * * [misc]progress: [ 102 / 157 ] simplifiying candidate # * * * * [misc]progress: [ 103 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 104 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 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 (35 enodes) * [exit]simplify: Simplified to (/ (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) (pow (* PI (* 2 n)) (/ 1 2))) * [exit]simplify: Simplified to (/ (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) (pow (* PI (* 2 n)) (/ 1 2))) * * * * [misc]progress: [ 105 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (45 enodes) * * [misc]simplify: iters left: 2 (46 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 106 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 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 (32 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2))) * [exit]simplify: Simplified to (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt (sqrt k))) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 107 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) 1) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 108 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (cbrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 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 (/ (sqrt k) (cbrt (/ (pow (* (* PI 2) n) (/ 1 2)) (pow (* (* PI 2) n) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (/ (pow (* (* PI 2) n) (/ 1 2)) (pow (* (* PI 2) n) (/ k 2))))) * * * * [misc]progress: [ 109 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (sqrt (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 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 (/ (sqrt k) (sqrt (/ (pow (* (* PI 2) n) (/ 1 2)) (pow (* (* PI 2) n) (/ k 2))))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (/ (pow (* (* PI 2) n) (/ 1 2)) (pow (* (* PI 2) n) (/ k 2))))) * * * * [misc]progress: [ 110 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow 2 (/ 1 2)) (pow 2 (/ k 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (14 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow 2 (/ 1 2))) (pow 2 (/ k 2))) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow 2 (/ 1 2))) (pow 2 (/ k 2))) * * * * [misc]progress: [ 111 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow 2 (/ 1 2)) (cbrt (pow (* (* n PI) 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 (35 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (/ (sqrt k) (pow 2 (/ 1 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* n (* PI 2)) (/ k 2))) (/ (sqrt k) (pow 2 (/ 1 2)))) * * * * [misc]progress: [ 112 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow 2 (/ 1 2)) (sqrt (pow (* (* n PI) 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 (35 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* n (* PI 2)) (/ k 2))) (/ (sqrt k) (pow 2 (/ 1 2)))) * [exit]simplify: Simplified to (* (sqrt (pow (* n (* PI 2)) (/ k 2))) (/ (sqrt k) (pow 2 (/ 1 2)))) * * * * [misc]progress: [ 113 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow 2 (/ 1 2)) (pow (* (* n PI) 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 (34 enodes) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow 2 (/ 1 2))) (pow (* PI (* n 2)) (/ k 2))) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow 2 (/ 1 2))) (pow (* PI (* n 2)) (/ k 2))) * * * * [misc]progress: [ 114 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow 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 (36 enodes) * [exit]simplify: Simplified to (/ (* (pow 2 (/ k 2)) (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (pow 2 (/ k 2)) (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ 1 2)))) * * * * [misc]progress: [ 115 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 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 (37 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (/ (sqrt k) (cbrt (pow (* PI (* 2 n)) (/ 1 2))))) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (/ (sqrt k) (cbrt (pow (* PI (* 2 n)) (/ 1 2))))) * * * * [misc]progress: [ 116 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 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 (37 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* PI (* 2 n)) (/ k 2))) (/ (sqrt k) (cbrt (pow (* PI (* 2 n)) (/ 1 2))))) * [exit]simplify: Simplified to (* (sqrt (pow (* PI (* 2 n)) (/ k 2))) (/ (sqrt k) (cbrt (pow (* PI (* 2 n)) (/ 1 2))))) * * * * [misc]progress: [ 117 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (cbrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 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 (36 enodes) * [exit]simplify: Simplified to (/ (* (pow (* (* PI 2) n) (/ k 2)) (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (pow (* (* PI 2) n) (/ k 2)) (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ 1 2)))) * * * * [misc]progress: [ 118 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow 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 (36 enodes) * [exit]simplify: Simplified to (/ (* (pow 2 (/ k 2)) (sqrt k)) (sqrt (pow (* (* PI 2) n) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (pow 2 (/ k 2)) (sqrt k)) (sqrt (pow (* (* PI 2) n) (/ 1 2)))) * * * * [misc]progress: [ 119 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 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 (37 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (/ (sqrt k) (sqrt (pow (* PI (* 2 n)) (/ 1 2))))) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (* 2 n)) (/ k 2))) (/ (sqrt k) (sqrt (pow (* PI (* 2 n)) (/ 1 2))))) * * * * [misc]progress: [ 120 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (sqrt (pow (* (* n PI) 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 (37 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* PI (* 2 n)) (/ k 2))) (/ (sqrt k) (sqrt (pow (* PI (* 2 n)) (/ 1 2))))) * [exit]simplify: Simplified to (* (sqrt (pow (* PI (* 2 n)) (/ k 2))) (/ (sqrt k) (sqrt (pow (* PI (* 2 n)) (/ 1 2))))) * * * * [misc]progress: [ 121 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (sqrt (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 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 (36 enodes) * [exit]simplify: Simplified to (/ (* (pow (* (* PI 2) n) (/ k 2)) (sqrt k)) (sqrt (pow (* (* PI 2) n) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (pow (* (* PI 2) n) (/ k 2)) (sqrt k)) (sqrt (pow (* (* PI 2) n) (/ 1 2)))) * * * * [misc]progress: [ 122 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (pow 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 (35 enodes) * [exit]simplify: Simplified to (/ (* (pow 2 (/ k 2)) (sqrt k)) (pow (* PI (* 2 n)) (/ 1 2))) * [exit]simplify: Simplified to (/ (* (pow 2 (/ k 2)) (sqrt k)) (pow (* PI (* 2 n)) (/ 1 2))) * * * * [misc]progress: [ 123 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (cbrt (pow (* (* n PI) 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 (36 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (/ k 2))) (/ (sqrt k) (pow (* (* PI 2) n) (/ 1 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (/ k 2))) (/ (sqrt k) (pow (* (* PI 2) n) (/ 1 2)))) * * * * [misc]progress: [ 124 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (sqrt (pow (* (* n PI) 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 (36 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* (* PI 2) n) (/ k 2))) (/ (sqrt k) (pow (* (* PI 2) n) (/ 1 2)))) * [exit]simplify: Simplified to (* (sqrt (pow (* (* PI 2) n) (/ k 2))) (/ (sqrt k) (pow (* (* PI 2) n) (/ 1 2)))) * * * * [misc]progress: [ 125 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 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 (35 enodes) * [exit]simplify: Simplified to (/ (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) (pow (* PI (* 2 n)) (/ 1 2))) * [exit]simplify: Simplified to (/ (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) (pow (* PI (* 2 n)) (/ 1 2))) * * * * [misc]progress: [ 126 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 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 (35 enodes) * [exit]simplify: Simplified to (/ (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) (pow (* PI (* 2 n)) (/ 1 2))) * [exit]simplify: Simplified to (/ (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) (pow (* PI (* 2 n)) (/ 1 2))) * * * * [misc]progress: [ 127 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (/ 1 (pow (* (* n PI) 2) (/ k 2)))) * * [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 (40 enodes) * * [misc]simplify: iters left: 2 (42 enodes) * * [misc]simplify: iters left: 1 (47 enodes) * [exit]simplify: Simplified to (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))) * [exit]simplify: Simplified to (* (sqrt k) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 128 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt k) (pow (* (* n PI) 2) (/ k 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (* (pow (* n (* PI 2)) (/ k 2)) (sqrt k)) * [exit]simplify: Simplified to (* (pow (* n (* PI 2)) (/ k 2)) (sqrt k)) * * * * [misc]progress: [ 129 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (pow (* (* n PI) 2) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (expm1 (pow (* (* PI n) 2) (/ 1 2))) * [exit]simplify: Simplified to (expm1 (pow (* (* PI n) 2) (/ 1 2))) * * * * [misc]progress: [ 130 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (pow (* (* n PI) 2) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (log1p (pow (* (* PI n) 2) (/ 1 2))) * [exit]simplify: Simplified to (log1p (pow (* (* PI n) 2) (/ 1 2))) * * * * [misc]progress: [ 131 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* n PI) 2)) (/ 1 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (180 enodes) * * [misc]simplify: iters left: 1 (390 enodes) * [exit]simplify: Simplified to (fma (/ 1 2) (log (* PI n)) (/ (log 2) 2)) * [exit]simplify: Simplified to (fma (/ 1 2) (log (* PI n)) (/ (log 2) 2)) * * * * [misc]progress: [ 132 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* n PI) 2)) (/ 1 2)) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (92 enodes) * * [misc]simplify: iters left: 2 (180 enodes) * * [misc]simplify: iters left: 1 (390 enodes) * [exit]simplify: Simplified to (fma (/ 1 2) (log (* PI n)) (/ (log 2) 2)) * [exit]simplify: Simplified to (fma (/ 1 2) (log (* PI n)) (/ (log 2) 2)) * * * * [misc]progress: [ 133 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ 1 2)) * * [misc]simplify: iters left: 4 (4 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * [exit]simplify: Simplified to (/ 1 2) * [exit]simplify: Simplified to (/ 1 2) * * * * [misc]progress: [ 134 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* n PI) 2) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) * * * * [misc]progress: [ 135 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* n PI) 2) (sqrt (/ 1 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) (sqrt (/ 1 2))) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (sqrt (/ 1 2))) * * * * [misc]progress: [ 136 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* n PI) 2) 1) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * [exit]simplify: Simplified to (* (* PI n) 2) * [exit]simplify: Simplified to (* (* PI n) 2) * * * * [misc]progress: [ 137 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* n PI) 2) 1) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * [exit]simplify: Simplified to (* (* PI n) 2) * [exit]simplify: Simplified to (* (* PI n) 2) * * * * [misc]progress: [ 138 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n PI) (/ 1 2)) * * [misc]simplify: iters left: 3 (7 enodes) * * [misc]simplify: iters left: 2 (10 enodes) * [exit]simplify: Simplified to (pow (* PI n) (/ 1 2)) * [exit]simplify: Simplified to (pow (* PI n) (/ 1 2)) * [enter]simplify: Simplifying (pow 2 (/ 1 2)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (pow 2 (/ 1 2)) * [exit]simplify: Simplified to (pow 2 (/ 1 2)) * * * * [misc]progress: [ 139 / 157 ] simplifiying candidate # * * * * [misc]progress: [ 140 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (* (* n PI) 2) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (33 enodes) * * [misc]simplify: iters left: 3 (72 enodes) * * [misc]simplify: iters left: 2 (182 enodes) * * [misc]simplify: iters left: 1 (442 enodes) * [exit]simplify: Simplified to (fma (/ 1 2) (log (* 2 PI)) (/ (log n) 2)) * [exit]simplify: Simplified to (fma (/ 1 2) (log (* 2 PI)) (/ (log n) 2)) * * * * [misc]progress: [ 141 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (* (* n PI) 2) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (exp (pow (* (* PI n) 2) (/ 1 2))) * [exit]simplify: Simplified to (exp (pow (* (* PI n) 2) (/ 1 2))) * * * * [misc]progress: [ 142 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* (* n PI) 2) (/ 1 2))) (cbrt (pow (* (* n PI) 2) (/ 1 2)))) * * [misc]simplify: iters left: 6 (10 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 (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) * [enter]simplify: Simplifying (cbrt (pow (* (* n PI) 2) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (cbrt (pow (* (* PI n) 2) (/ 1 2))) * [exit]simplify: Simplified to (cbrt (pow (* (* PI n) 2) (/ 1 2))) * * * * [misc]progress: [ 143 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ 1 2))) (pow (* (* n PI) 2) (/ 1 2))) * * [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 (pow (pow (* (* PI n) 2) (/ 1 2)) 3) * [exit]simplify: Simplified to (pow (pow (* (* PI n) 2) (/ 1 2)) 3) * * * * [misc]progress: [ 144 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* (* n PI) 2) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2))) * [enter]simplify: Simplifying (sqrt (pow (* (* n PI) 2) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (/ 1 2))) * * * * [misc]progress: [ 145 / 157 ] simplifiying candidate # * * * * [misc]progress: [ 146 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (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 (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 147 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (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 (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 148 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (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 (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 149 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (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 (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 150 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (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 (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 151 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* n PI) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (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 (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 152 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* k (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2)))) (- (+ (* +nan.0 (* k (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI))))) (- (+ (* +nan.0 (* (pow k 2) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))) (- (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))))))))))))))))))))) * * * * [misc]progress: [ 153 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (+ (log (/ 1 n)) (log (* 2 PI))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (+ (log (/ 1 n)) (log (* 2 PI))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (+ (log (/ 1 n)) (log (* 2 PI))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))))))))))) * * * * [misc]progress: [ 154 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (+ (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* -1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* 1/2 (+ (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* -1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (+ (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* -1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 3))))))))) * * * * [misc]progress: [ 155 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (67 enodes) * * [misc]simplify: iters left: 3 (118 enodes) * * [misc]simplify: iters left: 2 (195 enodes) * * [misc]simplify: iters left: 1 (308 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (* PI 2)) (/ (sqrt n) (sqrt k))) (pow (* n (* PI 2)) (/ k 2))) * * * * [misc]progress: [ 156 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (65 enodes) * * [misc]simplify: iters left: 3 (108 enodes) * * [misc]simplify: iters left: 2 (236 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (* PI 2)) (/ (sqrt n) (sqrt k))) (pow (* (* PI 2) n) (/ k 2))) * * * * [misc]progress: [ 157 / 157 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (114 enodes) * * [misc]simplify: iters left: 2 (276 enodes) * [exit]simplify: Simplified to (/ (/ (sqrt (* PI -2)) (pow (/ -1 n) 1/2)) (* (pow (* (* n 2) PI) (/ k 2)) (sqrt k))) * * * [misc]progress: adding candidates to table * * [misc]progress: iteration 3 / 4 * * * [misc]progress: picking best candidate * * * * [misc]pick: Picked # * * * [misc]progress: localizing error * * * [misc]progress: generating rewritten candidates * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 1 1 1 1) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 1 2 1 1) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1 1 1 1 2 1) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 1 1 1 1 1 1) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1 1 1 1) * [misc]approximate: Taking taylor expansion of (* (sqrt (* n PI)) (sqrt (* n PI))) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* n PI)) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ PI 0) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ PI 0) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (* (sqrt (* n PI)) (sqrt (* n PI))) in n * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ PI 0) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ PI 0) into (* +nan.0 PI) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (pow (* +nan.0 PI) 2) 0) into (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (pow (* +nan.0 PI) 2) 0) into (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) * [misc]backup-simplify: Simplify (* (* +nan.0 PI) (* +nan.0 PI)) into (* +nan.0 (pow PI 2)) * [misc]backup-simplify: Simplify (* +nan.0 (pow PI 2)) into (* +nan.0 (pow PI 2)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (* 2 (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 2))))) 0) into (* +nan.0 (* (pow +nan.0 2) (pow PI 3))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (* 2 (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 2))))) 0) into (* +nan.0 (* (pow +nan.0 2) (pow PI 3))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 2)))) (* (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) (* +nan.0 PI))) into (- (* +nan.0 (pow PI 3))) * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI 3))) into (- (* +nan.0 (pow PI 3))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (pow (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) 2) (* 2 (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 3)))))) 0) into (* +nan.0 (pow PI 4)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (pow (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) 2) (* 2 (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 3)))))) 0) into (* +nan.0 (pow PI 4)) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 3)))) (+ (* (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) (* +nan.0 (* (pow +nan.0 2) (pow PI 2)))) (* (* +nan.0 (* (pow +nan.0 2) (pow PI 3))) (* +nan.0 PI)))) into (- (* +nan.0 (pow PI 4))) * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI 4))) into (- (* +nan.0 (pow PI 4))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (pow PI 4))) (pow n 4)) (+ (* (- (* +nan.0 (pow PI 3))) (pow n 3)) (* (* +nan.0 (pow PI 2)) (pow n 2)))) into (- (+ (* +nan.0 (* (pow n 4) (pow PI 4))) (- (+ (* +nan.0 (* (pow n 3) (pow PI 3))) (- (* +nan.0 (* (pow n 2) (pow PI 2)))))))) * [misc]approximate: Taking taylor expansion of (* (sqrt (* (/ 1 n) PI)) (sqrt (* (/ 1 n) PI))) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* (/ 1 n) PI)) (sqrt (* (/ 1 n) PI))) in n * [misc]taylor: Taking taylor expansion of (sqrt (* (/ 1 n) PI)) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ PI 0) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (sqrt (* (/ 1 n) PI)) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ PI 0) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (* (sqrt (* (/ 1 n) PI)) (sqrt (* (/ 1 n) PI))) in n * [misc]taylor: Taking taylor expansion of (sqrt (* (/ 1 n) PI)) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ PI 0) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (sqrt (* (/ 1 n) PI)) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ PI 0) into (* +nan.0 PI) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (pow (* +nan.0 PI) 2) 0) into (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (pow (* +nan.0 PI) 2) 0) into (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) * [misc]backup-simplify: Simplify (* (* +nan.0 PI) (* +nan.0 PI)) into (* +nan.0 (pow PI 2)) * [misc]backup-simplify: Simplify (* +nan.0 (pow PI 2)) into (* +nan.0 (pow PI 2)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (* 2 (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 2))))) 0) into (* +nan.0 (* (pow +nan.0 2) (pow PI 3))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (* 2 (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 2))))) 0) into (* +nan.0 (* (pow +nan.0 2) (pow PI 3))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 2)))) (* (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) (* +nan.0 PI))) into (- (* +nan.0 (pow PI 3))) * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI 3))) into (- (* +nan.0 (pow PI 3))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (pow (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) 2) (* 2 (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 3)))))) 0) into (* +nan.0 (pow PI 4)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (pow (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) 2) (* 2 (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 3)))))) 0) into (* +nan.0 (pow PI 4)) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 3)))) (+ (* (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) (* +nan.0 (* (pow +nan.0 2) (pow PI 2)))) (* (* +nan.0 (* (pow +nan.0 2) (pow PI 3))) (* +nan.0 PI)))) into (- (* +nan.0 (pow PI 4))) * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI 4))) into (- (* +nan.0 (pow PI 4))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (pow PI 4))) (pow (/ 1 n) 2)) (+ (* (- (* +nan.0 (pow PI 3))) (/ 1 n)) (* +nan.0 (pow PI 2)))) into (- (+ (* +nan.0 (pow PI 2)) (- (+ (* +nan.0 (/ (pow PI 4) (pow n 2))) (- (* +nan.0 (/ (pow PI 3) n))))))) * [misc]approximate: Taking taylor expansion of (* (sqrt (* (/ 1 (- n)) PI)) (sqrt (* (/ 1 (- n)) PI))) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* (/ 1 (- n)) PI)) (sqrt (* (/ 1 (- n)) PI))) in n * [misc]taylor: Taking taylor expansion of (sqrt (* (/ 1 (- n)) PI)) in n * [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 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 0 into 0 * [misc]backup-simplify: Simplify (/ (* -1 PI) 0) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (sqrt (* (/ 1 (- n)) PI)) in n * [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 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 0 into 0 * [misc]backup-simplify: Simplify (/ (* -1 PI) 0) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (* (sqrt (* (/ 1 (- n)) PI)) (sqrt (* (/ 1 (- n)) PI))) in n * [misc]taylor: Taking taylor expansion of (sqrt (* (/ 1 (- n)) PI)) in n * [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 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 0 into 0 * [misc]backup-simplify: Simplify (/ (* -1 PI) 0) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (sqrt (* (/ 1 (- n)) PI)) in n * [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 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 0 into 0 * [misc]backup-simplify: Simplify (/ (* -1 PI) 0) into (* +nan.0 PI) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (pow (* +nan.0 PI) 2) 0) into (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (pow (* +nan.0 PI) 2) 0) into (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) * [misc]backup-simplify: Simplify (* (* +nan.0 PI) (* +nan.0 PI)) into (* +nan.0 (pow PI 2)) * [misc]backup-simplify: Simplify (* +nan.0 (pow PI 2)) into (* +nan.0 (pow PI 2)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]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 0 into 0 * [misc]backup-simplify: Simplify (/ (* 2 (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 2))))) 0) into (* +nan.0 (* (pow +nan.0 2) (pow PI 3))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (* 2 (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 2))))) 0) into (* +nan.0 (* (pow +nan.0 2) (pow PI 3))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 2)))) (* (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) (* +nan.0 PI))) into (- (* +nan.0 (pow PI 3))) * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI 3))) into (- (* +nan.0 (pow PI 3))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (pow (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) 2) (* 2 (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 3)))))) 0) into (* +nan.0 (pow PI 4)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (pow (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) 2) (* 2 (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 3)))))) 0) into (* +nan.0 (pow PI 4)) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 PI) (* +nan.0 (* (pow +nan.0 2) (pow PI 3)))) (+ (* (* +nan.0 (* (pow +nan.0 2) (pow PI 2))) (* +nan.0 (* (pow +nan.0 2) (pow PI 2)))) (* (* +nan.0 (* (pow +nan.0 2) (pow PI 3))) (* +nan.0 PI)))) into (- (* +nan.0 (pow PI 4))) * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI 4))) into (- (* +nan.0 (pow PI 4))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (pow PI 4))) (pow (/ 1 (- n)) 2)) (+ (* (- (* +nan.0 (pow PI 3))) (/ 1 (- n))) (* +nan.0 (pow PI 2)))) into (- (+ (* +nan.0 (pow PI 2)) (- (+ (* +nan.0 (/ (pow PI 4) (pow n 2))) (- (* +nan.0 (/ (pow PI 3) n))))))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1 2 1 1) * [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 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 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 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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 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 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 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 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 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 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 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [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 0 into 0 * [misc]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 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 0 into 0 * [misc]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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1 1 1 1 2 1) * [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 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 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 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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 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 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 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 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 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 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 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [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 0 into 0 * [misc]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 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 0 into 0 * [misc]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 0 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 1 1 1 1 1 1) * [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 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 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 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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 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 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 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 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 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 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 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [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 0 into 0 * [misc]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 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 0 into 0 * [misc]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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* (sqrt (* n PI)) (sqrt (* n PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (expm1 (* PI n)) * [exit]simplify: Simplified to (expm1 (* PI n)) * * * * [misc]progress: [ 2 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* (sqrt (* n PI)) (sqrt (* n PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (log1p (* PI n)) * [exit]simplify: Simplified to (log1p (* PI n)) * * * * [misc]progress: [ 3 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (+ 1/2 1/2) * * [misc]simplify: iters left: 2 (2 enodes) * [exit]simplify: Simplified to (+ 1/2 1/2) * [exit]simplify: Simplified to (+ 1/2 1/2) * * * * [misc]progress: [ 4 / 70 ] 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 1) * [exit]simplify: Simplified to (+ 1 1) * * * * [misc]progress: [ 5 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* n PI) (* n PI)) * * [misc]simplify: iters left: 4 (4 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * * [misc]simplify: iters left: 2 (16 enodes) * * [misc]simplify: iters left: 1 (20 enodes) * [exit]simplify: Simplified to (* (* PI n) (* PI n)) * [exit]simplify: Simplified to (* (* PI n) (* PI n)) * * * * [misc]progress: [ 6 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (* n PI)) (sqrt (* n PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (6 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 7 / 70 ] simplifiying candidate # * * * * [misc]progress: [ 8 / 70 ] 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 1) * [exit]simplify: Simplified to (+ 1 1) * * * * [misc]progress: [ 9 / 70 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (sqrt (* n PI))) (log (sqrt (* n PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (7 enodes) * [exit]simplify: Simplified to (+ (log (sqrt (* PI n))) (log (sqrt (* PI n)))) * [exit]simplify: Simplified to (+ (log (sqrt (* PI n))) (log (sqrt (* PI n)))) * * * * [misc]progress: [ 11 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (sqrt (* n PI)) (sqrt (* n PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * [exit]simplify: Simplified to (log (* PI n)) * [exit]simplify: Simplified to (log (* PI n)) * * * * [misc]progress: [ 12 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (sqrt (* n PI)) (sqrt (* n PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * [exit]simplify: Simplified to (exp (* PI n)) * [exit]simplify: Simplified to (exp (* PI n)) * * * * [misc]progress: [ 13 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (sqrt (* n PI)) (sqrt (* n PI))) (sqrt (* n PI))) (* (* (sqrt (* n PI)) (sqrt (* n PI))) (sqrt (* n PI)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (69 enodes) * * [misc]simplify: iters left: 2 (153 enodes) * * [misc]simplify: iters left: 1 (228 enodes) * [exit]simplify: Simplified to (pow (* PI n) 3) * [exit]simplify: Simplified to (pow (* PI n) 3) * * * * [misc]progress: [ 14 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (sqrt (* n PI)) (sqrt (* n PI)))) (cbrt (* (sqrt (* n PI)) (sqrt (* n PI))))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (9 enodes) * [exit]simplify: Simplified to (* (cbrt (* PI n)) (cbrt (* PI n))) * [exit]simplify: Simplified to (* (cbrt (* PI n)) (cbrt (* PI n))) * [enter]simplify: Simplifying (cbrt (* (sqrt (* n PI)) (sqrt (* n PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (cbrt (* PI n)) * [exit]simplify: Simplified to (cbrt (* PI n)) * * * * [misc]progress: [ 15 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (sqrt (* n PI)) (sqrt (* n PI))) (* (sqrt (* n PI)) (sqrt (* n PI)))) (* (sqrt (* n PI)) (sqrt (* n PI)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (237 enodes) * * [misc]simplify: iters left: 1 (336 enodes) * [exit]simplify: Simplified to (pow (* PI n) 3) * [exit]simplify: Simplified to (pow (* PI n) 3) * * * * [misc]progress: [ 16 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* n PI) (* n PI)) * * [misc]simplify: iters left: 4 (4 enodes) * * [misc]simplify: iters left: 3 (9 enodes) * * [misc]simplify: iters left: 2 (16 enodes) * * [misc]simplify: iters left: 1 (20 enodes) * [exit]simplify: Simplified to (* (* PI n) (* PI n)) * [exit]simplify: Simplified to (* (* PI n) (* PI n)) * * * * [misc]progress: [ 17 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (sqrt (* n PI)) (sqrt (* n PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * [enter]simplify: Simplifying (sqrt (* (sqrt (* n PI)) (sqrt (* n PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (9 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * * * * [misc]progress: [ 18 / 70 ] simplifiying candidate # * * * * [misc]progress: [ 19 / 70 ] simplifiying candidate # * * * * [misc]progress: [ 20 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (* n PI)) (* (cbrt (sqrt (* n PI))) (cbrt (sqrt (* n PI))))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (* PI n))) (* (cbrt (sqrt (* PI n))) (sqrt (* PI n)))) * [exit]simplify: Simplified to (* (cbrt (sqrt (* PI n))) (* (cbrt (sqrt (* PI n))) (sqrt (* PI n)))) * * * * [misc]progress: [ 21 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (* n PI)) (sqrt n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (* (sqrt n) (sqrt (* PI n))) * [exit]simplify: Simplified to (* (sqrt n) (sqrt (* PI n))) * * * * [misc]progress: [ 22 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (* n PI)) (sqrt (sqrt (* n PI)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (8 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (* PI n))) (sqrt (* PI n))) * [exit]simplify: Simplified to (* (sqrt (sqrt (* PI n))) (sqrt (* PI n))) * * * * [misc]progress: [ 23 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (* n PI)) 1) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (12 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * * * * [misc]progress: [ 24 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (sqrt (* n PI))) (sqrt (* n PI))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (8 enodes) * [exit]simplify: Simplified to (* (cbrt (sqrt (* PI n))) (sqrt (* PI n))) * [exit]simplify: Simplified to (* (cbrt (sqrt (* PI n))) (sqrt (* PI n))) * * * * [misc]progress: [ 25 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt PI) (sqrt (* n PI))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (8 enodes) * [exit]simplify: Simplified to (* (sqrt (* PI n)) (sqrt PI)) * [exit]simplify: Simplified to (* (sqrt (* PI n)) (sqrt PI)) * * * * [misc]progress: [ 26 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (sqrt (* n PI))) (sqrt (* n PI))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (8 enodes) * [exit]simplify: Simplified to (* (sqrt (sqrt (* PI n))) (sqrt (* PI n))) * [exit]simplify: Simplified to (* (sqrt (sqrt (* PI n))) (sqrt (* PI n))) * * * * [misc]progress: [ 27 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (* n PI)) (sqrt (* n PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (6 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 28 / 70 ] simplifiying candidate # * * * * [misc]progress: [ 29 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (expm1 (* PI n)) * [exit]simplify: Simplified to (expm1 (* PI n)) * * * * [misc]progress: [ 30 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (log1p (* PI n)) * [exit]simplify: Simplified to (log1p (* PI n)) * * * * [misc]progress: [ 31 / 70 ] simplifiying candidate # * * * * [misc]progress: [ 32 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (8 enodes) * * [misc]simplify: iters left: 1 (9 enodes) * [exit]simplify: Simplified to (log (* PI n)) * [exit]simplify: Simplified to (log (* PI n)) * * * * [misc]progress: [ 33 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (exp (* PI n)) * [exit]simplify: Simplified to (exp (* PI n)) * * * * [misc]progress: [ 34 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n PI)) (cbrt (* n PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (6 enodes) * [exit]simplify: Simplified to (* (cbrt (* PI n)) (cbrt (* PI n))) * [exit]simplify: Simplified to (* (cbrt (* PI n)) (cbrt (* PI n))) * [enter]simplify: Simplifying (cbrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (cbrt (* PI n)) * [exit]simplify: Simplified to (cbrt (* PI n)) * * * * [misc]progress: [ 35 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n PI) (* n PI)) (* n PI)) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (pow (* PI n) 3) * [exit]simplify: Simplified to (pow (* PI n) 3) * * * * [misc]progress: [ 36 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * [enter]simplify: Simplifying (sqrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * * * * [misc]progress: [ 37 / 70 ] simplifiying candidate # * * * * [misc]progress: [ 38 / 70 ] simplifiying candidate # * * * * [misc]progress: [ 39 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (expm1 (* PI n)) * [exit]simplify: Simplified to (expm1 (* PI n)) * * * * [misc]progress: [ 40 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (log1p (* PI n)) * [exit]simplify: Simplified to (log1p (* PI n)) * * * * [misc]progress: [ 41 / 70 ] simplifiying candidate # * * * * [misc]progress: [ 42 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (8 enodes) * * [misc]simplify: iters left: 1 (9 enodes) * [exit]simplify: Simplified to (log (* PI n)) * [exit]simplify: Simplified to (log (* PI n)) * * * * [misc]progress: [ 43 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (exp (* PI n)) * [exit]simplify: Simplified to (exp (* PI n)) * * * * [misc]progress: [ 44 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n PI)) (cbrt (* n PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (6 enodes) * [exit]simplify: Simplified to (* (cbrt (* PI n)) (cbrt (* PI n))) * [exit]simplify: Simplified to (* (cbrt (* PI n)) (cbrt (* PI n))) * [enter]simplify: Simplifying (cbrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (cbrt (* PI n)) * [exit]simplify: Simplified to (cbrt (* PI n)) * * * * [misc]progress: [ 45 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n PI) (* n PI)) (* n PI)) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (pow (* PI n) 3) * [exit]simplify: Simplified to (pow (* PI n) 3) * * * * [misc]progress: [ 46 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * [enter]simplify: Simplifying (sqrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * * * * [misc]progress: [ 47 / 70 ] simplifiying candidate # * * * * [misc]progress: [ 48 / 70 ] simplifiying candidate # * * * * [misc]progress: [ 49 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (expm1 (* PI n)) * [exit]simplify: Simplified to (expm1 (* PI n)) * * * * [misc]progress: [ 50 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (log1p (* PI n)) * [exit]simplify: Simplified to (log1p (* PI n)) * * * * [misc]progress: [ 51 / 70 ] simplifiying candidate # * * * * [misc]progress: [ 52 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (8 enodes) * * [misc]simplify: iters left: 1 (9 enodes) * [exit]simplify: Simplified to (log (* PI n)) * [exit]simplify: Simplified to (log (* PI n)) * * * * [misc]progress: [ 53 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (exp (* PI n)) * [exit]simplify: Simplified to (exp (* PI n)) * * * * [misc]progress: [ 54 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n PI)) (cbrt (* n PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (6 enodes) * [exit]simplify: Simplified to (* (cbrt (* PI n)) (cbrt (* PI n))) * [exit]simplify: Simplified to (* (cbrt (* PI n)) (cbrt (* PI n))) * [enter]simplify: Simplifying (cbrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (cbrt (* PI n)) * [exit]simplify: Simplified to (cbrt (* PI n)) * * * * [misc]progress: [ 55 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n PI) (* n PI)) (* n PI)) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (pow (* PI n) 3) * [exit]simplify: Simplified to (pow (* PI n) 3) * * * * [misc]progress: [ 56 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * [enter]simplify: Simplifying (sqrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * * * * [misc]progress: [ 57 / 70 ] simplifiying candidate # * * * * [misc]progress: [ 58 / 70 ] simplifiying candidate # * * * * [misc]progress: [ 59 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (- (+ (* +nan.0 (* (pow n 4) (pow PI 4))) (- (+ (* +nan.0 (* (pow n 3) (pow PI 3))) (- (* +nan.0 (* (pow n 2) (pow PI 2)))))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 60 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (- (+ (* +nan.0 (pow PI 2)) (- (+ (* +nan.0 (/ (pow PI 4) (pow n 2))) (- (* +nan.0 (/ (pow PI 3) n))))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 61 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (- (+ (* +nan.0 (pow PI 2)) (- (+ (* +nan.0 (/ (pow PI 4) (pow n 2))) (- (* +nan.0 (/ (pow PI 3) n))))))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 62 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))) * * * * [misc]progress: [ 63 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))) * * * * [misc]progress: [ 64 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))) * * * * [misc]progress: [ 65 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))) * * * * [misc]progress: [ 66 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))) * * * * [misc]progress: [ 67 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))) * * * * [misc]progress: [ 68 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))) * * * * [misc]progress: [ 69 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))) * * * * [misc]progress: [ 70 / 70 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (/ (pow (* (* (sqrt (* n PI)) (sqrt (* n PI))) 2) (/ 1 2)) (pow (* (* n PI) 2) (/ k 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (40 enodes) * * [misc]simplify: iters left: 3 (42 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))) * * * [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 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 (* n PI) (/ (- 1 k) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in k * [misc]taylor: Taking taylor expansion of (* n PI) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* n PI) into (* n PI) * [misc]backup-simplify: Simplify (log (* n PI)) into (log (* n PI)) * [misc]backup-simplify: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ 1 k) into (+ k 1) * [misc]backup-simplify: Simplify (/ (+ k 1) 2) into (* 1/2 (+ k 1)) * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ k 1)) (+ (log n) (log PI))) into (* 1/2 (* (+ k 1) (+ (log n) (log PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) into (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) * [misc]taylor: Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ 1 k) into (+ k 1) * [misc]backup-simplify: Simplify (/ (+ k 1) 2) into (* 1/2 (+ k 1)) * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ k 1)) (+ (log n) (log PI))) into (* 1/2 (* (+ k 1) (+ (log n) (log PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) into (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ k 1) (+ (log n) (log PI)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ k 1) (+ (log n) (log PI))) in k * [misc]taylor: Taking taylor expansion of (+ k 1) in k * [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 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log n) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log PI))) into (* 1/2 (+ (log n) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log PI)))) into (exp (* 1/2 (+ (log n) (log PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log PI)))) into (exp (* 1/2 (+ (log n) (log PI)))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 PI) 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 (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 n) into 0 * [misc]backup-simplify: Simplify (/ 0 PI) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log PI))) into (* 1/2 (+ (log n) (log PI))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (* 1/2 (+ (log n) (log PI)))) into (* 1/2 (* (+ (log n) (log PI)) (exp (* 1/2 (+ (log n) (log PI)))))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ (log n) (log PI)) (exp (* 1/2 (+ (log n) (log PI)))))) into (* 1/2 (* (+ (log n) (log PI)) (exp (* 1/2 (+ (log n) (log PI)))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow PI 2))) (/ 0 PI)) 2) 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 (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 (pow n 2))) (/ 0 n)) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow PI 2))) (/ 0 PI)) 2) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (/ (pow (* 1/2 (+ (log n) (log PI))) 2) 2)) into (* 1/8 (* (pow (+ (log n) (log PI)) 2) (exp (* 1/2 (+ (log n) (log PI)))))) * [misc]backup-simplify: Simplify (* 1/8 (* (pow (+ (log n) (log PI)) 2) (exp (* 1/2 (+ (log n) (log PI)))))) into (* 1/8 (* (pow (+ (log n) (log PI)) 2) (exp (* 1/2 (+ (log n) (log PI)))))) * [misc]backup-simplify: Simplify (+ (* (* 1/8 (* (pow (+ (log n) (log PI)) 2) (exp (* 1/2 (+ (log n) (log PI)))))) (pow k 2)) (+ (* (* 1/2 (* (+ (log n) (log PI)) (exp (* 1/2 (+ (log n) (log PI)))))) k) (exp (* 1/2 (+ (log n) (log PI)))))) into (+ (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log n) 2)))) (+ (exp (* 1/2 (+ (log n) (log PI)))) (+ (* 1/2 (* k (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log n) (log PI))))) (+ (* 1/2 (* k (* (log n) (exp (* 1/2 (+ (log n) (log PI))))))) (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))))))) * [misc]approximate: Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) PI)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) PI) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) * [misc]backup-simplify: Simplify (log (/ PI n)) into (log (/ PI n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ PI n))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) PI)) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log PI)) into (- (log PI) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log PI) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) PI)) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log PI)) into (- (log PI) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log PI) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log PI) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (- (log PI) (log n)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log PI) (log n)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log PI))) into (* 1/2 (+ (log n) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 PI) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log PI)) into (- (log PI) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 (/ 0 (pow PI 2))) (/ 0 PI)) 2) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log PI)) into (- (log PI) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow PI 3))) (+ (* -3 (/ 0 (pow PI 2))) (/ 0 PI))) 6) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log PI)) into (- (log PI) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 k)) 1) (- (log PI) (log (/ 1 n)))))) into (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (+ k 1)))) * [misc]approximate: Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) PI)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) PI) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) * [misc]backup-simplify: Simplify (log (/ PI n)) into (log (/ PI n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ PI n))) into (* 1/2 (log (/ PI n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -1 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) PI)) in n * [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 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 (log (* -1 PI)) into (log (* -1 PI)) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -1 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) PI)) in n * [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 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 (log (* -1 PI)) into (log (* -1 PI)) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -1 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (- (log (* -1 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -1 PI)) in k * [misc]taylor: Taking taylor expansion of (* -1 PI) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log (* -1 PI)) (log n)) into (+ (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (log (* -1 PI)) (log n)) into (+ (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* -1 PI)) (log n))) into (* 1/2 (+ (log (* -1 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 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 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* -1 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* -1 PI) 2))) (/ 0 (* -1 PI))) 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)) 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 (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow (* -1 PI) 3))) (+ (* -3 (/ 0 (pow (* -1 PI) 2))) (/ 0 (* -1 PI)))) 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)) 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 (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -1 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in k * [misc]taylor: Taking taylor expansion of (* n PI) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* n PI) into (* n PI) * [misc]backup-simplify: Simplify (log (* n PI)) into (log (* n PI)) * [misc]backup-simplify: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 2)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ 1 k) into (+ k 1) * [misc]backup-simplify: Simplify (/ (+ k 1) 2) into (* 1/2 (+ k 1)) * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ k 1)) (+ (log n) (log PI))) into (* 1/2 (* (+ k 1) (+ (log n) (log PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) into (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 2)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ 1 k) into (+ k 1) * [misc]backup-simplify: Simplify (/ (+ k 1) 2) into (* 1/2 (+ k 1)) * [misc]taylor: Taking taylor expansion of (log 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* (* 1/2 (+ k 1)) (log 2)) into (* 1/2 (* (+ k 1) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ k 1) (log 2)))) into (exp (* 1/2 (* (+ k 1) (log 2)))) * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ 1 k) into (+ k 1) * [misc]backup-simplify: Simplify (/ (+ k 1) 2) into (* 1/2 (+ k 1)) * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ k 1)) (+ (log n) (log PI))) into (* 1/2 (* (+ k 1) (+ (log n) (log PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) into (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 2)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ 1 k) into (+ k 1) * [misc]backup-simplify: Simplify (/ (+ k 1) 2) into (* 1/2 (+ k 1)) * [misc]taylor: Taking taylor expansion of (log 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* (* 1/2 (+ k 1)) (log 2)) into (* 1/2 (* (+ k 1) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ k 1) (log 2)))) into (exp (* 1/2 (* (+ k 1) (log 2)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) (exp (* 1/2 (* (+ k 1) (log 2))))) into (* (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) (exp (* 1/2 (* (+ k 1) (log 2))))) * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) (exp (* 1/2 (* (+ k 1) (log 2))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ k 1) (+ (log n) (log PI)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ k 1) (+ (log n) (log PI))) in k * [misc]taylor: Taking taylor expansion of (+ k 1) in k * [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 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log n) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log PI))) into (* 1/2 (+ (log n) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log PI)))) into (exp (* 1/2 (+ (log n) (log PI)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ k 1) (log 2)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ k 1) (log 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 1) (log 2)) in k * [misc]taylor: Taking taylor expansion of (+ k 1) in k * [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 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (pow 2 1/2)) into (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))) * [misc]backup-simplify: Simplify (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))) into (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 PI) 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 (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 into 1 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) * [misc]backup-simplify: Simplify (* (pow 2 1/2) (* 1/2 (log 2))) into (* 1/2 (* (log 2) (sqrt 2))) * [misc]backup-simplify: Simplify (/ 0 n) into 0 * [misc]backup-simplify: Simplify (/ 0 PI) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log PI))) into (* 1/2 (+ (log n) (log PI))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (* 1/2 (+ (log n) (log PI)))) into (* 1/2 (* (+ (log n) (log PI)) (exp (* 1/2 (+ (log n) (log PI)))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log PI)))) (* 1/2 (* (log 2) (sqrt 2)))) (* (* 1/2 (* (+ (log n) (log PI)) (exp (* 1/2 (+ (log n) (log PI)))))) (pow 2 1/2))) into (+ (* 1/2 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (* 1/2 (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))))) * [misc]backup-simplify: Simplify (+ (* 1/2 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (* 1/2 (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))))) into (+ (* 1/2 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (* 1/2 (* (sqrt 2) (* (log 2) (exp (* 1/2 (+ (log n) (log PI))))))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow PI 2))) (/ 0 PI)) 2) 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 (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (pow 2 1/2) (/ (pow (* 1/2 (log 2)) 2) 2)) into (* 1/8 (* (pow (log 2) 2) (sqrt 2))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow n 2))) (/ 0 n)) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow PI 2))) (/ 0 PI)) 2) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (/ (pow (* 1/2 (+ (log n) (log PI))) 2) 2)) into (* 1/8 (* (pow (+ (log n) (log PI)) 2) (exp (* 1/2 (+ (log n) (log PI)))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log PI)))) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))) (+ (* (* 1/2 (* (+ (log n) (log PI)) (exp (* 1/2 (+ (log n) (log PI)))))) (* 1/2 (* (log 2) (sqrt 2)))) (* (* 1/8 (* (pow (+ (log n) (log PI)) 2) (exp (* 1/2 (+ (log n) (log PI)))))) (pow 2 1/2)))) into (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 2)))) (+ (* 1/8 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (* 1/8 (* (pow (log 2) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/4 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (log PI))))) (+ (* 1/4 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2))))) (* 1/4 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))))))))) * [misc]backup-simplify: Simplify (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 2)))) (+ (* 1/8 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (* 1/8 (* (pow (log 2) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/4 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (log PI))))) (+ (* 1/4 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2))))) (* 1/4 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))))))))) into (+ (* 1/8 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (* 1/4 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 2)))) (+ (* 1/4 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (log PI))))) (+ (* 1/4 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2))))) (* 1/8 (* (pow (log 2) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))))))) * [misc]backup-simplify: Simplify (+ (* (+ (* 1/8 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (* 1/4 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 2)))) (+ (* 1/4 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (log PI))))) (+ (* 1/4 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2))))) (* 1/8 (* (pow (log 2) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))))))) (pow k 2)) (+ (* (+ (* 1/2 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (* 1/2 (* (sqrt 2) (* (log 2) (exp (* 1/2 (+ (log n) (log PI))))))))) k) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) into (+ (* 1/2 (* k (* (sqrt 2) (* (log 2) (exp (* 1/2 (+ (log n) (log PI)))))))) (+ (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log 2) 2))))) (+ (* 1/4 (* (pow k 2) (* (sqrt 2) (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))))) (+ (* 1/2 (* k (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (+ (* 1/8 (* (pow k 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))) (+ (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))) (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (* (sqrt 2) (log n)))))) (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log 2) (log PI)))))) (+ (* 1/8 (* (pow k 2) (* (sqrt 2) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log PI)))))))) (* 1/2 (* k (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI))))))))))))))))) * [misc]approximate: Taking taylor expansion of (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) PI)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) PI) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) * [misc]backup-simplify: Simplify (log (/ PI n)) into (log (/ PI n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ PI n))))) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 2)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log 2))) into (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) PI)) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log PI)) into (- (log PI) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log PI) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 2)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) into (* 1/2 (* (+ (/ 1 k) 1) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) * [misc]taylor: Taking taylor expansion of (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) PI)) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log PI)) into (- (log PI) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log PI) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 2)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) into (* 1/2 (* (+ (/ 1 k) 1) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log 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) 1) (log 2)) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log PI) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (- (log PI) (log n)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log PI) (log n)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log PI))) into (* 1/2 (+ (log n) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 PI) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log PI)) into (- (log PI) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow PI 2))) (/ 0 PI)) 2) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log PI)) into (- (log PI) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 0 into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow PI 3))) (+ (* -3 (/ 0 (pow PI 2))) (/ 0 PI))) 6) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log PI)) into (- (log PI) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 (/ 1 k)) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 (/ 1 k)) 1) (- (log PI) (log (/ 1 n))))))) into (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (+ k 1)))) (exp (* 1/2 (* (+ k 1) (log 2))))) * [misc]approximate: Taking taylor expansion of (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) PI)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) PI) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) * [misc]backup-simplify: Simplify (log (/ PI n)) into (log (/ PI n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ PI n))) into (* 1/2 (log (/ PI n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -1 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 2)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log 2))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) * [misc]taylor: Taking taylor expansion of (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) PI)) in n * [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 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 (log (* -1 PI)) into (log (* -1 PI)) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -1 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 2)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) into (* 1/2 (* (+ (/ 1 k) 1) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) * [misc]taylor: Taking taylor expansion of (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) PI)) in n * [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 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 (log (* -1 PI)) into (log (* -1 PI)) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -1 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 2)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) into (* 1/2 (* (+ (/ 1 k) 1) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log 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) 1) (log 2)) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (- (log (* -1 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -1 PI)) in k * [misc]taylor: Taking taylor expansion of (* -1 PI) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log (* -1 PI)) (log n)) into (+ (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (log (* -1 PI)) (log n)) into (+ (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* -1 PI)) (log n))) into (* 1/2 (+ (log (* -1 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* -1 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 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)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]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 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* -1 PI) 2))) (/ 0 (* -1 PI))) 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)) 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 (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 0 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)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]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 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow (* -1 PI) 3))) (+ (* -3 (/ 0 (pow (* -1 PI) 2))) (/ 0 (* -1 PI)))) 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)) 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 (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -1 PI)) (log (/ 1 (- n)))))))) into (* (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1 1 1) * [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 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 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 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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* 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 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 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 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 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 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 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [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 0 into 0 * [misc]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 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 0 into 0 * [misc]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 0 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) * [misc]approximate: Taking taylor expansion of (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in k * [misc]taylor: Taking taylor expansion of (* n PI) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* n PI) into (* n PI) * [misc]backup-simplify: Simplify (log (* n PI)) into (log (* n PI)) * [misc]backup-simplify: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 2)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log 2))) into (pow 2 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 0 into 0 * [misc]backup-simplify: Simplify (/ 1 0) into +nan.0 * [misc]backup-simplify: Simplify (* (pow (* n PI) 1/2) (pow 2 1/2)) into (sqrt (* 2 (* n PI))) * [misc]backup-simplify: Simplify (/ (sqrt (* 2 (* n PI))) +nan.0) into (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) * [misc]taylor: Taking taylor expansion of (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ 1 k) into (+ k 1) * [misc]backup-simplify: Simplify (/ (+ k 1) 2) into (* 1/2 (+ k 1)) * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ k 1)) (+ (log n) (log PI))) into (* 1/2 (* (+ k 1) (+ (log n) (log PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) into (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 2)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ 1 k) into (+ k 1) * [misc]backup-simplify: Simplify (/ (+ k 1) 2) into (* 1/2 (+ k 1)) * [misc]taylor: Taking taylor expansion of (log 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* (* 1/2 (+ k 1)) (log 2)) into (* 1/2 (* (+ k 1) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ k 1) (log 2)))) into (exp (* 1/2 (* (+ k 1) (log 2)))) * [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 (* (+ k 1) (+ (log n) (log PI))))) (exp (* 1/2 (* (+ k 1) (log 2))))) into (* (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) (exp (* 1/2 (* (+ k 1) (log 2))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) (exp (* 1/2 (* (+ k 1) (log 2))))) (sqrt k)) into (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) (exp (* 1/2 (* (+ k 1) (log 2)))))) * [misc]taylor: Taking taylor expansion of (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* n PI) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* n PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* n PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ 1 k) into (+ k 1) * [misc]backup-simplify: Simplify (/ (+ k 1) 2) into (* 1/2 (+ k 1)) * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ k 1)) (+ (log n) (log PI))) into (* 1/2 (* (+ k 1) (+ (log n) (log PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) into (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log 2)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (+ 1 k) into (+ k 1) * [misc]backup-simplify: Simplify (/ (+ k 1) 2) into (* 1/2 (+ k 1)) * [misc]taylor: Taking taylor expansion of (log 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* (* 1/2 (+ k 1)) (log 2)) into (* 1/2 (* (+ k 1) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ k 1) (log 2)))) into (exp (* 1/2 (* (+ k 1) (log 2)))) * [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 (* (+ k 1) (+ (log n) (log PI))))) (exp (* 1/2 (* (+ k 1) (log 2))))) into (* (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) (exp (* 1/2 (* (+ k 1) (log 2))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) (exp (* 1/2 (* (+ k 1) (log 2))))) (sqrt k)) into (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) (exp (* 1/2 (* (+ k 1) (log 2)))))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) (exp (* 1/2 (* (+ k 1) (log 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 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 1 0) into +nan.0 * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) (exp (* 1/2 (* (+ k 1) (log 2))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ k 1) (+ (log n) (log PI)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ k 1) (+ (log n) (log PI))) in k * [misc]taylor: Taking taylor expansion of (+ k 1) in k * [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 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log n) (log 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 PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log PI))) into (* 1/2 (+ (log n) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log PI)))) into (exp (* 1/2 (+ (log n) (log PI)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ k 1) (log 2)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ k 1) (log 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 1) (log 2)) in k * [misc]taylor: Taking taylor expansion of (+ k 1) in k * [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 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (pow 2 1/2)) into (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 PI) 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 (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt k)) (* (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) (exp (* 1/2 (* (+ k 1) (log 2)))))) (/ 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 into 1 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) * [misc]backup-simplify: Simplify (* (pow 2 1/2) (* 1/2 (log 2))) into (* 1/2 (* (log 2) (sqrt 2))) * [misc]backup-simplify: Simplify (/ 0 n) into 0 * [misc]backup-simplify: Simplify (/ 0 PI) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log PI))) into (* 1/2 (+ (log n) (log PI))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (* 1/2 (+ (log n) (log PI)))) into (* 1/2 (* (+ (log n) (log PI)) (exp (* 1/2 (+ (log n) (log PI)))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log PI)))) (* 1/2 (* (log 2) (sqrt 2)))) (* (* 1/2 (* (+ (log n) (log PI)) (exp (* 1/2 (+ (log n) (log PI)))))) (pow 2 1/2))) into (+ (* 1/2 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (* 1/2 (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) into (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) into (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow PI 2))) (/ 0 PI)) 2) 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 (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt k)) (* (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) (exp (* 1/2 (* (+ k 1) (log 2)))))) (/ 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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (pow 2 1/2) (/ (pow (* 1/2 (log 2)) 2) 2)) into (* 1/8 (* (pow (log 2) 2) (sqrt 2))) * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow n 2))) (/ 0 n)) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow PI 2))) (/ 0 PI)) 2) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (/ (pow (* 1/2 (+ (log n) (log PI))) 2) 2)) into (* 1/8 (* (pow (+ (log n) (log PI)) 2) (exp (* 1/2 (+ (log n) (log PI)))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log PI)))) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))) (+ (* (* 1/2 (* (+ (log n) (log PI)) (exp (* 1/2 (+ (log n) (log PI)))))) (* 1/2 (* (log 2) (sqrt 2)))) (* (* 1/8 (* (pow (+ (log n) (log PI)) 2) (exp (* 1/2 (+ (log n) (log PI)))))) (pow 2 1/2)))) into (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 2)))) (+ (* 1/8 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (* 1/8 (* (pow (log 2) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/4 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (log PI))))) (+ (* 1/4 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2))))) (* 1/4 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))))))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (pow +nan.0 2) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify (+ (* +nan.0 (+ (* 1/2 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (* 1/2 (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))))) (* (* +nan.0 (pow +nan.0 2)) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (log n) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (log n) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2)))) (- (* +nan.0 (* (log n) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))))))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow PI 3))) (+ (* -3 (/ 0 (pow PI 2))) (/ 0 PI))) 6) 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 (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt k)) (* (* (sqrt (/ 1 k)) (* (exp (* 1/2 (* (+ k 1) (+ (log n) (log PI))))) (exp (* 1/2 (* (+ k 1) (log 2)))))) (/ 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 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 (* (pow 2 1/2) (/ (pow (* 1/2 (log 2)) 3) 6)) into (* 1/48 (* (pow (log 2) 3) (sqrt 2))) * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow n 3))) (+ (* -3 (/ 0 (pow n 2))) (/ 0 n))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow PI 3))) (+ (* -3 (/ 0 (pow PI 2))) (/ 0 PI))) 6) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log PI)))) (/ (pow (* 1/2 (+ (log n) (log PI))) 3) 6)) into (* 1/48 (* (pow (+ (log n) (log PI)) 3) (exp (* 1/2 (+ (log n) (log PI)))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log PI)))) (* 1/48 (* (pow (log 2) 3) (sqrt 2)))) (+ (* (* 1/2 (* (+ (log n) (log PI)) (exp (* 1/2 (+ (log n) (log PI)))))) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))) (+ (* (* 1/8 (* (pow (+ (log n) (log PI)) 2) (exp (* 1/2 (+ (log n) (log PI)))))) (* 1/2 (* (log 2) (sqrt 2)))) (* (* 1/48 (* (pow (+ (log n) (log PI)) 3) (exp (* 1/2 (+ (log n) (log PI)))))) (pow 2 1/2))))) into (+ (* 1/8 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (* (sqrt 2) (log PI)))))) (+ (* 1/16 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (pow (log 2) 2) (sqrt 2))))) (+ (* 1/16 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (pow (log n) 2) (log PI))))) (+ (* 1/48 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 3)))) (+ (* 1/16 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (pow (log PI) 2))))) (+ (* 1/48 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 3)))) (+ (* 1/48 (* (pow (log 2) 3) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/16 (* (pow (log n) 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2))))) (+ (* 1/16 (* (log 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))) (* 1/16 (* (sqrt 2) (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))))))))))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (* 2 (* +nan.0 (* +nan.0 (pow +nan.0 2)))) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify (+ (* +nan.0 (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log n) 2)))) (+ (* 1/8 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (* 1/8 (* (pow (log 2) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (+ (* 1/4 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log n) (log PI))))) (+ (* 1/4 (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2))))) (* 1/4 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))))))))) (+ (* (* +nan.0 (pow +nan.0 2)) (+ (* 1/2 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (* 1/2 (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))))) (* (* +nan.0 (pow +nan.0 2)) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log 2) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (* (sqrt 2) (log PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (- (+ (* +nan.0 (* (log n) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (pow (log n) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (* (sqrt 2) (log n)))))))))))))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log 2) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (* (sqrt 2) (log PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (- (+ (* +nan.0 (* (log n) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (pow (log n) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (* (sqrt 2) (log n)))))))))))))))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (- (+ (* +nan.0 (* (log n) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log n))))) (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (pow (log 2) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log 2) (log PI))))) (- (+ (* +nan.0 (* (pow (log n) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (* +nan.0 (* (sqrt 2) (* (log 2) (exp (* 1/2 (+ (log n) (log PI)))))))))))))))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2)))) (- (+ (* +nan.0 (* (log n) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log n))))) (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (pow (log 2) 2) (sqrt 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log 2) (log PI))))) (- (+ (* +nan.0 (* (pow (log n) 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (* +nan.0 (* (sqrt 2) (* (log 2) (exp (* 1/2 (+ (log n) (log PI)))))))))))))))))))))))))) (pow k 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (sqrt 2)))) (- (* +nan.0 (* (log n) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))))))))) k) (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))))) into (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (- (+ (* +nan.0 (* k (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (- (+ (* +nan.0 (* (pow k 2) (* (log 2) (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI))))))))) (- (+ (* +nan.0 (* k (* (sqrt 2) (* (log 2) (exp (* 1/2 (+ (log n) (log PI)))))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log PI)))))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (* (sqrt 2) (log PI)))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (log 2) (exp (* 1/2 (+ (log n) (log PI)))))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))))) (- (+ (* +nan.0 (* k (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log 2) 2))))) (- (* +nan.0 (* k (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI))))))))))))))))))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) PI)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) PI) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) * [misc]backup-simplify: Simplify (log (/ PI n)) into (log (/ PI n)) * [misc]backup-simplify: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ PI n))))) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 2)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log 2))) into (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 1 0) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ PI n))))) (exp (* 1/2 (* (log 2) (- 1 (/ 1 k)))))) into (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ PI n)))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ PI n)))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (log 2) (- 1 (/ 1 k))))) (exp (* 1/2 (* (- 1 (/ 1 k)) (log (/ PI n))))))) * [misc]taylor: Taking taylor expansion of (/ (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) PI)) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log PI)) into (- (log PI) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log PI) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 2)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) into (* 1/2 (* (+ (/ 1 k) 1) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) * [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 k) 1) (- (log PI) (log n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) (sqrt (/ 1 k))) into (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (/ (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (* (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) (pow 2 (/ (- 1 (/ 1 k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) PI) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) PI)) in n * [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 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log PI)) into (- (log PI) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log PI) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log 2)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) into (* 1/2 (* (+ (/ 1 k) 1) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) * [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 k) 1) (- (log PI) (log n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) (sqrt (/ 1 k))) into (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log 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) 1) (log 2)) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log PI) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (- (log PI) (log n)) in k * [misc]taylor: Taking taylor expansion of (log PI) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (log PI) into (log PI) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log PI) (log n)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log PI))) into (* 1/2 (+ (log n) (log PI))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log 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 0 into 0 * [misc]backup-simplify: Simplify (/ 1 0) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ 0 PI) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log PI)) into (- (log PI) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt (/ 1 k))) (* (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log 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 0 into 0 * [misc]backup-simplify: Simplify (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n))))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow PI 2))) (/ 0 PI)) 2) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log PI)) into (- (log PI) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt (/ 1 k))) (* (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log 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 0 into 0 * [misc]backup-simplify: Simplify (/ (pow +nan.0 2) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) (* +nan.0 (pow +nan.0 2))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow PI 3))) (+ (* -3 (/ 0 (pow PI 2))) (/ 0 PI))) 6) into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log PI)) into (- (log PI) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt (/ 1 k))) (* (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log 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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (* 2 (* +nan.0 (* +nan.0 (pow +nan.0 2)))) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))) (* +nan.0 (pow +nan.0 2))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log PI) (log n)))))))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 k)) 1) (log 2)))) (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 (/ 1 k)) 1) (- (log PI) (log (/ 1 n))))))))) (pow (/ 1 k) 3)) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 k)) 1) (log 2)))) (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 (/ 1 k)) 1) (- (log PI) (log (/ 1 n))))))))) (pow (/ 1 k) 2)) (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 k)) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 (/ 1 k)) 1) (- (log PI) (log (/ 1 n)))))))) (/ 1 k)))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (+ k 1)))) (exp (* 1/2 (* (+ k 1) (log 2))))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (+ k 1)))) (exp (* 1/2 (* (+ k 1) (log 2))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (+ k 1)))) (exp (* 1/2 (* (+ k 1) (log 2))))) k))))))) * [misc]approximate: Taking taylor expansion of (/ (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) PI)) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) PI) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) * [misc]backup-simplify: Simplify (log (/ PI n)) into (log (/ PI n)) * [misc]backup-simplify: Simplify (* 1/2 (log (/ PI n))) into (* 1/2 (log (/ PI n))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -1 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 2)) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log 2))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 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 into -1 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ -1 0) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -1 (/ PI n)))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -1 (/ PI n))))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -1 (/ PI n))))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log (* -1 (/ PI n)))))))) * [misc]taylor: Taking taylor expansion of (/ (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) PI)) in n * [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 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 (log (* -1 PI)) into (log (* -1 PI)) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -1 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 2)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) into (* 1/2 (* (+ (/ 1 k) 1) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) (sqrt (/ 1 k))) into (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (/ (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (* (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) (pow 2 (/ (- 1 (/ 1 (- k))) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) PI) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) PI))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) PI)) in n * [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 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 (log (* -1 PI)) into (log (* -1 PI)) * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -1 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow 2 (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log 2)) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ (/ 1 k) 1) * [misc]backup-simplify: Simplify (/ (+ (/ 1 k) 1) 2) into (* 1/2 (+ (/ 1 k) 1)) * [misc]taylor: Taking taylor expansion of (log 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (log 2)) into (* 1/2 (* (+ (/ 1 k) 1) (log 2))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) * [misc]backup-simplify: Simplify (/ (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) (sqrt (/ 1 k))) into (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (log 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) 1) (log 2)) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (log 2) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (log 2) into (log 2) * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ (/ 1 k) 1) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (- (log (* -1 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -1 PI)) in k * [misc]taylor: Taking taylor expansion of (* -1 PI) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log (* -1 PI)) (log n)) into (+ (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (log (* -1 PI)) (log n)) into (+ (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* -1 PI)) (log n))) into (* 1/2 (+ (log (* -1 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 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 0 into 0 * [misc]backup-simplify: Simplify (/ 1 0) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) into (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 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 0 into 0 * [misc]backup-simplify: Simplify (/ 0 (* -1 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (* (/ 1 k) (/ 0 k)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -1 (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt (/ 1 k))) (* (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 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 0 into 0 * [misc]backup-simplify: Simplify (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) +nan.0) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n))))))) * [misc]backup-simplify: Simplify 0 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)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]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 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ 0 (pow (* -1 PI) 2))) (/ 0 (* -1 PI))) 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)) 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 (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 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)) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt (/ 1 k))) (* (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 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 0 into 0 * [misc]backup-simplify: Simplify (/ (pow +nan.0 2) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) (* +nan.0 (pow +nan.0 2))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))))) * [misc]backup-simplify: Simplify 0 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)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]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 0 into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ 0 (pow (* -1 PI) 3))) (+ (* -3 (/ 0 (pow (* -1 PI) 2))) (/ 0 (* -1 PI)))) 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)) 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 (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 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)) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (/ 0 (sqrt (/ 1 k))) (* (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 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 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (* 2 (* +nan.0 (* +nan.0 (pow +nan.0 2)))) 0) into (* +nan.0 (pow +nan.0 2)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))) (* +nan.0 (pow +nan.0 2))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))))) * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))))) into (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 k) 1) (log 2)))) (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -1 PI)) (log n)))))))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log 2)))) (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -1 PI)) (log (/ 1 (- n)))))))))) (pow (/ 1 (- k)) 3)) (+ (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log 2)))) (* (pow +nan.0 2) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -1 PI)) (log (/ 1 (- n)))))))))) (pow (/ 1 (- k)) 2)) (* (* +nan.0 (* (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (log 2)))) (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -1 PI)) (log (/ 1 (- n))))))))) (/ 1 (- k))))) into (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) k)) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k))))) (pow k 3)))))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (pow (* n PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (expm1 (pow (* PI n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (expm1 (pow (* PI n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 2 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (pow (* n PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (log1p (pow (* PI n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (log1p (pow (* PI n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 3 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* n PI)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI n))) * * * * [misc]progress: [ 4 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* n PI)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (396 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI n))) * * * * [misc]progress: [ 5 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (51 enodes) * * [misc]simplify: iters left: 2 (79 enodes) * * [misc]simplify: iters left: 1 (117 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [exit]simplify: Simplified to (/ (- 1 k) 2) * * * * [misc]progress: [ 6 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n PI) (/ 1 2)) * * [misc]simplify: iters left: 3 (7 enodes) * * [misc]simplify: iters left: 2 (10 enodes) * [exit]simplify: Simplified to (pow (* PI n) (/ 1 2)) * [exit]simplify: Simplified to (pow (* PI n) (/ 1 2)) * [enter]simplify: Simplifying (pow (* n PI) (/ k 2)) * * [misc]simplify: iters left: 3 (7 enodes) * * [misc]simplify: iters left: 2 (8 enodes) * [exit]simplify: Simplified to (pow (* PI n) (/ k 2)) * [exit]simplify: Simplified to (pow (* PI n) (/ k 2)) * * * * [misc]progress: [ 7 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n PI) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (pow (* PI n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow (* PI n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 8 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n PI) (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (pow (* PI n) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (* PI n) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 9 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n PI) 1) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (8 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 10 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* n PI) (- 1 k)) * * [misc]simplify: iters left: 3 (7 enodes) * * [misc]simplify: iters left: 2 (12 enodes) * * [misc]simplify: iters left: 1 (13 enodes) * [exit]simplify: Simplified to (pow (* PI n) (- 1 k)) * [exit]simplify: Simplified to (pow (* PI n) (- 1 k)) * * * * [misc]progress: [ 11 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (pow n (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * * [misc]simplify: iters left: 2 (19 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow PI (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * * [misc]simplify: iters left: 2 (19 enodes) * [exit]simplify: Simplified to (pow PI (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow PI (/ (- 1 k) 2)) * * * * [misc]progress: [ 12 / 99 ] simplifiying candidate # * * * * [misc]progress: [ 13 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (* n PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (58 enodes) * * [misc]simplify: iters left: 2 (133 enodes) * * [misc]simplify: iters left: 1 (491 enodes) * [exit]simplify: Simplified to (* (log (* PI n)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (* (log (* PI n)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 14 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (* n PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (exp (pow (* PI n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (* PI n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 15 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* n PI) (/ (- 1 k) 2))) (cbrt (pow (* n PI) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* PI n) (/ (- 1 k) 2))) (cbrt (pow (* PI n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* PI n) (/ (- 1 k) 2))) (cbrt (pow (* PI n) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow (* n PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (cbrt (pow (* PI n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (* PI n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 16 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (* n PI) (/ (- 1 k) 2)) (pow (* n PI) (/ (- 1 k) 2))) (pow (* n PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * [exit]simplify: Simplified to (pow (pow (* PI n) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (* PI n) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 17 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* n PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (sqrt (pow (* PI n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* PI n) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow (* n PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (sqrt (pow (* PI n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* PI n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 18 / 99 ] simplifiying candidate # * * * * [misc]progress: [ 19 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (expm1 (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (expm1 (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 20 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (log1p (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (log1p (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 21 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* n PI) 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 (* (* PI n) 2) * [exit]simplify: Simplified to (* (* PI n) 2) * * * * [misc]progress: [ 22 / 99 ] simplifiying candidate # * * * * [misc]progress: [ 23 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log (* n PI)) (/ (- 1 k) 2)) (* (log 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (235 enodes) * [exit]simplify: Simplified to (* (+ (log 2) (log (* PI n))) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (* (+ (log 2) (log (* PI n))) (/ (- 1 k) 2)) * * * * [misc]progress: [ 24 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log (* n PI)) (/ (- 1 k) 2)) (log (pow 2 (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (+ (log 2) (log (* PI n)))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (+ (log 2) (log (* PI n)))) * * * * [misc]progress: [ 25 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log (* n PI)) (/ (- 1 k) 2)) (* (log 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (235 enodes) * [exit]simplify: Simplified to (* (+ (log 2) (log (* PI n))) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (* (+ (log 2) (log (* PI n))) (/ (- 1 k) 2)) * * * * [misc]progress: [ 26 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log (* n PI)) (/ (- 1 k) 2)) (log (pow 2 (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (+ (log 2) (log (* PI n)))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (+ (log 2) (log (* PI n)))) * * * * [misc]progress: [ 27 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (pow (* n PI) (/ (- 1 k) 2))) (* (log 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (151 enodes) * * [misc]simplify: iters left: 2 (423 enodes) * [exit]simplify: Simplified to (* (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (* (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 28 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (pow (* n PI) (/ (- 1 k) 2))) (log (pow 2 (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (98 enodes) * * [misc]simplify: iters left: 2 (274 enodes) * [exit]simplify: Simplified to (* (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (* (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 29 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (50 enodes) * * [misc]simplify: iters left: 2 (105 enodes) * * [misc]simplify: iters left: 1 (297 enodes) * [exit]simplify: Simplified to (* (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (* (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2)) * * * * [misc]progress: [ 30 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (exp (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (exp (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 31 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (pow (* n PI) (/ (- 1 k) 2)) (pow (* n PI) (/ (- 1 k) 2))) (pow (* n PI) (/ (- 1 k) 2))) (* (* (pow 2 (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (94 enodes) * * [misc]simplify: iters left: 2 (111 enodes) * * [misc]simplify: iters left: 1 (114 enodes) * [exit]simplify: Simplified to (pow (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) 3) * [exit]simplify: Simplified to (pow (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) 3) * * * * [misc]progress: [ 32 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (cbrt (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * [exit]simplify: Simplified to (* (cbrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) (cbrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (cbrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) (cbrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))) * [enter]simplify: Simplifying (cbrt (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (cbrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (cbrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 33 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (76 enodes) * * [misc]simplify: iters left: 2 (106 enodes) * * [misc]simplify: iters left: 1 (109 enodes) * [exit]simplify: Simplified to (pow (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) 3) * [exit]simplify: Simplified to (pow (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) 3) * * * * [misc]progress: [ 34 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (sqrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (sqrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (sqrt (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (sqrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (sqrt (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 35 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* n PI) (/ 1 2)) (pow 2 (/ 1 2))) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * [exit]simplify: Simplified to (* (pow 2 (/ 1 2)) (pow (* PI n) (/ 1 2))) * [exit]simplify: Simplified to (* (pow 2 (/ 1 2)) (pow (* PI n) (/ 1 2))) * [enter]simplify: Simplifying (* (pow (* n PI) (/ k 2)) (pow 2 (/ k 2))) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * [exit]simplify: Simplified to (* (pow 2 (/ k 2)) (pow (* PI n) (/ k 2))) * [exit]simplify: Simplified to (* (pow 2 (/ k 2)) (pow (* PI n) (/ k 2))) * * * * [misc]progress: [ 36 / 99 ] simplifiying candidate # * * * * [misc]progress: [ 37 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* n PI) (/ (- 1 k) 2)) (* (cbrt (pow 2 (/ (- 1 k) 2))) (cbrt (pow 2 (/ (- 1 k) 2))))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (* (* (cbrt (pow 2 (/ (- 1 k) 2))) (cbrt (pow 2 (/ (- 1 k) 2)))) (pow (* PI n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (* (cbrt (pow 2 (/ (- 1 k) 2))) (cbrt (pow 2 (/ (- 1 k) 2)))) (pow (* PI n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 38 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* n PI) (/ (- 1 k) 2)) (sqrt (pow 2 (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (* (sqrt (pow 2 (/ (- 1 k) 2))) (pow (* PI n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (sqrt (pow 2 (/ (- 1 k) 2))) (pow (* PI n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 39 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* n PI) (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (pow (* PI n) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* PI n) (/ (- 1 k) 2)) * * * * [misc]progress: [ 40 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow PI (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (pow 2 (/ (- 1 k) 2)) (pow PI (/ (- 1 k) 2))) * * * * [misc]progress: [ 41 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* n PI) (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* PI n) (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (cbrt (pow (* PI n) (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2))) * * * * [misc]progress: [ 42 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow (* n PI) (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* PI n) (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (sqrt (pow (* PI n) (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2))) * * * * [misc]progress: [ 43 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 44 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ 1 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (* (pow 2 (/ 1 2)) (pow (* PI n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (pow 2 (/ 1 2)) (pow (* PI n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 45 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow (* n PI) (/ 1 2)) (pow 2 (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ 1 2))) * [exit]simplify: Simplified to (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ 1 2))) * * * * [misc]progress: [ 46 / 99 ] simplifiying candidate # * * * * [misc]progress: [ 47 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (expm1 (* PI n)) * [exit]simplify: Simplified to (expm1 (* PI n)) * * * * [misc]progress: [ 48 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (log1p (* PI n)) * [exit]simplify: Simplified to (log1p (* PI n)) * * * * [misc]progress: [ 49 / 99 ] simplifiying candidate # * * * * [misc]progress: [ 50 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (8 enodes) * * [misc]simplify: iters left: 1 (9 enodes) * [exit]simplify: Simplified to (log (* PI n)) * [exit]simplify: Simplified to (log (* PI n)) * * * * [misc]progress: [ 51 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (exp (* PI n)) * [exit]simplify: Simplified to (exp (* PI n)) * * * * [misc]progress: [ 52 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n PI)) (cbrt (* n PI))) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (6 enodes) * [exit]simplify: Simplified to (* (cbrt (* PI n)) (cbrt (* PI n))) * [exit]simplify: Simplified to (* (cbrt (* PI n)) (cbrt (* PI n))) * [enter]simplify: Simplifying (cbrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (cbrt (* PI n)) * [exit]simplify: Simplified to (cbrt (* PI n)) * * * * [misc]progress: [ 53 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n PI) (* n PI)) (* n PI)) * * [misc]simplify: iters left: 6 (5 enodes) * * [misc]simplify: iters left: 5 (13 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (86 enodes) * * [misc]simplify: iters left: 1 (89 enodes) * [exit]simplify: Simplified to (pow (* PI n) 3) * [exit]simplify: Simplified to (pow (* PI n) 3) * * * * [misc]progress: [ 54 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * [enter]simplify: Simplifying (sqrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * * * * [misc]progress: [ 55 / 99 ] simplifiying candidate # * * * * [misc]progress: [ 56 / 99 ] simplifiying candidate # * * * * [misc]progress: [ 57 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (expm1 (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * * [misc]simplify: iters left: 1 (38 enodes) * [exit]simplify: Simplified to (expm1 (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (expm1 (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))) * * * * [misc]progress: [ 58 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (log1p (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * * [misc]simplify: iters left: 1 (38 enodes) * [exit]simplify: Simplified to (log1p (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (log1p (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))) * * * * [misc]progress: [ 59 / 99 ] simplifiying candidate # * * * * [misc]progress: [ 60 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* (log (* n PI)) (/ (- 1 k) 2)) (* (log 2) (/ (- 1 k) 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (285 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log 2) (log (* PI n))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log 2) (log (* PI n))) (- (log (sqrt k)))) * * * * [misc]progress: [ 61 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* (log (* n PI)) (/ (- 1 k) 2)) (log (pow 2 (/ (- 1 k) 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (204 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log (* PI n)) (log 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log (* PI n)) (log 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 62 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* (log (* n PI)) (/ (- 1 k) 2)) (* (log 2) (/ (- 1 k) 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (93 enodes) * * [misc]simplify: iters left: 3 (285 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log 2) (log (* PI n))) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log 2) (log (* PI n))) (- (log (sqrt k)))) * * * * [misc]progress: [ 63 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* (log (* n PI)) (/ (- 1 k) 2)) (log (pow 2 (/ (- 1 k) 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (38 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (204 enodes) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log (* PI n)) (log 2)) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (/ (- 1 k) 2) (+ (log (* PI n)) (log 2)) (- (log (sqrt k)))) * * * * [misc]progress: [ 64 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (log (pow (* n PI) (/ (- 1 k) 2))) (* (log 2) (/ (- 1 k) 2))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (185 enodes) * [exit]simplify: Simplified to (fma (+ (log 2) (log (* PI n))) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (+ (log 2) (log (* PI n))) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 65 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (log (pow (* n PI) (/ (- 1 k) 2))) (log (pow 2 (/ (- 1 k) 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (132 enodes) * * [misc]simplify: iters left: 2 (406 enodes) * [exit]simplify: Simplified to (fma (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 66 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (log (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (42 enodes) * * [misc]simplify: iters left: 3 (71 enodes) * * [misc]simplify: iters left: 2 (140 enodes) * * [misc]simplify: iters left: 1 (483 enodes) * [exit]simplify: Simplified to (fma (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 67 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (39 enodes) * * [misc]simplify: iters left: 3 (61 enodes) * * [misc]simplify: iters left: 2 (96 enodes) * * [misc]simplify: iters left: 1 (168 enodes) * [exit]simplify: Simplified to (fma (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2) (- (log (sqrt k)))) * [exit]simplify: Simplified to (fma (+ (log (* PI n)) (log 2)) (/ (- 1 k) 2) (- (log (sqrt k)))) * * * * [misc]progress: [ 68 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * * [misc]simplify: iters left: 2 (39 enodes) * * [misc]simplify: iters left: 1 (40 enodes) * [exit]simplify: Simplified to (exp (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (exp (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))) * * * * [misc]progress: [ 69 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (* (pow (* n PI) (/ (- 1 k) 2)) (pow (* n PI) (/ (- 1 k) 2))) (pow (* n PI) (/ (- 1 k) 2))) (* (* (pow 2 (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (pow 2 (/ (- 1 k) 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (42 enodes) * * [misc]simplify: iters left: 4 (126 enodes) * * [misc]simplify: iters left: 3 (421 enodes) * [exit]simplify: Simplified to (* (/ (* (pow (* PI n) (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) (/ k (pow 2 (/ (- 1 k) 2)))) (* (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt k)) (* (pow 2 (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (/ (* (pow (* PI n) (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) (/ k (pow 2 (/ (- 1 k) 2)))) (* (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt k)) (* (pow 2 (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))))) * * * * [misc]progress: [ 70 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (110 enodes) * * [misc]simplify: iters left: 3 (376 enodes) * [exit]simplify: Simplified to (* (/ (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) (* k (sqrt k))) (* (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (* (/ (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) (* k (sqrt k))) (* (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 71 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))) (cbrt (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (38 enodes) * * [misc]simplify: iters left: 1 (39 enodes) * [exit]simplify: Simplified to (* (cbrt (* (pow 2 (/ (- 1 k) 2)) (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (* (pow 2 (/ (- 1 k) 2)) (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt k))))) * [exit]simplify: Simplified to (* (cbrt (* (pow 2 (/ (- 1 k) 2)) (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (* (pow 2 (/ (- 1 k) 2)) (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt k))))) * [enter]simplify: Simplifying (cbrt (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * * [misc]simplify: iters left: 1 (38 enodes) * [exit]simplify: Simplified to (cbrt (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (cbrt (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))) * * * * [misc]progress: [ 72 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)) (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))) (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (208 enodes) * [exit]simplify: Simplified to (/ (* (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt k)) (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) (/ (/ k (pow 2 (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (/ (* (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt k)) (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) (/ (/ k (pow 2 (/ (- 1 k) 2))) (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))))) * * * * [misc]progress: [ 73 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * * [misc]simplify: iters left: 1 (38 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (sqrt (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))) * [enter]simplify: Simplifying (sqrt (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * * [misc]simplify: iters left: 1 (38 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))) * [exit]simplify: Simplified to (sqrt (/ (pow (* PI n) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))) * * * * [misc]progress: [ 74 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (- (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (- (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (- (sqrt k)) * * [misc]simplify: iters left: 3 (3 enodes) * [exit]simplify: Simplified to (- (sqrt k)) * [exit]simplify: Simplified to (- (sqrt k)) * * * * [misc]progress: [ 75 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n PI) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (28 enodes) * [exit]simplify: Simplified to (/ (pow (* PI n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow (* PI n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (cbrt (sqrt k))) * * * * [misc]progress: [ 76 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* PI n) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (19 enodes) * * [misc]simplify: iters left: 3 (21 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 77 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n PI) (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (pow (* PI n) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* PI n) (/ (- 1 k) 2)) * [enter]simplify: Simplifying (/ (pow 2 (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 78 / 99 ] simplifiying candidate # * * * * [misc]progress: [ 79 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 80 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2)))) * * * * [misc]progress: [ 81 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (31 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 (68 enodes) * [exit]simplify: Simplified to (* (pow 2 (/ (- 1 k) 2)) (/ (pow (* PI n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * [exit]simplify: Simplified to (* (pow 2 (/ (- 1 k) 2)) (/ (pow (* PI n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) * * * * [misc]progress: [ 82 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * * [misc]simplify: iters left: 2 (37 enodes) * * [misc]simplify: iters left: 1 (38 enodes) * [exit]simplify: Simplified to (/ (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 83 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) 1) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (49 enodes) * * [misc]simplify: iters left: 1 (60 enodes) * [exit]simplify: Simplified to (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (pow 2 (/ (- 1 k) 2)) (pow (* PI n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 84 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow 2 (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (18 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow 2 (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow 2 (/ (- 1 k) 2))) * * * * [misc]progress: [ 85 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt k) (* (pow (* n PI) (/ k 2)) (pow 2 (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (* (* (pow (* n PI) (/ k 2)) (sqrt k)) (pow 2 (/ k 2))) * [exit]simplify: Simplified to (* (* (pow (* n PI) (/ k 2)) (sqrt k)) (pow 2 (/ k 2))) * * * * [misc]progress: [ 86 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt k) (pow 2 (/ k 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (7 enodes) * [exit]simplify: Simplified to (* (pow 2 (/ k 2)) (sqrt k)) * [exit]simplify: Simplified to (* (pow 2 (/ k 2)) (sqrt k)) * * * * [misc]progress: [ 87 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt k) (pow (* n PI) (/ k 2))) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (11 enodes) * [exit]simplify: Simplified to (* (pow (* n PI) (/ k 2)) (sqrt k)) * [exit]simplify: Simplified to (* (pow (* n PI) (/ k 2)) (sqrt k)) * * * * [misc]progress: [ 88 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (+ (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log n) 2)))) (+ (exp (* 1/2 (+ (log n) (log PI)))) (+ (* 1/2 (* k (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))) (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log n) (log PI))))) (+ (* 1/2 (* k (* (log n) (exp (* 1/2 (+ (log n) (log PI))))))) (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))))))) (pow 2 (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (43 enodes) * * [misc]simplify: iters left: 5 (116 enodes) * * [misc]simplify: iters left: 4 (337 enodes) * [exit]simplify: Simplified to (/ (+ (fma (* (* (pow n 1/2) (pow PI 1/2)) (* (log n) (log n))) (* k (* k 1/8)) (fma (* (log PI) (* 1/2 k)) (* (pow n 1/2) (pow PI 1/2)) (* (pow n 1/2) (pow PI 1/2)))) (fma 1/4 (* (log n) (* (* (pow n 1/2) (pow PI 1/2)) (* (* k k) (log PI)))) (fma (* k (* k 1/8)) (* (* (pow n 1/2) (pow PI 1/2)) (* (log PI) (log PI))) (* (* (log n) (* 1/2 k)) (* (pow n 1/2) (pow PI 1/2)))))) (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))) * * * * [misc]progress: [ 89 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (+ k 1)))) (pow 2 (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (49 enodes) * * [misc]simplify: iters left: 4 (101 enodes) * * [misc]simplify: iters left: 3 (309 enodes) * [exit]simplify: Simplified to (* (/ (pow 2 (/ (- 1 k) 2)) (sqrt k)) (exp (* (+ (log n) (log PI)) (fma 1/2 k 1/2)))) * * * * [misc]progress: [ 90 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))) (pow 2 (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (46 enodes) * * [misc]simplify: iters left: 4 (91 enodes) * * [misc]simplify: iters left: 3 (333 enodes) * [exit]simplify: Simplified to (/ (pow (exp (* (- 1 k) 1/2)) (+ (+ (log PI) 0) (log n))) (/ (sqrt k) (pow 2 (/ (- 1 k) 2)))) * * * * [misc]progress: [ 91 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (+ (* 1/2 (* k (* (sqrt 2) (* (log 2) (exp (* 1/2 (+ (log n) (log PI)))))))) (+ (* 1/8 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log 2) 2))))) (+ (* 1/4 (* (pow k 2) (* (sqrt 2) (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))))) (+ (* 1/2 (* k (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (+ (* 1/8 (* (pow k 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))) (+ (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))) (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (* (sqrt 2) (log n)))))) (+ (* 1/4 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (* (log 2) (log PI)))))) (+ (* 1/8 (* (pow k 2) (* (sqrt 2) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log PI)))))))) (* 1/2 (* k (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI))))))))))))))))) (sqrt k)) * * [misc]simplify: iters left: 6 (68 enodes) * * [misc]simplify: iters left: 5 (194 enodes) * [exit]simplify: Simplified to (/ (+ (+ (fma (* (* (* (sqrt 2) k) (log 2)) (pow (exp 1/2) (+ (log PI) (log n)))) 1/2 (* (* (* k k) (pow (exp 1/2) (+ (log PI) (log n)))) (* (* (sqrt 2) (* (log 2) (log 2))) 1/8))) (fma (* (* 1/4 k) k) (* (* (* (log n) (sqrt 2)) (log PI)) (pow (exp 1/2) (+ (log PI) (log n)))) (* (* 1/2 (* (sqrt 2) k)) (* (pow (exp 1/2) (+ (log PI) (log n))) (log PI))))) (+ (+ (fma 1/8 (* (* (* (* k k) (sqrt 2)) (* (log PI) (log PI))) (pow (exp 1/2) (+ (log PI) (log n)))) (* (sqrt 2) (pow (exp 1/2) (+ (log PI) (log n))))) (* (* (* 1/4 k) k) (* (pow (exp 1/2) (+ (log PI) (log n))) (* (* (log 2) (sqrt 2)) (log n))))) (fma (* (* (* k k) (pow (exp 1/2) (+ (log PI) (log n)))) (* (* (log PI) (log 2)) (sqrt 2))) 1/4 (fma (* 1/8 (* k k)) (* (* (* (log n) (sqrt 2)) (log n)) (pow (exp 1/2) (+ (log PI) (log n)))) (* (* (* k 1/2) (* (log n) (sqrt 2))) (pow (exp 1/2) (+ (log PI) (log n)))))))) (sqrt k)) * * * * [misc]progress: [ 92 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (+ k 1)))) (exp (* 1/2 (* (+ k 1) (log 2))))) (sqrt k)) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (128 enodes) * * [misc]simplify: iters left: 3 (449 enodes) * [exit]simplify: Simplified to (/ (exp (fma (fma 1/2 k 1/2) (+ (log n) (log PI)) (* (log 2) (fma 1/2 k 1/2)))) (sqrt k)) * * * * [misc]progress: [ 93 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) (sqrt k)) * * [misc]simplify: iters left: 6 (23 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (120 enodes) * * [misc]simplify: iters left: 3 (466 enodes) * [exit]simplify: Simplified to (/ (pow (exp (* (- 1 k) 1/2)) (+ (+ 0 (log PI)) (log n))) (/ (sqrt k) (pow (pow 2 1/2) (- 1 k)))) * * * * [misc]progress: [ 94 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * * [misc]simplify: iters left: 1 (37 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 95 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * * [misc]simplify: iters left: 1 (37 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 96 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (pow (* n PI) (/ (- 1 k) 2)) (pow 2 (/ (- 1 k) 2))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * * [misc]simplify: iters left: 2 (36 enodes) * * [misc]simplify: iters left: 1 (37 enodes) * [exit]simplify: Simplified to (/ (pow 2 (/ (- 1 k) 2)) (/ (sqrt k) (pow (* PI n) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 97 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (- (+ (* +nan.0 (* k (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI))))) (- (+ (* +nan.0 (* (pow k 2) (* (log 2) (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI))))))))) (- (+ (* +nan.0 (* k (* (sqrt 2) (* (log 2) (exp (* 1/2 (+ (log n) (log PI)))))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (pow (log n) 2) (exp (* 1/2 (+ (log n) (log PI)))))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (log 2) (* (sqrt 2) (log PI)))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (log 2) (exp (* 1/2 (+ (log n) (log PI)))))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (log n) (* (exp (* 1/2 (+ (log n) (log PI)))) (log PI)))))) (- (+ (* +nan.0 (* k (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (+ (* +nan.0 (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI)))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (pow (log PI) 2))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (log n))))) (- (+ (* +nan.0 (* (pow k 2) (* (sqrt 2) (exp (* 1/2 (+ (log n) (log PI))))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/2 (+ (log n) (log PI)))) (* (sqrt 2) (pow (log 2) 2))))) (- (* +nan.0 (* k (* (sqrt 2) (* (log n) (exp (* 1/2 (+ (log n) (log PI))))))))))))))))))))))))))))))))))))) * * * * [misc]progress: [ 98 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (+ k 1)))) (exp (* 1/2 (* (+ k 1) (log 2))))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (+ k 1)))) (exp (* 1/2 (* (+ k 1) (log 2))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (- (log PI) (log (/ 1 n))) (+ k 1)))) (exp (* 1/2 (* (+ k 1) (log 2))))) k))))))) * * * * [misc]progress: [ 99 / 99 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) k)) (- (+ (* +nan.0 (/ (* (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k)))) (exp (* 1/2 (* (log 2) (- 1 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* 1/2 (* (log 2) (- 1 k)))) (exp (* 1/2 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1 k))))) (pow k 3)))))))) * * * [misc]progress: adding candidates to table * [misc]progress: [Phase 3 of 3] Extracting. * * [misc]regime-changes: Finding splitpoints for: (# # # # # # # # # # # #) * [misc]regimes: Found splitpoints: (#s(sp 0 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) +nan.0)) , with alts (#) * [enter]simplify: Simplifying (sqrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * [enter]simplify: Simplifying (sqrt (* n PI)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (5 enodes) * [exit]simplify: Simplified to (sqrt (* PI n)) * [exit]simplify: Simplified to (sqrt (* PI n)) * * * * [misc]points: Sampling 8000 additional inputs, on iter 0 have 0 / 8000 * * * * [misc]points: Computing exacts on every 500 of 8000 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 250 of 8000 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 125 of 8000 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 62 of 8000 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 31 of 8000 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 15 of 8000 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 7 of 8000 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 8000 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 8000 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 6497 additional inputs, on iter 1 have 1503 / 8000 * * * * [misc]points: Computing exacts on every 406 of 6497 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 203 of 6497 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 101 of 6497 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 50 of 6497 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 25 of 6497 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 12 of 6497 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 6497 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 6497 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 6497 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 5227 additional inputs, on iter 2 have 2773 / 8000 * * * * [misc]points: Computing exacts on every 326 of 5227 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 163 of 5227 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 81 of 5227 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 40 of 5227 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 20 of 5227 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 10 of 5227 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 5227 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 5227 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 5227 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 4212 additional inputs, on iter 3 have 3788 / 8000 * * * * [misc]points: Computing exacts on every 263 of 4212 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 131 of 4212 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 65 of 4212 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 32 of 4212 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 16 of 4212 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 8 of 4212 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 4212 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 4212 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 4212 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 3382 additional inputs, on iter 4 have 4618 / 8000 * * * * [misc]points: Computing exacts on every 211 of 3382 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 105 of 3382 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 52 of 3382 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 26 of 3382 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 13 of 3382 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 3382 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 3382 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 3382 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 2788 additional inputs, on iter 5 have 5212 / 8000 * * * * [misc]points: Computing exacts on every 174 of 2788 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 87 of 2788 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 43 of 2788 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 21 of 2788 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 10 of 2788 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 2788 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 2788 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 2788 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 2254 additional inputs, on iter 6 have 5746 / 8000 * * * * [misc]points: Computing exacts on every 140 of 2254 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 70 of 2254 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 35 of 2254 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 17 of 2254 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 8 of 2254 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 2254 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 2254 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 2254 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 1833 additional inputs, on iter 7 have 6167 / 8000 * * * * [misc]points: Computing exacts on every 114 of 1833 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 57 of 1833 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 28 of 1833 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 14 of 1833 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 7 of 1833 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 1833 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 1833 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 1492 additional inputs, on iter 8 have 6508 / 8000 * * * * [misc]points: Computing exacts on every 93 of 1492 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 46 of 1492 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 23 of 1492 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 11 of 1492 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 1492 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 1492 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 1492 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 1215 additional inputs, on iter 9 have 6785 / 8000 * * * * [misc]points: Computing exacts on every 75 of 1215 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 37 of 1215 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 18 of 1215 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 9 of 1215 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 1215 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 1215 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 1215 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 1004 additional inputs, on iter 10 have 6996 / 8000 * * * * [misc]points: Computing exacts on every 62 of 1004 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 31 of 1004 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 15 of 1004 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 7 of 1004 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 1004 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 1004 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 822 additional inputs, on iter 11 have 7178 / 8000 * * * * [misc]points: Computing exacts on every 51 of 822 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 25 of 822 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 12 of 822 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 822 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 822 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 822 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 667 additional inputs, on iter 12 have 7333 / 8000 * * * * [misc]points: Computing exacts on every 41 of 667 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 20 of 667 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 10 of 667 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 667 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 667 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 667 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 544 additional inputs, on iter 13 have 7456 / 8000 * * * * [misc]points: Computing exacts on every 34 of 544 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 17 of 544 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 8 of 544 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 544 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 544 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 544 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 421 additional inputs, on iter 14 have 7579 / 8000 * * * * [misc]points: Computing exacts on every 26 of 421 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 13 of 421 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 421 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 421 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 421 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 350 additional inputs, on iter 15 have 7650 / 8000 * * * * [misc]points: Computing exacts on every 21 of 350 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 10 of 350 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 350 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 350 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 350 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 281 additional inputs, on iter 16 have 7719 / 8000 * * * * [misc]points: Computing exacts on every 17 of 281 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 8 of 281 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 281 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 281 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 281 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 221 additional inputs, on iter 17 have 7779 / 8000 * * * * [misc]points: Computing exacts on every 13 of 221 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 221 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 221 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 221 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 164 additional inputs, on iter 18 have 7836 / 8000 * * * * [misc]points: Computing exacts on every 10 of 164 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 164 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 164 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 164 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 132 additional inputs, on iter 19 have 7868 / 8000 * * * * [misc]points: Computing exacts on every 8 of 132 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 132 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 132 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 132 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 103 additional inputs, on iter 20 have 7897 / 8000 * * * * [misc]points: Computing exacts on every 6 of 103 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 103 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 103 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 76 additional inputs, on iter 21 have 7924 / 8000 * * * * [misc]points: Computing exacts on every 4 of 76 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 76 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 76 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 65 additional inputs, on iter 22 have 7935 / 8000 * * * * [misc]points: Computing exacts on every 4 of 65 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 65 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 65 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 55 additional inputs, on iter 23 have 7945 / 8000 * * * * [misc]points: Computing exacts on every 3 of 55 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 55 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 24 have 7955 / 8000 * * * * [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 36 additional inputs, on iter 25 have 7964 / 8000 * * * * [misc]points: Computing exacts on every 2 of 36 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 36 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 26 additional inputs, on iter 26 have 7974 / 8000 * * * * [misc]points: Computing exacts for 26 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 21 additional inputs, on iter 27 have 7979 / 8000 * * * * [misc]points: Computing exacts for 21 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 15 additional inputs, on iter 28 have 7985 / 8000 * * * * [misc]points: Computing exacts for 15 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 11 additional inputs, on iter 29 have 7989 / 8000 * * * * [misc]points: Computing exacts for 11 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 10 additional inputs, on iter 30 have 7990 / 8000 * * * * [misc]points: Computing exacts for 10 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 9 additional inputs, on iter 31 have 7991 / 8000 * * * * [misc]points: Computing exacts for 9 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 8 additional inputs, on iter 32 have 7992 / 8000 * * * * [misc]points: Computing exacts for 8 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 33 have 7994 / 8000 * * * * [misc]points: Computing exacts for 6 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 34 have 7996 / 8000 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 35 have 7996 / 8000 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 36 have 7996 / 8000 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 37 have 7997 / 8000 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 38 have 7997 / 8000 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 39 have 7998 / 8000 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 40 have 7999 / 8000 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [exit]points: Sampled 8000 points with exact outputs