* [misc]progress: [Phase 1 of 3] Setting up. * * * [misc]progress: [1/2] Preparing points * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 * * * * [misc]points: Computing exacts on every 16 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 64 * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Setting MPFR precision to 576 * * * * [misc]points: Computing exacts on every 8 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 320 * * * * [misc]points: Setting MPFR precision to 576 * * * * [misc]points: Setting MPFR precision to 832 * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Computing exacts on every 4 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 832 * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Computing exacts on every 2 of 256 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 832 * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts 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 203 additional inputs, on iter 1 have 53 / 256 * * * * [misc]points: Computing exacts on every 12 of 203 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 203 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 203 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 203 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 165 additional inputs, on iter 2 have 91 / 256 * * * * [misc]points: Computing exacts on every 10 of 165 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 165 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 165 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 165 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 136 additional inputs, on iter 3 have 120 / 256 * * * * [misc]points: Computing exacts on every 8 of 136 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 136 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 136 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 136 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 110 additional inputs, on iter 4 have 146 / 256 * * * * [misc]points: Computing exacts on every 6 of 110 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 110 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 110 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 85 additional inputs, on iter 5 have 171 / 256 * * * * [misc]points: Computing exacts on every 5 of 85 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 85 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 85 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 68 additional inputs, on iter 6 have 188 / 256 * * * * [misc]points: Computing exacts on every 4 of 68 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 2 of 68 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 68 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 55 additional inputs, on iter 7 have 201 / 256 * * * * [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 42 additional inputs, on iter 8 have 214 / 256 * * * * [misc]points: Computing exacts on every 2 of 42 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 42 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 40 additional inputs, on iter 9 have 216 / 256 * * * * [misc]points: Computing exacts on every 2 of 40 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 40 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 29 additional inputs, on iter 10 have 227 / 256 * * * * [misc]points: Computing exacts for 29 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 20 additional inputs, on iter 11 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 15 additional inputs, on iter 12 have 241 / 256 * * * * [misc]points: Computing exacts for 15 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 14 additional inputs, on iter 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 10 additional inputs, on iter 14 have 246 / 256 * * * * [misc]points: Computing exacts for 10 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 6 additional inputs, on iter 15 have 250 / 256 * * * * [misc]points: Computing exacts for 6 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 5 additional inputs, on iter 16 have 251 / 256 * * * * [misc]points: Computing exacts for 5 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 17 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 18 have 254 / 256 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 19 have 254 / 256 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 20 have 254 / 256 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 21 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 * * * * [misc]points: Sampling 4 additional inputs, on iter 22 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 257 points with exact outputs * * * [misc]progress: [2/2] Setting up program. * [misc]progress: [Phase 2 of 3] Improving. * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* 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 1) * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1) * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1 1) * [misc]approximate: Taking taylor expansion of (* n (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 2 / 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 0) 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 in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 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 (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 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 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 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 (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 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 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))))) * [misc]approximate: Taking taylor expansion of (pow (* (/ 1 n) (* PI 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 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [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 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 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 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) * [misc]approximate: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 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 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 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]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 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 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) * * * * [misc]progress: [ 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 0) 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 in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* n PI)) 1/2) +nan.0) into (* +nan.0 (sqrt (* n (* 2 PI)))) * [misc]taylor: Taking taylor expansion of (/ (pow (* n (* PI 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 (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 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 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* n (* PI 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 (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 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 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (sqrt k)) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (+ (* 0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))) (+ (* +nan.0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt k)) (+ (* (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))))) (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))) (* 0 (/ 0 (sqrt k))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2))))))))) (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))))) (+ (* +nan.0 (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))))) (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 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 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in k * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (/ 1 n) (* PI 2))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 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 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 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 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 n) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ 1 k))) (+ (* (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))) (* 0 (/ 0 (sqrt (/ 1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 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 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in k * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (/ 1 (- n)) (* PI 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]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 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 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 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 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (/ 1 (- n)) (* PI 2))) in n * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k * [misc]taylor: Taking taylor expansion of (/ -1 k) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ -1 1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 68 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * [exit]simplify: Simplified to (log (* (* PI n) 2)) * [exit]simplify: Simplified to (log (* (* PI n) 2)) * * * * [misc]progress: [ 3 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (35 enodes) * * [misc]simplify: iters left: 1 (45 enodes) * [exit]simplify: Simplified to (pow (exp 2) (* PI n)) * [exit]simplify: Simplified to (pow (exp 2) (* PI n)) * * * * [misc]progress: [ 4 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * [exit]simplify: Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2))) * [exit]simplify: Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2))) * [enter]simplify: Simplifying (cbrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (cbrt (* (* n 2) PI)) * [exit]simplify: Simplified to (cbrt (* (* n 2) PI)) * * * * [misc]progress: [ 5 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (203 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) 3) * [exit]simplify: Simplified to (pow (* (* PI n) 2) 3) * * * * [misc]progress: [ 6 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [enter]simplify: Simplifying (sqrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * * * * [misc]progress: [ 7 / 68 ] simplifiying candidate # * * * * [misc]progress: [ 8 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 9 / 68 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 68 ] 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 (141 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * * * * [misc]progress: [ 11 / 68 ] 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 (141 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * * * * [misc]progress: [ 12 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (62 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [exit]simplify: Simplified to (/ (- 1 k) 2) * * * * [misc]progress: [ 13 / 68 ] 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 (* 2 (* PI n)) (/ 1 2)) * [exit]simplify: Simplified to (pow (* 2 (* PI n)) (/ 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: [ 14 / 68 ] 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: [ 15 / 68 ] 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 (* (* n 2) PI) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (* (* n 2) PI) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 16 / 68 ] 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 (20 enodes) * [exit]simplify: Simplified to (* (* PI n) 2) * [exit]simplify: Simplified to (* (* PI n) 2) * * * * [misc]progress: [ 17 / 68 ] 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: [ 18 / 68 ] 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 2) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* 2 PI) (/ (- 1 k) 2)) * * * * [misc]progress: [ 19 / 68 ] simplifiying candidate # * * * * [misc]progress: [ 20 / 68 ] 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 (232 enodes) * [exit]simplify: Simplified to (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) * [exit]simplify: Simplified to (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) * * * * [misc]progress: [ 21 / 68 ] 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 (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (* (* n 2) PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 22 / 68 ] 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 (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 23 / 68 ] 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 (* (* n 2) PI) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (* (* n 2) PI) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 24 / 68 ] 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 (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* n 2) PI) (/ (- 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 (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) * * * * [misc]progress: [ 25 / 68 ] simplifiying candidate # * * * * [misc]progress: [ 26 / 68 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 68 ] 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 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) (log (sqrt k))) * * * * [misc]progress: [ 28 / 68 ] 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 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) (log (sqrt k))) * * * * [misc]progress: [ 29 / 68 ] 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 (49 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (286 enodes) * [exit]simplify: Simplified to (- (* (log (* 2 (* PI n))) (/ (- 1 k) 2)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (* 2 (* PI n))) (/ (- 1 k) 2)) (log (sqrt k))) * * * * [misc]progress: [ 30 / 68 ] 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 (61 enodes) * * [misc]simplify: iters left: 2 (133 enodes) * * [misc]simplify: iters left: 1 (394 enodes) * [exit]simplify: Simplified to (- (/ (log (* 2 (* PI n))) (/ 2 (- 1 k))) (log (sqrt k))) * [exit]simplify: Simplified to (- (/ (log (* 2 (* PI n))) (/ 2 (- 1 k))) (log (sqrt k))) * * * * [misc]progress: [ 31 / 68 ] 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: [ 32 / 68 ] 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 (73 enodes) * * [misc]simplify: iters left: 3 (133 enodes) * * [misc]simplify: iters left: 2 (215 enodes) * * [misc]simplify: iters left: 1 (353 enodes) * [exit]simplify: Simplified to (* (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow (* (* PI n) 2) (/ (- 1 k) 2))) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (* k (sqrt k)))) * [exit]simplify: Simplified to (* (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow (* (* PI n) 2) (/ (- 1 k) 2))) (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (* k (sqrt k)))) * * * * [misc]progress: [ 33 / 68 ] 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 (38 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (/ (- 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: [ 34 / 68 ] 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 (61 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (156 enodes) * [exit]simplify: Simplified to (/ (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* (* n 2) PI) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 35 / 68 ] 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: [ 36 / 68 ] 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 (* (* n 2) PI) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (- (pow (* (* n 2) PI) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (- (sqrt k)) * * [misc]simplify: iters left: 3 (3 enodes) * [exit]simplify: Simplified to (- (sqrt k)) * [exit]simplify: Simplified to (- (sqrt k)) * * * * [misc]progress: [ 37 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [enter]simplify: Simplifying (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k))) * * * * [misc]progress: [ 38 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) * [enter]simplify: Simplifying (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (22 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k))) * * * * [misc]progress: [ 39 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ (- 1 k) 2)) 1) * * [misc]simplify: iters left: 6 (8 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (20 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [enter]simplify: Simplifying (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 40 / 68 ] 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 (57 enodes) * * [misc]simplify: iters left: 2 (60 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 (38 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 41 / 68 ] 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))) (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (/ (cbrt (pow (* PI (* n 2)) (/ (- 1 k) 2))) (sqrt (sqrt k)))) * [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 (38 enodes) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 42 / 68 ] 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 (59 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 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: [ 43 / 68 ] 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 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (cbrt (sqrt k))) * * * * [misc]progress: [ 44 / 68 ] 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 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 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 (38 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k))) * * * * [misc]progress: [ 45 / 68 ] 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: [ 46 / 68 ] 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: [ 47 / 68 ] 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: [ 48 / 68 ] 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: [ 49 / 68 ] simplifiying candidate # * * * * [misc]progress: [ 50 / 68 ] 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: [ 51 / 68 ] 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 (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 52 / 68 ] 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 (* (* 2 PI) n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 53 / 68 ] 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: [ 54 / 68 ] 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 (* (* n 2) PI) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* (* n 2) PI) (/ (- 1 k) 2)) * * * * [misc]progress: [ 55 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2))) * * * * [misc]progress: [ 56 / 68 ] 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 (* n (* PI 2)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 57 / 68 ] 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 (* n (* PI 2)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 58 / 68 ] 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 (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (/ (sqrt k) (pow (* PI (* n 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 59 / 68 ] 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 (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) * [exit]simplify: Simplified to (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) * * * * [misc]progress: [ 60 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 61 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 62 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 63 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))))) (sqrt k)) * * [misc]simplify: iters left: 6 (39 enodes) * * [misc]simplify: iters left: 5 (110 enodes) * * [misc]simplify: iters left: 4 (354 enodes) * [exit]simplify: Simplified to (/ (+ (+ (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* k k) 1/8)) (+ (* (log (* PI 2)) (log (* PI 2))) (* (log n) (log n))))) (- (* (* (log (* PI 2)) (* (* k k) (log n))) (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4))) (* 1/2 (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) k)) (+ (log (* PI 2)) (log n)))))) (sqrt k)) * * * * [misc]progress: [ 64 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k)) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (259 enodes) * [exit]simplify: Simplified to (/ (* (pow (* PI 2) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (sqrt k)) * * * * [misc]progress: [ 65 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k)) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (78 enodes) * * [misc]simplify: iters left: 3 (269 enodes) * [exit]simplify: Simplified to (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* PI -2)) (log (/ -1 n)))) (sqrt k)) * * * * [misc]progress: [ 66 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * * * * [misc]progress: [ 67 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))) * * * * [misc]progress: [ 68 / 68 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))) * * * [misc]progress: 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) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 1) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 1) * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt k)) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* (- +nan.0) k) (+ (- +nan.0) (* +nan.0 (/ 1 k)))) into (- (+ +nan.0 (- (+ (* +nan.0 k) (- (* +nan.0 (/ 1 k))))))) * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 2)) (+ (* (- +nan.0) (/ 1 k)) +nan.0)) into (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) * [misc]approximate: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in (k) around 0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (- +nan.0) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 1) * [misc]approximate: Taking taylor expansion of (* (* 2 PI) n) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 1) (* 0 0))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 1) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) -1) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 3 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt k)) in n * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k)) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]backup-simplify: Simplify (* +nan.0 (pow (* 2 (* n PI)) 1/2)) into (* +nan.0 (sqrt (* n (* 2 PI)))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (sqrt (* n (* 2 PI)))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (sqrt (* n (* 2 PI))) in n * [misc]taylor: Taking taylor expansion of (* n (* 2 PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (* 2 PI) (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 n)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI))))) * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI)))))) (* (- +nan.0) (pow (* 2 (* n PI)) 1/2))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))) in n * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (* 2 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* n PI)) (sqrt 2)) in n * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log (* 2 PI)) (log n))) into (* (+ (log (* 2 PI)) (log n)) (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 (* (+ (log (* 2 PI)) (log n)) (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* 0 (sqrt 2)) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 PI)) * [misc]backup-simplify: Simplify (- (* +nan.0 PI)) into (- (* +nan.0 PI)) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 n))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* n (* 2 PI))) (pow (log (* 2 (* n PI))) 2))) * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 (* 1/8 (* (sqrt (* n (* 2 PI))) (pow (log (* 2 (* n PI))) 2)))) (+ (* (- +nan.0) (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI)))))) (* (- +nan.0) (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI)))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* n PI)) (* (sqrt 2) (log (* 2 (* n PI))))) in n * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (* 2 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))))) in n * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* n PI)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n * [misc]taylor: Taking taylor expansion of (exp (* 2 (log (log (* 2 (* n PI)))))) in n * [misc]taylor: Taking taylor expansion of (* 2 (log (log (* 2 (* n PI))))) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (log (log (* 2 (* n PI)))) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (* 2 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (log (+ (log (* 2 PI)) (log n))) into (log (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 2 (log (+ (log (* 2 PI)) (log n)))) into (* 2 (log (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 2 (log (+ (log (* 2 PI)) (log n))))) into (pow (+ (log (* 2 PI)) (log n)) 2) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt (* n PI)) (sqrt 2)))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt (* n PI)) (sqrt 2))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (* (sqrt (* n PI)) (sqrt 2)) in n * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log (* 2 PI)) (log n))) into (* (+ (log (* 2 PI)) (log n)) (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 (* (+ (log (* 2 PI)) (log n)) (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log (* 2 PI)) (log n)) 2)) into (* (pow (+ (log (* 2 PI)) (log n)) 2) (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 (* (pow (+ (log (* 2 PI)) (log n)) 2) (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (* 0 (sqrt 2)) into 0 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (* +nan.0 PI) (* (+ (log (* 2 PI)) (log n)) (sqrt 2)))) into (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))) (* 0 0)) into (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))) * [misc]backup-simplify: Simplify (+ (* 0 0) (* (* +nan.0 PI) (sqrt 2))) into (- (* +nan.0 (* PI (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* PI (sqrt 2))))) (* 0 0)) into (- (* +nan.0 (* PI (sqrt 2)))) * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* PI (sqrt 2))))) into (- (* +nan.0 (* PI (sqrt 2)))) * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))) (- (* +nan.0 (* PI (sqrt 2))))) into (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2)))))))))) into (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) into (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) * [misc]backup-simplify: Simplify (+ (* +nan.0 (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (pow PI 2))) * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI 2))) into (- (* +nan.0 (pow PI 2))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (pow PI 2))) (* (pow n 2) (/ 1 k))) (+ (* (- (+ (* +nan.0 (* PI (sqrt 2))) (- (+ (* +nan.0 (* PI (* (log (* 2 PI)) (sqrt 2)))) (- (* +nan.0 (* PI (* (log n) (sqrt 2))))))))) (* n 1)) (* (- (* +nan.0 PI)) (* n (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* n (* PI (sqrt 2)))) (- (+ (* +nan.0 (/ (* n PI) k)) (- (+ (* +nan.0 (* n (* PI (* (log n) (sqrt 2))))) (- (* +nan.0 (* n (* PI (* (log (* 2 PI)) (sqrt 2)))))))))))))) * [misc]approximate: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 1) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) into (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* (- +nan.0) (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- (log (* 2 PI)) (log n)) 0) (* 0 (- 1 (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* (- +nan.0) 0) (* (- +nan.0) (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))) * [misc]approximate: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) -1) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (sqrt (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (/ 1 +nan.0) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of -2 in n * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* (- +nan.0) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of -2 in n * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (+ 1 (/ 1 k)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (+ (* (- +nan.0) 0) (* (- +nan.0) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) in n * [misc]taylor: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n * [misc]taylor: Taking taylor expansion of +nan.0 in n * [misc]backup-simplify: Simplify +nan.0 into +nan.0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of -2 in n * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))) * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 1) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))))) * [misc]approximate: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 1) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 1) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) * [misc]approximate: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) -1) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) -1) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (- 1/2) * * [misc]simplify: iters left: 2 (2 enodes) * [exit]simplify: Simplified to (- 1/2) * [exit]simplify: Simplified to (- 1/2) * * * * [misc]progress: [ 3 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (- 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (- 1) * [exit]simplify: Simplified to (- 1) * * * * [misc]progress: [ 4 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 5 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (sqrt k))) * * [misc]simplify: iters left: 4 (4 enodes) * [exit]simplify: Simplified to (- (log (sqrt k))) * [exit]simplify: Simplified to (- (log (sqrt k))) * * * * [misc]progress: [ 6 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (11 enodes) * * [misc]simplify: iters left: 2 (12 enodes) * * [misc]simplify: iters left: 1 (16 enodes) * [exit]simplify: Simplified to (- (log (sqrt k))) * [exit]simplify: Simplified to (- (log (sqrt k))) * * * * [misc]progress: [ 7 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (exp (/ 1 (sqrt k))) * [exit]simplify: Simplified to (exp (/ 1 (sqrt k))) * * * * [misc]progress: [ 8 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (8 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) * [enter]simplify: Simplifying (cbrt (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (cbrt (/ 1 (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ 1 (sqrt k))) * * * * [misc]progress: [ 9 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (36 enodes) * * [misc]simplify: iters left: 2 (60 enodes) * * [misc]simplify: iters left: 1 (79 enodes) * [exit]simplify: Simplified to (/ (/ 1 k) (sqrt k)) * [exit]simplify: Simplified to (/ (/ 1 k) (sqrt k)) * * * * [misc]progress: [ 10 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * [enter]simplify: Simplifying (sqrt (/ 1 (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ 1 (sqrt k))) * * * * [misc]progress: [ 11 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (- 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (- 1) * [exit]simplify: Simplified to (- 1) * [enter]simplify: Simplifying (- (sqrt k)) * * [misc]simplify: iters left: 3 (3 enodes) * [exit]simplify: Simplified to (- (sqrt k)) * [exit]simplify: Simplified to (- (sqrt k)) * * * * [misc]progress: [ 12 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 13 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt k)) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 14 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt k) 1) * * [misc]simplify: iters left: 3 (4 enodes) * * [misc]simplify: iters left: 2 (6 enodes) * * [misc]simplify: iters left: 1 (8 enodes) * [exit]simplify: Simplified to (sqrt k) * [exit]simplify: Simplified to (sqrt k) * * * * [misc]progress: [ 15 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (10 enodes) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * [exit]simplify: Simplified to (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) * * * * [misc]progress: [ 16 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) * * [misc]simplify: iters left: 4 (5 enodes) * * [misc]simplify: iters left: 3 (7 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) * * * * [misc]progress: [ 17 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 1) * * [misc]simplify: iters left: 2 (2 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to 1 * [exit]simplify: Simplified to 1 * * * * [misc]progress: [ 18 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 19 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (40 enodes) * [exit]simplify: Simplified to (log (* (* n PI) 2)) * [exit]simplify: Simplified to (log (* (* n PI) 2)) * * * * [misc]progress: [ 20 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * * [misc]simplify: iters left: 1 (40 enodes) * [exit]simplify: Simplified to (pow (exp PI) (* n 2)) * [exit]simplify: Simplified to (pow (exp PI) (* n 2)) * * * * [misc]progress: [ 21 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * [exit]simplify: Simplified to (* (cbrt (* (* n PI) 2)) (cbrt (* (* n PI) 2))) * [exit]simplify: Simplified to (* (cbrt (* (* n PI) 2)) (cbrt (* (* n PI) 2))) * [enter]simplify: Simplifying (cbrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (cbrt (* 2 (* n PI))) * [exit]simplify: Simplified to (cbrt (* 2 (* n PI))) * * * * [misc]progress: [ 22 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n)) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * [exit]simplify: Simplified to (pow (* (* n 2) PI) 3) * [exit]simplify: Simplified to (pow (* (* n 2) PI) 3) * * * * [misc]progress: [ 23 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* 2 (* n PI))) * [exit]simplify: Simplified to (sqrt (* 2 (* n PI))) * [enter]simplify: Simplifying (sqrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* 2 (* n PI))) * [exit]simplify: Simplified to (sqrt (* 2 (* n PI))) * * * * [misc]progress: [ 24 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 25 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* PI n) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [exit]simplify: Simplified to (* n PI) * * * * [misc]progress: [ 26 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 27 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 28 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * [exit]simplify: Simplified to (- (/ (log (* n (* PI 2))) (/ 2 (- 1 k))) (log (sqrt k))) * [exit]simplify: Simplified to (- (/ (log (* n (* PI 2))) (/ 2 (- 1 k))) (log (sqrt k))) * * * * [misc]progress: [ 29 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (64 enodes) * * [misc]simplify: iters left: 3 (159 enodes) * [exit]simplify: Simplified to (- (/ (log (* n (* PI 2))) (/ 2 (- 1 k))) (log (sqrt k))) * [exit]simplify: Simplified to (- (/ (log (* n (* PI 2))) (/ 2 (- 1 k))) (log (sqrt k))) * * * * [misc]progress: [ 30 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (49 enodes) * * [misc]simplify: iters left: 3 (96 enodes) * * [misc]simplify: iters left: 2 (286 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* n (* PI 2)))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* n (* PI 2)))) (log (sqrt k))) * * * * [misc]progress: [ 31 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* n (* PI 2)))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* n (* PI 2)))) (log (sqrt k))) * * * * [misc]progress: [ 32 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (187 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* n (* PI 2)))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* n (* PI 2)))) (log (sqrt k))) * * * * [misc]progress: [ 33 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (116 enodes) * * [misc]simplify: iters left: 2 (418 enodes) * [exit]simplify: Simplified to (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) * [exit]simplify: Simplified to (- (/ (log (* (* n 2) PI)) (/ 2 (- 1 k))) (log (sqrt k))) * * * * [misc]progress: [ 34 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (56 enodes) * * [misc]simplify: iters left: 3 (102 enodes) * * [misc]simplify: iters left: 2 (196 enodes) * [exit]simplify: Simplified to (- (* (log (* PI (* n 2))) (/ (- 1 k) 2)) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (* PI (* n 2))) (/ (- 1 k) 2)) (log (sqrt k))) * * * * [misc]progress: [ 35 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (46 enodes) * * [misc]simplify: iters left: 3 (55 enodes) * * [misc]simplify: iters left: 2 (59 enodes) * * [misc]simplify: iters left: 1 (68 enodes) * [exit]simplify: Simplified to (pow (exp (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (exp (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 36 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (97 enodes) * * [misc]simplify: iters left: 3 (179 enodes) * * [misc]simplify: iters left: 2 (347 enodes) * [exit]simplify: Simplified to (* (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (* k (sqrt k)))) * [exit]simplify: Simplified to (* (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (* k (sqrt k)))) * * * * [misc]progress: [ 37 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (45 enodes) * * [misc]simplify: iters left: 3 (54 enodes) * * [misc]simplify: iters left: 2 (58 enodes) * * [misc]simplify: iters left: 1 (65 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)))) * [enter]simplify: Simplifying (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (cbrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 38 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (94 enodes) * * [misc]simplify: iters left: 3 (202 enodes) * * [misc]simplify: iters left: 2 (465 enodes) * [exit]simplify: Simplified to (/ (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (/ (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow (* n (* PI 2)) (/ (- 1 k) 2))) (/ (* (sqrt k) k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))) * * * * [misc]progress: [ 39 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * [enter]simplify: Simplifying (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * [exit]simplify: Simplified to (sqrt (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k))) * * * * [misc]progress: [ 40 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (pow (* (* 2 PI) n) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ 1 2)) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ 1 2)) * [enter]simplify: Simplifying (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2))) * * [misc]simplify: iters left: 6 (10 enodes) * * [misc]simplify: iters left: 5 (15 enodes) * * [misc]simplify: iters left: 4 (21 enodes) * * [misc]simplify: iters left: 3 (22 enodes) * [exit]simplify: Simplified to (* (sqrt k) (pow (* 2 (* PI n)) (/ k 2))) * [exit]simplify: Simplified to (* (sqrt k) (pow (* 2 (* PI n)) (/ k 2))) * * * * [misc]progress: [ 41 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 42 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (40 enodes) * * [misc]simplify: iters left: 2 (44 enodes) * * [misc]simplify: iters left: 1 (51 enodes) * [exit]simplify: Simplified to (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 43 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (48 enodes) * * [misc]simplify: iters left: 3 (74 enodes) * * [misc]simplify: iters left: 2 (102 enodes) * * [misc]simplify: iters left: 1 (106 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2)))) (sqrt k)) * * * * [misc]progress: [ 44 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (53 enodes) * * [misc]simplify: iters left: 2 (57 enodes) * * [misc]simplify: iters left: 1 (64 enodes) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (sqrt k)) * * * * [misc]progress: [ 45 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) 1) * * [misc]simplify: iters left: 5 (5 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * [exit]simplify: Simplified to (/ 1 (sqrt k)) * * * * [misc]progress: [ 46 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (cbrt (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 47 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (sqrt (/ 1 (sqrt k))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 48 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 49 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* n (* PI 2)) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 50 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * * [misc]simplify: iters left: 2 (45 enodes) * * [misc]simplify: iters left: 1 (52 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) * * * * [misc]progress: [ 51 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ (- 1 k) 2)) * * * * [misc]progress: [ 52 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 53 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * * * * [misc]progress: [ 54 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * * * * [misc]progress: [ 55 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (62 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [exit]simplify: Simplified to (/ (- 1 k) 2) * * * * [misc]progress: [ 56 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ 1 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (22 enodes) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (/ 1 2)) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (/ 1 2)) * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * * [misc]simplify: iters left: 2 (20 enodes) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) * * * * [misc]progress: [ 57 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 58 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 59 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) 1) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (20 enodes) * [exit]simplify: Simplified to (* (* n PI) 2) * [exit]simplify: Simplified to (* (* n PI) 2) * * * * [misc]progress: [ 60 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (- 1 k)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (25 enodes) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (- 1 k)) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (- 1 k)) * * * * [misc]progress: [ 61 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* 2 PI) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * [exit]simplify: Simplified to (pow (* PI 2) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* PI 2) (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow n (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * * [misc]simplify: iters left: 2 (19 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * * * * [misc]progress: [ 62 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 63 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (232 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* PI 2) n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* PI 2) n))) * * * * [misc]progress: [ 64 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (exp (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (* (* PI 2) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 65 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 66 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (pow (pow (* PI (* n 2)) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (* PI (* n 2)) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 67 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 68 / 80 ] simplifiying candidate # * * * * [misc]progress: [ 69 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (+ +nan.0 (- (+ (* +nan.0 k) (- (* +nan.0 (/ 1 k))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 70 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 71 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (- (+ +nan.0 (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 2)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 72 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 73 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 74 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (52 enodes) * * [misc]simplify: iters left: 2 (56 enodes) * * [misc]simplify: iters left: 1 (63 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ (- 1 k) 2)) (sqrt k)) * * * * [misc]progress: [ 75 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) k)) (- (+ (* +nan.0 (* n (* PI (sqrt 2)))) (- (+ (* +nan.0 (/ (* n PI) k)) (- (+ (* +nan.0 (* n (* PI (* (log n) (sqrt 2))))) (- (* +nan.0 (* n (* PI (* (log (* 2 PI)) (sqrt 2)))))))))))))) * * * * [misc]progress: [ 76 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k))))))) * * * * [misc]progress: [ 77 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2)))))))) * * * * [misc]progress: [ 78 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k)))))) * * [misc]simplify: iters left: 6 (41 enodes) * * [misc]simplify: iters left: 5 (114 enodes) * * [misc]simplify: iters left: 4 (382 enodes) * [exit]simplify: Simplified to (/ (+ (* (* 1/8 (* (pow (* PI 2) 1/2) (* (pow n 1/2) (* k k)))) (+ (* (log (* PI 2)) (log (* PI 2))) (* (log n) (log n)))) (- (+ (* (pow (* PI 2) 1/2) (pow n 1/2)) (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4)) (* (* (log n) (* k k)) (log (* PI 2))))) (* (* (* (pow (* PI 2) 1/2) (* (pow n 1/2) k)) (+ (log (* PI 2)) (log n))) 1/2))) (sqrt k)) * * * * [misc]progress: [ 79 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (285 enodes) * [exit]simplify: Simplified to (/ (* (pow (* PI 2) (- 1/2 (* k 1/2))) (pow n (- 1/2 (* k 1/2)))) (sqrt k)) * * * * [misc]progress: [ 80 / 80 ] simplifiying candidate # * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (86 enodes) * * [misc]simplify: iters left: 3 (299 enodes) * [exit]simplify: Simplified to (/ (pow (pow (exp 1/2) (- 1 k)) (- (log (* PI -2)) (log (/ -1 n)))) (sqrt k)) * * * [misc]progress: 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 / 3 ] rewriting at (2 2 1) * * * * [misc]progress: [ 2 / 3 ] rewriting at (2) * * * * [misc]progress: [ 3 / 3 ] rewriting at (2 2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 3 ] generating series at (2 2 1) * [misc]approximate: Taking taylor expansion of (* (* 2 PI) n) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 1) (* 0 0))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 1) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) -1) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 2 / 3 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (pow k (- 1/2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2) (log k))) in n * [misc]taylor: Taking taylor expansion of (* (- 1/2) (log k)) in n * [misc]taylor: Taking taylor expansion of (- 1/2) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (log k) into (log k) * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (* -1/2 (log k)) into (* -1/2 (log k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (log k))) into (pow k -1/2) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow k (- 1/2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2) (log k))) in k * [misc]taylor: Taking taylor expansion of (* (- 1/2) (log k)) in k * [misc]taylor: Taking taylor expansion of (- 1/2) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) * [misc]backup-simplify: Simplify (* -1/2 (log k)) into (* -1/2 (log k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (log k))) into (pow k -1/2) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (pow k (- 1/2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2) (log k))) in k * [misc]taylor: Taking taylor expansion of (* (- 1/2) (log k)) in k * [misc]taylor: Taking taylor expansion of (- 1/2) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) * [misc]backup-simplify: Simplify (* -1/2 (log k)) into (* -1/2 (log k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (log k))) into (pow k -1/2) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]backup-simplify: Simplify (* (pow k -1/2) (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ (* n (* 2 PI)) k)) * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n (* 2 PI)) k)) in n * [misc]taylor: Taking taylor expansion of (/ (* n (* 2 PI)) k) in n * [misc]taylor: Taking taylor expansion of (* n (* 2 PI)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (/ (* 2 PI) k) into (* 2 (/ PI k)) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (* 2 (/ PI k)) (* 2 (sqrt 0))) into (* +nan.0 (/ PI k)) * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 n)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (/ -1 2) (+ (* 1/2 (/ 0 2)))) into -1/2 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI))))) * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 0 (log k))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow k -1/2) (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI)))))) (* 0 (pow (* 2 (* n PI)) 1/2))) into (- (* 1/2 (* (sqrt (/ (* n PI) k)) (* (sqrt 2) (log (* 2 (* n PI))))))) * [misc]taylor: Taking taylor expansion of (- (* 1/2 (* (sqrt (/ (* n PI) k)) (* (sqrt 2) (log (* 2 (* n PI))))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (sqrt (/ (* n PI) k)) (* (sqrt 2) (log (* 2 (* n PI)))))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ (* n PI) k)) (* (sqrt 2) (log (* 2 (* n PI))))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) 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 k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (/ PI k) into (/ PI k) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (/ PI k) (* 2 (sqrt 0))) into (* +nan.0 (/ PI k)) * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (* 2 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log (* 2 PI)) (log n))) into (* (+ (log (* 2 PI)) (log n)) (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 (* (+ (log (* 2 PI)) (log n)) (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* +nan.0 (/ PI k)) into (* +nan.0 (/ PI k)) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 n))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* 1/2 (/ 0 2)) (* -1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* n (* 2 PI))) (pow (log (* 2 (* n PI))) 2))) * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log k)) 0) into (log k) * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 0 0) (* 0 (log k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow k -1/2) (* 1/8 (* (sqrt (* n (* 2 PI))) (pow (log (* 2 (* n PI))) 2)))) (+ (* 0 (* -1/2 (* (sqrt (* n (* 2 PI))) (log (* 2 (* n PI)))))) (* 0 (pow (* 2 (* n PI)) 1/2)))) into (* 1/8 (* (sqrt (/ (* n PI) k)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) * [misc]taylor: Taking taylor expansion of (* 1/8 (* (sqrt (/ (* n PI) k)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)))) in n * [misc]taylor: Taking taylor expansion of 1/8 in n * [misc]backup-simplify: Simplify 1/8 into 1/8 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ (* n PI) k)) (* (sqrt 2) (pow (log (* 2 (* n PI))) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n * [misc]taylor: Taking taylor expansion of (/ (* n PI) k) 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 k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (/ PI k) into (/ PI k) * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ (/ PI k) (* 2 (sqrt 0))) into (* +nan.0 (/ PI k)) * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n * [misc]taylor: Taking taylor expansion of (sqrt 2) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 * [misc]taylor: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n * [misc]taylor: Taking taylor expansion of (exp (* 2 (log (log (* 2 (* n PI)))))) in n * [misc]taylor: Taking taylor expansion of (* 2 (log (log (* 2 (* n PI))))) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (log (log (* 2 (* n PI)))) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n PI) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 0 PI) into 0 * [misc]backup-simplify: Simplify (* 2 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (log (+ (log (* 2 PI)) (log n))) into (log (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 2 (log (+ (log (* 2 PI)) (log n)))) into (* 2 (log (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 2 (log (+ (log (* 2 PI)) (log n))))) into (pow (+ (log (* 2 PI)) (log n)) 2) * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log (* 2 PI)) (log n)) 2)) into (* (pow (+ (log (* 2 PI)) (log n)) 2) (sqrt 2)) * [misc]backup-simplify: Simplify (* 0 (* (pow (+ (log (* 2 PI)) (log n)) 2) (sqrt 2))) into 0 * [misc]backup-simplify: Simplify (* 1/8 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* (* +nan.0 (/ PI k)) (* (+ (log (* 2 PI)) (log n)) (sqrt 2)))) into (- (+ (* +nan.0 (/ (* PI (* (log (* 2 PI)) (sqrt 2))) k)) (- (* +nan.0 (/ (* PI (* (log n) (sqrt 2))) k))))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (* +nan.0 (/ (* PI (* (log (* 2 PI)) (sqrt 2))) k)) (- (* +nan.0 (/ (* PI (* (log n) (sqrt 2))) k)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* PI (* (log (* 2 PI)) (sqrt 2))) k)) (- (* +nan.0 (/ (* PI (* (log n) (sqrt 2))) k))))) * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (/ (* PI (* (log (* 2 PI)) (sqrt 2))) k)) (- (* +nan.0 (/ (* PI (* (log n) (sqrt 2))) k)))))) into (- (+ (* +nan.0 (/ (* PI (* (log (* 2 PI)) (sqrt 2))) k)) (- (* +nan.0 (/ (* PI (* (log n) (sqrt 2))) k))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (/ (* PI (* (log (* 2 PI)) (sqrt 2))) k)) (- (* +nan.0 (/ (* PI (* (log n) (sqrt 2))) k))))) into (- (+ (* +nan.0 (/ (* PI (* (log (* 2 PI)) (sqrt 2))) k)) (- (* +nan.0 (/ (* PI (* (log n) (sqrt 2))) k))))) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (* 2 (/ PI k)) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 (/ PI k)) 2) (+)) (* 2 0)) into (* +nan.0 (/ (pow PI 2) (pow k 2))) * [misc]backup-simplify: Simplify (* +nan.0 (/ (pow PI 2) (pow k 2))) into (* +nan.0 (/ (pow PI 2) (pow k 2))) * [misc]backup-simplify: Simplify (+ (* (* +nan.0 (/ (pow PI 2) (pow k 2))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (/ (* PI (* (log (* 2 PI)) (sqrt 2))) k)) (- (* +nan.0 (/ (* PI (* (log n) (sqrt 2))) k))))) (* n k)) (* (* +nan.0 (/ PI k)) (* n 1)))) into (- (+ (* +nan.0 (/ (* n PI) k)) (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) (pow k 2))) (- (+ (* +nan.0 (* n (* PI (* (log n) (sqrt 2))))) (- (* +nan.0 (* n (* PI (* (log (* 2 PI)) (sqrt 2)))))))))))) * [misc]approximate: Taking taylor expansion of (* (pow (/ 1 k) (- 1/2)) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 k) (- 1/2)) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (/ 1 k) (- 1/2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2) (log (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of (* (- 1/2) (log (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (- 1/2) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (/ 1 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 (log (/ 1 k)) into (log (/ 1 k)) * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 1 k))) into (* -1/2 (log (/ 1 k))) * [misc]backup-simplify: Simplify (exp (* -1/2 (log (/ 1 k)))) into (pow (/ 1 k) -1/2) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 1) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 k) (- 1/2)) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (/ 1 k) (- 1/2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2) (log (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (* (- 1/2) (log (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (- 1/2) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) * [misc]backup-simplify: Simplify (* -1/2 (- (log k))) into (* 1/2 (log k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log k))) into (pow k 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 k) (- 1/2)) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (/ 1 k) (- 1/2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2) (log (/ 1 k)))) in k * [misc]taylor: Taking taylor expansion of (* (- 1/2) (log (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (- 1/2) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (log 1) into 0 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) * [misc]backup-simplify: Simplify (* -1/2 (- (log k))) into (* 1/2 (log k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (log k))) into (pow k 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]backup-simplify: Simplify (* (pow k 1/2) (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) into (* (sqrt k) (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) * [misc]taylor: Taking taylor expansion of (* (sqrt k) (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))) in n * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))) in n * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (* (- (log (* 2 PI)) (log n)) (- 1 (/ 1 k))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 0 (- (log k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow k 1/2) 0) (* 0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ (* (- (log (* 2 PI)) (log n)) 0) (* 0 (- 1 (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow k 1/2) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ (* (- (log (* 2 PI)) (log n)) 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (pow k 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt (/ 1 k))) * [misc]approximate: Taking taylor expansion of (* (pow (/ 1 (- k)) (- 1/2)) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in (k n) around 0 * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 (- k)) (- 1/2)) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in n * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- k)) (- 1/2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2) (log (/ 1 (- k))))) in n * [misc]taylor: Taking taylor expansion of (* (- 1/2) (log (/ 1 (- k)))) in n * [misc]taylor: Taking taylor expansion of (- 1/2) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (/ 1 (- 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 (log (/ -1 k)) into (log (/ -1 k)) * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (* -1/2 (log (/ -1 k))) into (* -1/2 (log (/ -1 k))) * [misc]backup-simplify: Simplify (exp (* -1/2 (log (/ -1 k)))) into (pow (/ -1 k) -1/2) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) -1) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 (- k)) (- 1/2)) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- k)) (- 1/2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2) (log (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (* (- 1/2) (log (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (- 1/2) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (log -1) into (log -1) * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) (log -1)) into (- (log -1) (log k)) * [misc]backup-simplify: Simplify (* -1/2 (- (log -1) (log k))) into (* -1/2 (- (log -1) (log k))) * [misc]backup-simplify: Simplify (exp (* -1/2 (- (log -1) (log k)))) into (exp (* -1/2 (- (log -1) (log k)))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (* (pow (/ 1 (- k)) (- 1/2)) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) in k * [misc]taylor: Taking taylor expansion of (pow (/ 1 (- k)) (- 1/2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2) (log (/ 1 (- k))))) in k * [misc]taylor: Taking taylor expansion of (* (- 1/2) (log (/ 1 (- k)))) in k * [misc]taylor: Taking taylor expansion of (- 1/2) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (log (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (log -1) into (log -1) * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) (log -1)) into (- (log -1) (log k)) * [misc]backup-simplify: Simplify (* -1/2 (- (log -1) (log k))) into (* -1/2 (- (log -1) (log k))) * [misc]backup-simplify: Simplify (exp (* -1/2 (- (log -1) (log k)))) into (exp (* -1/2 (- (log -1) (log k)))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]backup-simplify: Simplify (* (exp (* -1/2 (- (log -1) (log k)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) into (* (exp (* -1/2 (- (log -1) (log k)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (- (log -1) (log k)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))) in n * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (- (log -1) (log k)))) in n * [misc]taylor: Taking taylor expansion of (* -1/2 (- (log -1) (log k))) in n * [misc]taylor: Taking taylor expansion of -1/2 in n * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (- (log -1) (log k)) in n * [misc]taylor: Taking taylor expansion of (log -1) in n * [misc]taylor: Taking taylor expansion of -1 in n * [misc]backup-simplify: Simplify -1 into -1 * [misc]backup-simplify: Simplify (log -1) into (log -1) * [misc]taylor: Taking taylor expansion of (log k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (log k) into (log k) * [misc]backup-simplify: Simplify (- (log k)) into (- (log k)) * [misc]backup-simplify: Simplify (+ (log -1) (- (log k))) into (- (log -1) (log k)) * [misc]backup-simplify: Simplify (* -1/2 (- (log -1) (log k))) into (* -1/2 (- (log -1) (log k))) * [misc]backup-simplify: Simplify (exp (* -1/2 (- (log -1) (log k)))) into (exp (* -1/2 (- (log -1) (log k)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) in n * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))) in n * [misc]taylor: Taking taylor expansion of 1/2 in n * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))) in n * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n * [misc]taylor: Taking taylor expansion of -2 in n * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of (/ PI n) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ PI 1) into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) into (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* (exp (* -1/2 (- (log -1) (log k)))) (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (exp (* -1/2 (- (log -1) (log k))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (exp (* -1/2 (- (log -1) (log k))))) into (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (exp (* -1/2 (- (log -1) (log k))))) * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) (log -1)) into (- (log -1) (log k)) * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 0 (- (log -1) (log k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (- (log -1) (log k)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (- (log -1) (log k)))) 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (+ 1 (/ 1 k)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow k 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (* 0 (- (log -1) (log k)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (- (log -1) (log k)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (- (log -1) (log k)))) 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [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 (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) (log -1)) into (- (log -1) (log k)) * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 0 0) (* 0 (- (log -1) (log k))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (- (log -1) (log k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (- (log -1) (log k)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n))))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (+ 1 (/ 1 k)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow k 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow k 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 0 0) (* 0 (- (log -1) (log k))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (- (log -1) (log k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (- (log -1) (log k)))) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 * [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 (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -1 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log k)) (log -1)) into (- (log -1) (log k)) * [misc]backup-simplify: Simplify (+ (* -1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log k)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (- (log -1) (log k)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (- (log -1) (log k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) (exp (* -1/2 (- (log -1) (log (/ 1 (- k))))))) into (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (exp (* -1/2 (- (log -1) (log (/ -1 k)))))) * * * * [misc]progress: [ 3 / 3 ] generating series at (2 2) * [misc]approximate: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) n) (/ (- 1 k) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 k) 2) (log (* (* 2 PI) n)))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 k) 2) (log (* (* 2 PI) n))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 k) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 k) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (+ 1 (- k)) into (- 1 k) * [misc]backup-simplify: Simplify (/ (- 1 k) 2) into (* 1/2 (- 1 k)) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) n)) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) n) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 1) (* 0 0)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 k)) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 k) (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 k) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 1 0) into 1 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (+ (log (* 2 PI)) (log n))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 1) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (+ (* 1 0) (* -1 (+ (log (* 2 PI)) (log n)))) into (- (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n)))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 k)) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) into (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))))) * [misc]approximate: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (/ -1 2) into -1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) into (exp (* 1/2 (* (log (* 2 (/ PI n))) (- 1 (/ 1 k))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 1) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 k)) 2) (log (* (* 2 PI) (/ 1 n)))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 k)) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ 1 k)) into (- (/ 1 k)) * [misc]backup-simplify: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (- 1 (/ 1 k)) 2) into (* 1/2 (- 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 n))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 n)) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) 1) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (+ 0 -1) into -1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 1)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 1))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (- 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) * [misc]approximate: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in k * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in k * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in k * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in k * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- -1) into 1 * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (/ 1 2) into 1/2 * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in k * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in k * [misc]taylor: Taking taylor expansion of (- n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (- n) into (- n) * [misc]backup-simplify: Simplify (/ 1 (- n)) into (/ -1 n) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) (/ -1 n)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (log (* -2 (/ PI n)))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) -1) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) in n * [misc]taylor: Taking taylor expansion of (exp (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n)))))) in n * [misc]taylor: Taking taylor expansion of (* (/ (- 1 (/ 1 (- k))) 2) (log (* (* 2 PI) (/ 1 (- n))))) in n * [misc]taylor: Taking taylor expansion of (/ (- 1 (/ 1 (- k))) 2) in n * [misc]taylor: Taking taylor expansion of (- 1 (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of 1 in n * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (- (/ -1 k)) into (/ 1 k) * [misc]backup-simplify: Simplify (+ 1 (/ 1 k)) into (+ 1 (/ 1 k)) * [misc]backup-simplify: Simplify (/ (+ 1 (/ 1 k)) 2) into (* 1/2 (+ 1 (/ 1 k))) * [misc]taylor: Taking taylor expansion of (log (* (* 2 PI) (/ 1 (- n)))) in n * [misc]taylor: Taking taylor expansion of (* (* 2 PI) (/ 1 (- n))) in n * [misc]taylor: Taking taylor expansion of (* 2 PI) in n * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (* (* 2 PI) -1) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 (+ 1 (/ 1 k))) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of (+ 1 (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of 1 in k * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ 0 1) into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (* 0 -1)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (* 0 -1))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (+ (* (* 2 PI) 0) (+ (* 0 0) (+ (* 0 0) (* 0 -1)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 (+ 1 (/ 1 k))) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 (+ 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* (+ 1 (/ 1 k)) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (* (+ 1 (/ 1 (/ 1 (- k)))) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 61 ] simplifiying candidate # * * * * [misc]progress: [ 2 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (40 enodes) * [exit]simplify: Simplified to (log (* (* n PI) 2)) * [exit]simplify: Simplified to (log (* (* n PI) 2)) * * * * [misc]progress: [ 3 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (23 enodes) * * [misc]simplify: iters left: 2 (29 enodes) * * [misc]simplify: iters left: 1 (40 enodes) * [exit]simplify: Simplified to (pow (exp PI) (* n 2)) * [exit]simplify: Simplified to (pow (exp PI) (* n 2)) * * * * [misc]progress: [ 4 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * [exit]simplify: Simplified to (* (cbrt (* (* n PI) 2)) (cbrt (* (* n PI) 2))) * [exit]simplify: Simplified to (* (cbrt (* (* n PI) 2)) (cbrt (* (* n PI) 2))) * [enter]simplify: Simplifying (cbrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (cbrt (* 2 (* n PI))) * [exit]simplify: Simplified to (cbrt (* 2 (* n PI))) * * * * [misc]progress: [ 5 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n)) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (53 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * [exit]simplify: Simplified to (pow (* (* n 2) PI) 3) * [exit]simplify: Simplified to (pow (* (* n 2) PI) 3) * * * * [misc]progress: [ 6 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* 2 (* n PI))) * [exit]simplify: Simplified to (sqrt (* 2 (* n PI))) * [enter]simplify: Simplifying (sqrt (* (* 2 PI) n)) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* 2 (* n PI))) * [exit]simplify: Simplified to (sqrt (* 2 (* n PI))) * * * * [misc]progress: [ 7 / 61 ] simplifiying candidate # * * * * [misc]progress: [ 8 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* PI n) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* n PI) * [exit]simplify: Simplified to (* n PI) * * * * [misc]progress: [ 9 / 61 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 61 ] simplifiying candidate # * * * * [misc]progress: [ 11 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log k) (- 1/2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* n (* PI 2)))) (* 1/2 (log k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* n (* PI 2)))) (* 1/2 (log k))) * * * * [misc]progress: [ 12 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log k) (- 1/2)) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (72 enodes) * * [misc]simplify: iters left: 3 (168 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* n (* PI 2)))) (* 1/2 (log k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* n (* PI 2)))) (* 1/2 (log k))) * * * * [misc]progress: [ 13 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (* (log k) (- 1/2)) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (33 enodes) * * [misc]simplify: iters left: 4 (57 enodes) * * [misc]simplify: iters left: 3 (105 enodes) * * [misc]simplify: iters left: 2 (295 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (* 1/2 (log k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (* 1/2 (log k))) * * * * [misc]progress: [ 14 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (pow k (- 1/2))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* PI (* n 2)))) (* (log k) 1/2)) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* PI (* n 2)))) (* (log k) 1/2)) * * * * [misc]progress: [ 15 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (pow k (- 1/2))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (69 enodes) * * [misc]simplify: iters left: 3 (164 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* PI (* n 2)))) (* (log k) 1/2)) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* PI (* n 2)))) (* (log k) 1/2)) * * * * [misc]progress: [ 16 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (+ (log (pow k (- 1/2))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (106 enodes) * * [misc]simplify: iters left: 2 (297 enodes) * [exit]simplify: Simplified to (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (* (log k) 1/2)) * [exit]simplify: Simplified to (- (* (log (* n (* PI 2))) (/ (- 1 k) 2)) (* (log k) 1/2)) * * * * [misc]progress: [ 17 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (44 enodes) * * [misc]simplify: iters left: 3 (66 enodes) * * [misc]simplify: iters left: 2 (142 enodes) * * [misc]simplify: iters left: 1 (404 enodes) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* n (* PI 2)))) (* 1/2 (log k))) * [exit]simplify: Simplified to (- (* (/ (- 1 k) 2) (log (* n (* PI 2)))) (* 1/2 (log k))) * * * * [misc]progress: [ 18 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (29 enodes) * * [misc]simplify: iters left: 4 (38 enodes) * * [misc]simplify: iters left: 3 (41 enodes) * [exit]simplify: Simplified to (pow (exp (pow k (- 1/2))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (exp (pow k (- 1/2))) (pow (* n (* PI 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 19 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (pow k (- 1/2)) (pow k (- 1/2))) (pow k (- 1/2))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (70 enodes) * * [misc]simplify: iters left: 3 (104 enodes) * * [misc]simplify: iters left: 2 (125 enodes) * * [misc]simplify: iters left: 1 (128 enodes) * [exit]simplify: Simplified to (pow (* (pow k (- 1/2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) 3) * [exit]simplify: Simplified to (pow (* (pow k (- 1/2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) 3) * * * * [misc]progress: [ 20 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) * * [misc]simplify: iters left: 6 (16 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 (* (cbrt (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow k (- 1/2)))) (cbrt (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow k (- 1/2))))) * [exit]simplify: Simplified to (* (cbrt (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow k (- 1/2)))) (cbrt (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow k (- 1/2))))) * [enter]simplify: Simplifying (cbrt (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 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 (cbrt (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow k (- 1/2)))) * [exit]simplify: Simplified to (cbrt (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow k (- 1/2)))) * * * * [misc]progress: [ 21 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (60 enodes) * * [misc]simplify: iters left: 3 (87 enodes) * * [misc]simplify: iters left: 2 (117 enodes) * * [misc]simplify: iters left: 1 (120 enodes) * [exit]simplify: Simplified to (pow (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow k (- 1/2))) 3) * [exit]simplify: Simplified to (pow (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow k (- 1/2))) 3) * * * * [misc]progress: [ 22 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (sqrt (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow k (- 1/2)))) * [exit]simplify: Simplified to (sqrt (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow k (- 1/2)))) * [enter]simplify: Simplifying (sqrt (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (sqrt (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow k (- 1/2)))) * [exit]simplify: Simplified to (sqrt (* (pow (* n (* PI 2)) (/ (- 1 k) 2)) (pow k (- 1/2)))) * * * * [misc]progress: [ 23 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (pow (* (* 2 PI) n) (/ 1 2))) * * [misc]simplify: iters left: 6 (9 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ 1 2)) * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ 1 2)) * [enter]simplify: Simplifying (* (pow k 1/2) (pow (* (* 2 PI) n) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) * [exit]simplify: Simplified to (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) * * * * [misc]progress: [ 24 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow k 0) (pow (* (* 2 PI) n) (/ 1 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (28 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 k 1/2) (pow (* (* 2 PI) n) (/ k 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) * [exit]simplify: Simplified to (* (pow (* PI (* 2 n)) (/ k 2)) (sqrt k)) * * * * [misc]progress: [ 25 / 61 ] simplifiying candidate # * * * * [misc]progress: [ 26 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow k (- 1/2)) (pow (* 2 PI) (/ (- 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 (* (pow (* PI 2) (/ (- 1 k) 2)) (pow k (- 1/2))) * [exit]simplify: Simplified to (* (pow (* PI 2) (/ (- 1 k) 2)) (pow k (- 1/2))) * * * * [misc]progress: [ 27 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow k (- 1/2)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (44 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow k (- 1/2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (* (cbrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow k (- 1/2)))) * * * * [misc]progress: [ 28 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow k (- 1/2)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow k (- 1/2))) * [exit]simplify: Simplified to (* (sqrt (pow (* n (* PI 2)) (/ (- 1 k) 2))) (pow k (- 1/2))) * * * * [misc]progress: [ 29 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow k (- 1/2)) 1) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (9 enodes) * * [misc]simplify: iters left: 3 (11 enodes) * [exit]simplify: Simplified to (pow k (- 1/2)) * [exit]simplify: Simplified to (pow k (- 1/2)) * * * * [misc]progress: [ 30 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow k (- 1/2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 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 (* (cbrt (pow k (- 1/2))) (pow (* PI (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (cbrt (pow k (- 1/2))) (pow (* PI (* n 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 31 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (sqrt (pow k (- 1/2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (36 enodes) * * [misc]simplify: iters left: 3 (39 enodes) * [exit]simplify: Simplified to (* (sqrt (pow k (- 1/2))) (pow (* PI (* n 2)) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (* (sqrt (pow k (- 1/2))) (pow (* PI (* n 2)) (/ (- 1 k) 2))) * * * * [misc]progress: [ 32 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow k (- 1/2))) * [exit]simplify: Simplified to (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (pow k (- 1/2))) * * * * [misc]progress: [ 33 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ 1 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (26 enodes) * * [misc]simplify: iters left: 3 (27 enodes) * [exit]simplify: Simplified to (* (pow k (- 1/2)) (pow (* (* PI n) 2) (/ 1 2))) * [exit]simplify: Simplified to (* (pow k (- 1/2)) (pow (* (* PI n) 2) (/ 1 2))) * * * * [misc]progress: [ 34 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (34 enodes) * * [misc]simplify: iters left: 3 (37 enodes) * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ (- 1 k) 2)) * * * * [misc]progress: [ 35 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow k 0) (pow (* (* 2 PI) n) (/ (- 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 (39 enodes) * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ (- 1 k) 2)) * * * * [misc]progress: [ 36 / 61 ] simplifiying candidate # * * * * [misc]progress: [ 37 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * * * * [misc]progress: [ 38 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (28 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (141 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* PI (* n 2)))) * * * * [misc]progress: [ 39 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* 1 (/ (- 1 k) 2)) * * [misc]simplify: iters left: 6 (6 enodes) * * [misc]simplify: iters left: 5 (16 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (49 enodes) * * [misc]simplify: iters left: 2 (62 enodes) * * [misc]simplify: iters left: 1 (75 enodes) * [exit]simplify: Simplified to (/ (- 1 k) 2) * [exit]simplify: Simplified to (/ (- 1 k) 2) * * * * [misc]progress: [ 40 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ 1 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (22 enodes) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (/ 1 2)) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (/ 1 2)) * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (/ k 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * * [misc]simplify: iters left: 2 (20 enodes) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) * [exit]simplify: Simplified to (pow (* 2 (* n PI)) (/ k 2)) * * * * [misc]progress: [ 41 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) * * * * [misc]progress: [ 42 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2))) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2))) * * * * [misc]progress: [ 43 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) 1) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (20 enodes) * [exit]simplify: Simplified to (* (* n PI) 2) * [exit]simplify: Simplified to (* (* n PI) 2) * * * * [misc]progress: [ 44 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* (* 2 PI) n) (- 1 k)) * * [misc]simplify: iters left: 5 (9 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (25 enodes) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (- 1 k)) * [exit]simplify: Simplified to (pow (* (* PI 2) n) (- 1 k)) * * * * [misc]progress: [ 45 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (pow (* 2 PI) (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (16 enodes) * * [misc]simplify: iters left: 3 (19 enodes) * * [misc]simplify: iters left: 2 (21 enodes) * [exit]simplify: Simplified to (pow (* PI 2) (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow (* PI 2) (/ (- 1 k) 2)) * [enter]simplify: Simplifying (pow n (/ (- 1 k) 2)) * * [misc]simplify: iters left: 5 (7 enodes) * * [misc]simplify: iters left: 4 (14 enodes) * * [misc]simplify: iters left: 3 (17 enodes) * * [misc]simplify: iters left: 2 (19 enodes) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * [exit]simplify: Simplified to (pow n (/ (- 1 k) 2)) * * * * [misc]progress: [ 46 / 61 ] simplifiying candidate # * * * * [misc]progress: [ 47 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (43 enodes) * * [misc]simplify: iters left: 3 (90 enodes) * * [misc]simplify: iters left: 2 (232 enodes) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* PI 2) n))) * [exit]simplify: Simplified to (* (/ (- 1 k) 2) (log (* (* PI 2) n))) * * * * [misc]progress: [ 48 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (exp (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (exp (pow (* (* PI 2) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 49 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (23 enodes) * * [misc]simplify: iters left: 4 (32 enodes) * * [misc]simplify: iters left: 3 (35 enodes) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) * [enter]simplify: Simplifying (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 50 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (pow (pow (* PI (* n 2)) (/ (- 1 k) 2)) 3) * [exit]simplify: Simplified to (pow (pow (* PI (* n 2)) (/ (- 1 k) 2)) 3) * * * * [misc]progress: [ 51 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [enter]simplify: Simplifying (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (22 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (34 enodes) * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * [exit]simplify: Simplified to (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) * * * * [misc]progress: [ 52 / 61 ] simplifiying candidate # * * * * [misc]progress: [ 53 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow k (- 1/2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow k (- 1/2))) * * * * [misc]progress: [ 54 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow k (- 1/2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow k (- 1/2))) * * * * [misc]progress: [ 55 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow k (- 1/2)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (26 enodes) * * [misc]simplify: iters left: 4 (35 enodes) * * [misc]simplify: iters left: 3 (38 enodes) * [exit]simplify: Simplified to (* (pow (* (* PI n) 2) (/ (- 1 k) 2)) (pow k (- 1/2))) * * * * [misc]progress: [ 56 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* n PI) k)) (- (+ (* +nan.0 (/ (* (pow n 2) (pow PI 2)) (pow k 2))) (- (+ (* +nan.0 (* n (* PI (* (log n) (sqrt 2))))) (- (* +nan.0 (* n (* PI (* (log (* 2 PI)) (sqrt 2)))))))))))) * * * * [misc]progress: [ 57 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt (/ 1 k))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (260 enodes) * [exit]simplify: Simplified to (* (* (pow n (- 1/2 (* 1/2 k))) (pow (* PI 2) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) * * * * [misc]progress: [ 58 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (exp (* -1/2 (- (log -1) (log (/ -1 k)))))) * * [misc]simplify: iters left: 6 (24 enodes) * * [misc]simplify: iters left: 5 (52 enodes) * * [misc]simplify: iters left: 4 (106 enodes) * * [misc]simplify: iters left: 3 (345 enodes) * [exit]simplify: Simplified to (* (pow (exp -1/2) (log k)) (pow (exp (- 1/2 (* 1/2 k))) (- (log (* PI -2)) (log (/ -1 n))))) * * * * [misc]progress: [ 59 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow k (- 1/2)) (- (+ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (log n) (pow k 2)))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k)))))) * * [misc]simplify: iters left: 6 (40 enodes) * * [misc]simplify: iters left: 5 (109 enodes) * * [misc]simplify: iters left: 4 (360 enodes) * [exit]simplify: Simplified to (* (+ (+ (* (* (* (* k k) (log n)) (log (* PI 2))) (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/4))) (* (* 1/8 (* (pow (* PI 2) 1/2) (* (pow n 1/2) (* k k)))) (+ (* (log (* PI 2)) (log (* PI 2))) (* (log n) (log n))))) (- (* (pow n 1/2) (pow (* PI 2) 1/2)) (* (* k (* (pow (* PI 2) 1/2) (* (pow n 1/2) 1/2))) (+ (log n) (log (* PI 2)))))) (pow k (- 1/2))) * * * * [misc]progress: [ 60 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow k (- 1/2)) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (265 enodes) * [exit]simplify: Simplified to (* (pow (* PI 2) (- 1/2 (* 1/2 k))) (* (pow n (- 1/2 (* 1/2 k))) (pow k (- 1/2)))) * * * * [misc]progress: [ 61 / 61 ] simplifiying candidate # * [enter]simplify: Simplifying (* (pow k (- 1/2)) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) * * [misc]simplify: iters left: 6 (19 enodes) * * [misc]simplify: iters left: 5 (39 enodes) * * [misc]simplify: iters left: 4 (80 enodes) * * [misc]simplify: iters left: 3 (271 enodes) * [exit]simplify: Simplified to (* (pow k (- 1/2)) (pow (exp (- 1/2 (* 1/2 k))) (- (log (* PI -2)) (log (/ -1 n))))) * * * [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) * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 2 1) * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 1 1) * * * * [misc]progress: [ 4 / 4 ] rewriting at (2) * * * [misc]progress: generating series expansions * * * * [misc]progress: [ 1 / 4 ] generating series at (2 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 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* n (* PI 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 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]approximate: Taking taylor expansion of (pow (* (/ 1 n) (* PI 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) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* PI 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) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* 2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* 2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* 2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 1)))) 24) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* 2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* 2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 1)))) 120) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* 2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* 2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* 2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* 2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* 2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* 2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* 2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* 2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* 2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* 2 PI) 1)))) 720) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) * [misc]approximate: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 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)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* PI 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)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow (* -2 PI) 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow (* -2 PI) 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow (* -2 PI) 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 1)))) 24) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow (* -2 PI) 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow (* -2 PI) 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 1)))) 120) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow (* -2 PI) 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow (* -2 PI) 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow (* -2 PI) 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow (* -2 PI) 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow (* -2 PI) 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow (* -2 PI) 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow (* -2 PI) 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow (* -2 PI) 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow (* -2 PI) 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow (* -2 PI) 1)))) 720) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 2 1) * [misc]approximate: Taking taylor expansion of (* n (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 3 / 4 ] generating series at (2 1 1) * [misc]approximate: Taking taylor expansion of (* n (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* n (* PI 2)) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (/ 1 n) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) * [misc]approximate: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in (n) around 0 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of (* (/ 1 (- n)) (* PI 2)) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- n)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))))) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) * * * * [misc]progress: [ 4 / 4 ] generating series at (2) * [misc]approximate: Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (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 in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) in k * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* n (* 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 in k * [misc]backup-simplify: Simplify n into n * [misc]taylor: Taking taylor expansion of (* PI 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (* 0 1) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (* 1/2 (log (* 2 (* n PI)))) 1) 1)))) into (* 1/2 (log (* 2 (* n PI)))) * [misc]backup-simplify: Simplify (+ (* 0 (* 1/2 (log (* 2 (* n PI))))) (* +nan.0 1)) into (- +nan.0) * [misc]backup-simplify: Simplify (/ (pow (* 2 (* n PI)) 1/2) (- +nan.0)) into (* +nan.0 (sqrt (* n (* 2 PI)))) * [misc]taylor: Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (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 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* n (* 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 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* (sqrt k) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) into (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (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 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* n (* 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 in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 0 (* 2 PI)) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (* 2 PI))) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (* 1/2 k) (+ (log (* 2 PI)) (log n))) into (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) * [misc]backup-simplify: Simplify (* (sqrt k) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) into (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) into (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) * [misc]taylor: Taking taylor expansion of (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) in k * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (+ (log (* 2 PI)) (log n))) into (* 1/2 (+ (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (* k (+ (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]taylor: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (log n)) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 0 (+ (log (* 2 PI)) (log n))) into 0 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 (+ (log (* 2 PI)) (log n)))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 (+ (log (* 2 PI)) (log n))) (* 0 0)) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) * [misc]backup-simplify: Simplify (exp 0) into 1 * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 1) into (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (+ (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1) 1)))) into (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))) (* 0 (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (+ (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) +nan.0) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) 0))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 2))))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI)))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (* 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (* 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k))) (+ (* (* (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) (sqrt (/ 1 k))) (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))) (* 0 (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))) (* 0 (/ 0 (* (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) (sqrt k)))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (+ (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (+ (log (* 2 PI)) (log n))) (* 0 0)))) into 0 * [misc]backup-simplify: Simplify (* (exp 0) (+ (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 3) 6)) (* (/ (pow (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))) * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (/ (+ (* 1/16 (* (pow (log (* 2 PI)) 2) (log n))) (+ (* 1/48 (pow (log (* 2 PI)) 3)) (+ (* 1/48 (pow (log n) 3)) (* 1/16 (* (log (* 2 PI)) (pow (log n) 2)))))) 1)) (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) (/ (+ (* 1/8 (pow (log (* 2 PI)) 2)) (+ (* 1/4 (* (log (* 2 PI)) (log n))) (* 1/8 (pow (log n) 2)))) 1)) (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) (/ (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))) 1)))) into (- (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2)))))))) * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) +nan.0) (+ (* (- (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (* 1/2 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))))) +nan.0) (+ (* (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (+ (* 1/8 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (* 1/4 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))))) +nan.0) (* (- (+ (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (log n)))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 3))) (+ (* 1/48 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 3))) (* 1/16 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow (log n) 2)))))))) 0)))) into (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (log n))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log (* 2 PI)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 k)) (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) 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 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k * [misc]taylor: Taking taylor expansion of (/ 1 k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* 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 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) 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 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (/ PI n)))) into (* 1/2 (log (* 2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 k) 2) (log (* (/ 1 n) (* PI 2))))) into (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (* 0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) into (- (* +nan.0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (/ (pow (* 2 (/ PI n)) 1/2) (- (* +nan.0 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) into (* +nan.0 (* (sqrt (/ (* 2 PI) n)) (/ 1 (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 k)) (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) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* 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) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 n) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 k)) (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) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* (/ 1 n) (* PI 2)) (/ (/ 1 k) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n * [misc]taylor: Taking taylor expansion of (/ 1 k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 n) (* 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) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ 1 1) into 1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* 1 (* 2 PI)) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ 1/2 k) (- (log (* 2 PI)) (log n))) into (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) * [misc]taylor: Taking taylor expansion of (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) in k * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log (* 2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log (* 2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* 2 PI)) (log n)))) into (exp (* 1/2 (- (log (* 2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k * [misc]taylor: Taking taylor expansion of (* 2 PI) in k * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* 2 PI)) (log n)) 1) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* 2 PI)) (log n))) into (* 1/2 (- (log (* 2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) into (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) into (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) * [misc]taylor: Taking taylor expansion of (sqrt k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) 0) into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (* 0 (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (+ (* 0 0) (* 0 2)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* 2 PI))))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ 1/2 k) (/ 0 2)) (* 0 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ 1/2 k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (+ (* (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (sqrt k)) (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (* 0 (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) (* 0 (/ 0 (* (sqrt (/ 1 k)) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) (* 0 (/ 0 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))))) into 0 * [misc]backup-simplify: Simplify (+ (* (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log n)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log (/ 1 n))) (/ 1 k))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))))))))))) * [misc]approximate: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2)))) in (n k) around 0 * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 (- k))) (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)) 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 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* -2 (/ PI n))))) into (pow (* -2 (/ PI n)) 1/2) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) in k * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in k * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in k * [misc]taylor: Taking taylor expansion of (- k) in k * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* 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 -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)) 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 2) in k * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in k * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* (/ -1 n) (* 2 PI)) into (* -2 (/ PI n)) * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) * [misc]backup-simplify: Simplify (* -1/2 (log (* -2 (/ PI n)))) into (* -1/2 (log (* -2 (/ PI n)))) * [misc]backup-simplify: Simplify (exp (* (/ (/ 1 (- k)) 2) (log (* (/ 1 (- n)) (* PI 2))))) into (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) * [misc]backup-simplify: Simplify (* 0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) into 0 * [misc]backup-simplify: Simplify (+ (* 0 0) (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) into (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) * [misc]backup-simplify: Simplify (/ (pow (* -2 (/ PI n)) 1/2) (- (* +nan.0 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) into (* +nan.0 (* (sqrt (/ (* PI -2) n)) (/ 1 (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 (- k))) (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)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* 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)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) * [misc]taylor: Taking taylor expansion of (/ (pow (* (/ 1 (- n)) (* PI 2)) (/ 1 2)) (* (sqrt (/ 1 (- k))) (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)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 (- k))) (pow (* (/ 1 (- n)) (* PI 2)) (/ (/ 1 (- k)) 2))) in n * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 (- k))) in n * [misc]taylor: Taking taylor expansion of (/ 1 (- k)) in n * [misc]taylor: Taking taylor expansion of (- k) in n * [misc]taylor: Taking taylor expansion of k in n * [misc]backup-simplify: Simplify k into k * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (/ 1 (- k)) into (/ -1 k) * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 * [misc]taylor: Taking taylor expansion of (pow (* (/ 1 (- n)) (* 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)) in n * [misc]taylor: Taking taylor expansion of (- n) in n * [misc]taylor: Taking taylor expansion of n in n * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (/ 1 -1) into -1 * [misc]taylor: Taking taylor expansion of (* PI 2) in n * [misc]taylor: Taking taylor expansion of PI in n * [misc]backup-simplify: Simplify PI into PI * [misc]taylor: Taking taylor expansion of 2 in n * [misc]backup-simplify: Simplify 2 into 2 * [misc]backup-simplify: Simplify (* PI 2) into (* 2 PI) * [misc]backup-simplify: Simplify (* -1 (* 2 PI)) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* (/ -1/2 k) (- (log (* -2 PI)) (log n))) into (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]backup-simplify: Simplify (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) into (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) into (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) * [misc]taylor: Taking taylor expansion of (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) in k * [misc]taylor: Taking taylor expansion of (exp (* 1/2 (- (log (* -2 PI)) (log n)))) in k * [misc]taylor: Taking taylor expansion of (* 1/2 (- (log (* -2 PI)) (log n))) in k * [misc]taylor: Taking taylor expansion of 1/2 in k * [misc]backup-simplify: Simplify 1/2 into 1/2 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* 1/2 (- (log (* -2 PI)) (log n)))) into (exp (* 1/2 (- (log (* -2 PI)) (log n)))) * [misc]taylor: Taking taylor expansion of (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))) in k * [misc]taylor: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k * [misc]taylor: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k * [misc]taylor: Taking taylor expansion of -1/2 in k * [misc]backup-simplify: Simplify -1/2 into -1/2 * [misc]taylor: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k * [misc]taylor: Taking taylor expansion of (* -2 PI) in k * [misc]taylor: Taking taylor expansion of -2 in k * [misc]backup-simplify: Simplify -2 into -2 * [misc]taylor: Taking taylor expansion of PI in k * [misc]backup-simplify: Simplify PI into PI * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) * [misc]taylor: Taking taylor expansion of (log n) in k * [misc]taylor: Taking taylor expansion of n in k * [misc]backup-simplify: Simplify n into n * [misc]backup-simplify: Simplify (log n) into (log n) * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (/ (- (log (* -2 PI)) (log n)) 1) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (* -1/2 (- (log (* -2 PI)) (log n))) into (* -1/2 (- (log (* -2 PI)) (log n))) * [misc]backup-simplify: Simplify (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) into (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k * [misc]taylor: Taking taylor expansion of (/ -1 k) in k * [misc]taylor: Taking taylor expansion of -1 in k * [misc]backup-simplify: Simplify -1 into -1 * [misc]taylor: Taking taylor expansion of k in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 1 into 1 * [misc]backup-simplify: Simplify (/ -1 1) into -1 * [misc]backup-simplify: Simplify (sqrt 0) into 0 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) 0) into 0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (* 0 2)) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 (* 2 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ -1 k)) 0) (* 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- (+ (* 1/2 (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (+ (* PI 0) (+ (* 0 0) (* 0 2))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- 1) into -1 * [misc]backup-simplify: Simplify (- (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (* 2 PI)))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 2) (+ (* (/ -1/2 k) (/ 0 2)) (* 0 (/ 0 2)))) into 0 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) * [misc]backup-simplify: Simplify (+ (* (/ -1/2 k) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (- k) into (- k) * [misc]backup-simplify: Simplify (- (+ (* (/ -1 k) (/ 0 (- k))) (* 0 (/ 0 (- k))))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ -1 k)) 0) (+ (* 0 0) (* 0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (+ (* (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k)))) (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))) (* 0 (/ 0 (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) (sqrt (/ -1 k))))))) into 0 * [misc]taylor: Taking taylor expansion of 0 in k * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify 0 into 0 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 * [misc]backup-simplify: Simplify (- 0) into 0 * [misc]backup-simplify: Simplify (+ 0 0) into 0 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 * [misc]backup-simplify: Simplify (+ (* (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) * [misc]backup-simplify: Simplify (- (/ 0 (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (+ (* (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))) (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) (/ (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) (- (* +nan.0 (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) into (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log n)))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))))) * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ 1 (- n)))))) (exp (* -1/2 (/ (- (log (* -2 PI)) (log (/ 1 (- n)))) (/ 1 (- k))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))) * * * [misc]progress: simplifying candidates * * * * [misc]progress: [ 1 / 78 ] 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 (90 enodes) * * [misc]simplify: iters left: 2 (168 enodes) * * [misc]simplify: iters left: 1 (326 enodes) * [exit]simplify: Simplified to (/ (log (* (* PI n) 2)) 2) * [exit]simplify: Simplified to (/ (log (* (* PI n) 2)) 2) * * * * [misc]progress: [ 2 / 78 ] 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 (90 enodes) * * [misc]simplify: iters left: 2 (168 enodes) * * [misc]simplify: iters left: 1 (326 enodes) * [exit]simplify: Simplified to (/ (log (* (* PI n) 2)) 2) * [exit]simplify: Simplified to (/ (log (* (* PI n) 2)) 2) * * * * [misc]progress: [ 3 / 78 ] 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: [ 4 / 78 ] 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 (* (* n 2) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) * [exit]simplify: Simplified to (pow (* (* n 2) PI) (* (cbrt (/ 1 2)) (cbrt (/ 1 2)))) * * * * [misc]progress: [ 5 / 78 ] 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: [ 6 / 78 ] 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 (20 enodes) * [exit]simplify: Simplified to (* (* PI n) 2) * [exit]simplify: Simplified to (* (* PI n) 2) * * * * [misc]progress: [ 7 / 78 ] 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 (20 enodes) * [exit]simplify: Simplified to (* (* PI n) 2) * [exit]simplify: Simplified to (* (* PI n) 2) * * * * [misc]progress: [ 8 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (pow n (/ 1 2)) * * [misc]simplify: iters left: 3 (5 enodes) * * [misc]simplify: iters left: 2 (7 enodes) * [exit]simplify: Simplified to (pow n (/ 1 2)) * [exit]simplify: Simplified to (pow n (/ 1 2)) * [enter]simplify: Simplifying (pow (* PI 2) (/ 1 2)) * * [misc]simplify: iters left: 3 (6 enodes) * * [misc]simplify: iters left: 2 (9 enodes) * [exit]simplify: Simplified to (pow (* 2 PI) (/ 1 2)) * [exit]simplify: Simplified to (pow (* 2 PI) (/ 1 2)) * * * * [misc]progress: [ 9 / 78 ] simplifiying candidate # * * * * [misc]progress: [ 10 / 78 ] 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 (170 enodes) * * [misc]simplify: iters left: 1 (380 enodes) * [exit]simplify: Simplified to (/ (log (* (* PI n) 2)) 2) * [exit]simplify: Simplified to (/ (log (* (* PI n) 2)) 2) * * * * [misc]progress: [ 11 / 78 ] 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: [ 12 / 78 ] 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 (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 1 2)))) * [exit]simplify: Simplified to (* (cbrt (pow (* (* n 2) PI) (/ 1 2))) (cbrt (pow (* (* n 2) PI) (/ 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: [ 13 / 78 ] 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 (* (* n 2) PI) (/ 1 2)) 3) * [exit]simplify: Simplified to (pow (pow (* (* n 2) PI) (/ 1 2)) 3) * * * * [misc]progress: [ 14 / 78 ] 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: [ 15 / 78 ] simplifiying candidate # * * * * [misc]progress: [ 16 / 78 ] simplifiying candidate # * * * * [misc]progress: [ 17 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * [exit]simplify: Simplified to (log (* (* PI n) 2)) * [exit]simplify: Simplified to (log (* (* PI n) 2)) * * * * [misc]progress: [ 18 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (35 enodes) * * [misc]simplify: iters left: 1 (45 enodes) * [exit]simplify: Simplified to (pow (exp 2) (* PI n)) * [exit]simplify: Simplified to (pow (exp 2) (* PI n)) * * * * [misc]progress: [ 19 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * [exit]simplify: Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2))) * [exit]simplify: Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2))) * [enter]simplify: Simplifying (cbrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (cbrt (* (* n 2) PI)) * [exit]simplify: Simplified to (cbrt (* (* n 2) PI)) * * * * [misc]progress: [ 20 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (203 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) 3) * [exit]simplify: Simplified to (pow (* (* PI n) 2) 3) * * * * [misc]progress: [ 21 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [enter]simplify: Simplifying (sqrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * * * * [misc]progress: [ 22 / 78 ] simplifiying candidate # * * * * [misc]progress: [ 23 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 24 / 78 ] simplifiying candidate # * * * * [misc]progress: [ 25 / 78 ] simplifiying candidate # * * * * [misc]progress: [ 26 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (log (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (13 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * * [misc]simplify: iters left: 2 (41 enodes) * [exit]simplify: Simplified to (log (* (* PI n) 2)) * [exit]simplify: Simplified to (log (* (* PI n) 2)) * * * * [misc]progress: [ 27 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (12 enodes) * * [misc]simplify: iters left: 3 (20 enodes) * * [misc]simplify: iters left: 2 (35 enodes) * * [misc]simplify: iters left: 1 (45 enodes) * [exit]simplify: Simplified to (pow (exp 2) (* PI n)) * [exit]simplify: Simplified to (pow (exp 2) (* PI n)) * * * * [misc]progress: [ 28 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (11 enodes) * * [misc]simplify: iters left: 4 (17 enodes) * * [misc]simplify: iters left: 3 (18 enodes) * [exit]simplify: Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2))) * [exit]simplify: Simplified to (* (cbrt (* (* PI n) 2)) (cbrt (* (* PI n) 2))) * [enter]simplify: Simplifying (cbrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (cbrt (* (* n 2) PI)) * [exit]simplify: Simplified to (cbrt (* (* n 2) PI)) * * * * [misc]progress: [ 29 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2))) * * [misc]simplify: iters left: 6 (7 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (59 enodes) * * [misc]simplify: iters left: 3 (203 enodes) * [exit]simplify: Simplified to (pow (* (* PI n) 2) 3) * [exit]simplify: Simplified to (pow (* (* PI n) 2) 3) * * * * [misc]progress: [ 30 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [enter]simplify: Simplifying (sqrt (* n (* PI 2))) * * [misc]simplify: iters left: 5 (6 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * * [misc]simplify: iters left: 3 (16 enodes) * * [misc]simplify: iters left: 2 (18 enodes) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * [exit]simplify: Simplified to (sqrt (* (* n 2) PI)) * * * * [misc]progress: [ 31 / 78 ] simplifiying candidate # * * * * [misc]progress: [ 32 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (* n PI) * * [misc]simplify: iters left: 2 (3 enodes) * * [misc]simplify: iters left: 1 (4 enodes) * [exit]simplify: Simplified to (* PI n) * [exit]simplify: Simplified to (* PI n) * * * * [misc]progress: [ 33 / 78 ] simplifiying candidate # * * * * [misc]progress: [ 34 / 78 ] simplifiying candidate # * * * * [misc]progress: [ 35 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (225 enodes) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k))) * * * * [misc]progress: [ 36 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (225 enodes) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k))) * * * * [misc]progress: [ 37 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (log (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (222 enodes) * [exit]simplify: Simplified to (- (* (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * * * * [misc]progress: [ 38 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (log (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (465 enodes) * [exit]simplify: Simplified to (- (* (log (* PI (* n 2))) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (* PI (* n 2))) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * * * * [misc]progress: [ 39 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (225 enodes) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k))) * * * * [misc]progress: [ 40 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (36 enodes) * * [misc]simplify: iters left: 4 (75 enodes) * * [misc]simplify: iters left: 3 (225 enodes) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k))) * * * * [misc]progress: [ 41 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (+ (log (sqrt k)) (log (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (222 enodes) * [exit]simplify: Simplified to (- (* (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * * * * [misc]progress: [ 42 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (- (* (log (* n (* PI 2))) (/ 1 2)) (log (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (34 enodes) * * [misc]simplify: iters left: 4 (63 enodes) * * [misc]simplify: iters left: 3 (154 enodes) * * [misc]simplify: iters left: 2 (465 enodes) * [exit]simplify: Simplified to (- (* (log (* PI (* n 2))) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (* PI (* n 2))) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * * * * [misc]progress: [ 43 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* n (* PI 2)) (/ 1 2))) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (206 enodes) * [exit]simplify: Simplified to (- (* (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * * * * [misc]progress: [ 44 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* n (* PI 2)) (/ 1 2))) (+ (log (sqrt k)) (* (log (* n (* PI 2))) (/ k 2)))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (35 enodes) * * [misc]simplify: iters left: 4 (73 enodes) * * [misc]simplify: iters left: 3 (206 enodes) * [exit]simplify: Simplified to (- (* (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (* (* PI n) 2)) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * * * * [misc]progress: [ 45 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* n (* PI 2)) (/ 1 2))) (+ (log (sqrt k)) (log (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (17 enodes) * * [misc]simplify: iters left: 5 (31 enodes) * * [misc]simplify: iters left: 4 (58 enodes) * * [misc]simplify: iters left: 3 (148 enodes) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* PI (* n 2)))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* PI (* n 2)))) (log (sqrt k))) * * * * [misc]progress: [ 46 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (- (log (pow (* n (* PI 2)) (/ 1 2))) (log (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (30 enodes) * * [misc]simplify: iters left: 4 (54 enodes) * * [misc]simplify: iters left: 3 (122 enodes) * * [misc]simplify: iters left: 2 (459 enodes) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* (* n 2) PI))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (- (/ 1 2) (/ k 2)) (log (* (* n 2) PI))) (log (sqrt k))) * * * * [misc]progress: [ 47 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (log (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (41 enodes) * * [misc]simplify: iters left: 3 (70 enodes) * * [misc]simplify: iters left: 2 (178 enodes) * [exit]simplify: Simplified to (- (* (log (* (* 2 PI) n)) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * [exit]simplify: Simplified to (- (* (log (* (* 2 PI) n)) (- (/ 1 2) (/ k 2))) (log (sqrt k))) * * * * [misc]progress: [ 48 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (exp (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (exp (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (exp (/ (/ (pow (* PI (* n 2)) (/ 1 2)) (sqrt k)) (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 49 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2))) (* (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* n (* PI 2)) (/ k 2)) (pow (* n (* PI 2)) (/ k 2))) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (41 enodes) * * [misc]simplify: iters left: 4 (134 enodes) * [exit]simplify: Simplified to (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (pow (* (* PI n) 2) (/ k 2)) (pow (* (* PI n) 2) (/ k 2)))) (/ (pow (* (* PI n) 2) (/ 1 2)) (/ (* (sqrt k) k) (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) (/ k 2)) (pow (* (* PI n) 2) (/ k 2)))) (/ (pow (* (* PI n) 2) (/ 1 2)) (/ (* (sqrt k) k) (pow (* (* PI n) 2) (/ 1 2))))) * * * * [misc]progress: [ 50 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (* (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ 1 2))) (* (* (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (121 enodes) * * [misc]simplify: iters left: 3 (448 enodes) * [exit]simplify: Simplified to (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (pow (* (* PI n) 2) (/ k 2)) k)) (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)))) * [exit]simplify: Simplified to (* (/ (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (* (pow (* (* PI n) 2) (/ k 2)) k)) (* (/ (pow (* (* PI n) 2) (/ 1 2)) (pow (* (* PI n) 2) (/ k 2))) (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)))) * * * * [misc]progress: [ 51 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (* (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (25 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * * [misc]simplify: iters left: 3 (33 enodes) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* (* n 2) PI) (/ k 2)) (sqrt k)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* (* n 2) PI) (/ k 2)) (sqrt k))))) * [exit]simplify: Simplified to (* (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* (* n 2) PI) (/ k 2)) (sqrt k)))) (cbrt (/ (pow (* (* n 2) PI) (/ 1 2)) (* (pow (* (* n 2) PI) (/ k 2)) (sqrt k))))) * [enter]simplify: Simplifying (cbrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (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: [ 52 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (* (* (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (32 enodes) * * [misc]simplify: iters left: 4 (81 enodes) * * [misc]simplify: iters left: 3 (299 enodes) * [exit]simplify: Simplified to (/ (* (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2))) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))) (* (/ (sqrt k) (pow (* (* 2 PI) n) (/ 1 2))) (* k (pow (* (* 2 PI) n) (/ k 2))))) * [exit]simplify: Simplified to (/ (* (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2))) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))) (* (/ (sqrt k) (pow (* (* 2 PI) n) (/ 1 2))) (* k (pow (* (* 2 PI) n) (/ k 2))))) * * * * [misc]progress: [ 53 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ (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)))) * [enter]simplify: Simplifying (sqrt (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (30 enodes) * * [misc]simplify: iters left: 3 (31 enodes) * [exit]simplify: Simplified to (sqrt (/ (/ (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: [ 54 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (- (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 (- (pow (* (* PI n) 2) (/ 1 2))) * [exit]simplify: Simplified to (- (pow (* (* PI n) 2) (/ 1 2))) * [enter]simplify: Simplifying (- (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (20 enodes) * * [misc]simplify: iters left: 4 (28 enodes) * * [misc]simplify: iters left: 3 (30 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: [ 55 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow n (/ 1 2)) (sqrt k)) * * [misc]simplify: iters left: 5 (8 enodes) * * [misc]simplify: iters left: 4 (10 enodes) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow n (/ 1 2)) (sqrt k)) * [enter]simplify: Simplifying (/ (pow (* PI 2) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2))) * [exit]simplify: Simplified to (/ (pow (* 2 PI) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2))) * * * * [misc]progress: [ 56 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n (* PI 2)) (/ 1 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) (sqrt k)) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (29 enodes) * * [misc]simplify: iters left: 3 (32 enodes) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) (sqrt k)) * [exit]simplify: Simplified to (/ (* (cbrt (pow (* (* PI n) 2) (/ 1 2))) (cbrt (pow (* (* PI n) 2) (/ 1 2)))) (sqrt k)) * [enter]simplify: Simplifying (/ (cbrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 enodes) * [exit]simplify: Simplified to (/ (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))) * * * * [misc]progress: [ 57 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (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 (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (/ 1 2))) (sqrt k)) * [enter]simplify: Simplifying (/ (sqrt (pow (* n (* PI 2)) (/ 1 2))) (pow (* n (* PI 2)) (/ k 2))) * * [misc]simplify: iters left: 6 (13 enodes) * * [misc]simplify: iters left: 5 (19 enodes) * * [misc]simplify: iters left: 4 (25 enodes) * * [misc]simplify: iters left: 3 (26 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))) * * * * [misc]progress: [ 58 / 78 ] 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)) * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (pow (* n (* PI 2)) (/ k 2))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (18 enodes) * * [misc]simplify: iters left: 4 (24 enodes) * * [misc]simplify: iters left: 3 (25 enodes) * [exit]simplify: Simplified to (/ (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: [ 59 / 78 ] simplifiying candidate # * * * * [misc]progress: [ 60 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ 1 (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (12 enodes) * * [misc]simplify: iters left: 5 (21 enodes) * * [misc]simplify: iters left: 4 (27 enodes) * * [misc]simplify: iters left: 3 (29 enodes) * [exit]simplify: Simplified to (/ (/ 1 (sqrt k)) (pow (* PI (* n 2)) (/ k 2))) * [exit]simplify: Simplified to (/ (/ 1 (sqrt k)) (pow (* PI (* n 2)) (/ k 2))) * * * * [misc]progress: [ 61 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (pow (* n (* PI 2)) (/ 1 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 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 (/ (sqrt k) (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 62 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (sqrt k)) * * [misc]simplify: iters left: 6 (11 enodes) * * [misc]simplify: iters left: 5 (17 enodes) * * [misc]simplify: iters left: 4 (23 enodes) * * [misc]simplify: iters left: 3 (24 enodes) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (/ 1 2)) (sqrt k)) * * * * [misc]progress: [ 63 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (pow (* PI 2) (/ 1 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 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 (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (pow (* PI (* n 2)) (/ k 2))) * [exit]simplify: Simplified to (* (/ (sqrt k) (pow (* PI 2) (/ 1 2))) (pow (* PI (* n 2)) (/ k 2))) * * * * [misc]progress: [ 64 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (cbrt (pow (* n (* PI 2)) (/ 1 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (32 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 (/ (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))) (cbrt (pow (* 2 (* n PI)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))) (cbrt (pow (* 2 (* n PI)) (/ 1 2)))) * * * * [misc]progress: [ 65 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (sqrt (pow (* n (* PI 2)) (/ 1 2)))) * * [misc]simplify: iters left: 6 (15 enodes) * * [misc]simplify: iters left: 5 (24 enodes) * * [misc]simplify: iters left: 4 (32 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 (/ (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))) (sqrt (pow (* 2 (* n PI)) (/ 1 2)))) * [exit]simplify: Simplified to (/ (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))) (sqrt (pow (* 2 (* n PI)) (/ 1 2)))) * * * * [misc]progress: [ 66 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (* (sqrt k) (pow (* n (* PI 2)) (/ k 2))) (pow (* n (* PI 2)) (/ 1 2))) * * [misc]simplify: iters left: 6 (14 enodes) * * [misc]simplify: iters left: 5 (23 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 (/ (sqrt k) (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) * [exit]simplify: Simplified to (/ (sqrt k) (/ (pow (* PI (* n 2)) (/ 1 2)) (pow (* PI (* n 2)) (/ k 2)))) * * * * [misc]progress: [ 67 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (18 enodes) * * [misc]simplify: iters left: 5 (37 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (109 enodes) * * [misc]simplify: iters left: 2 (177 enodes) * * [misc]simplify: iters left: 1 (279 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (* n 2)) (/ (sqrt PI) (sqrt k))) (pow (* (* n PI) 2) (/ k 2))) * * * * [misc]progress: [ 68 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (20 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (107 enodes) * * [misc]simplify: iters left: 2 (226 enodes) * [exit]simplify: Simplified to (/ (* (sqrt (* PI 2)) (/ (sqrt n) (sqrt k))) (pow (* (* PI n) 2) (/ k 2))) * * * * [misc]progress: [ 69 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (21 enodes) * * [misc]simplify: iters left: 5 (40 enodes) * * [misc]simplify: iters left: 4 (62 enodes) * * [misc]simplify: iters left: 3 (110 enodes) * * [misc]simplify: iters left: 2 (261 enodes) * [exit]simplify: Simplified to (/ (/ (/ (sqrt (* PI -2)) (pow (/ -1 n) 1/2)) (pow (* PI (* 2 n)) (/ k 2))) (sqrt k)) * * * * [misc]progress: [ 70 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 (* PI n)) (/ 1 2)) (sqrt k)) (pow (* 2 (* PI n)) (/ k 2))) * * * * [misc]progress: [ 71 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 (* PI n)) (/ 1 2)) (sqrt k)) (pow (* 2 (* PI n)) (/ k 2))) * * * * [misc]progress: [ 72 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* n (* PI 2)) (/ 1 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* 2 (* PI n)) (/ 1 2)) (sqrt k)) (pow (* 2 (* PI n)) (/ k 2))) * * * * [misc]progress: [ 73 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* 2 PI) n) (/ 1 2)) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2))) * * * * [misc]progress: [ 74 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* 2 PI) n) (/ 1 2)) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2))) * * * * [misc]progress: [ 75 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* PI 2)) (/ k 2)))) * * [misc]simplify: iters left: 6 (16 enodes) * * [misc]simplify: iters left: 5 (27 enodes) * * [misc]simplify: iters left: 4 (31 enodes) * [exit]simplify: Simplified to (/ (/ (pow (* (* 2 PI) n) (/ 1 2)) (sqrt k)) (pow (* (* 2 PI) n) (/ k 2))) * * * * [misc]progress: [ 76 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (log n)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow k 2) (pow (log n) 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (pow (log (* 2 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) k))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log (* 2 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) k)) (- (* +nan.0 (* (exp (* 1/2 (+ (log (* 2 PI)) (log n)))) (* (log (* 2 PI)) (* (pow k 2) (log n)))))))))))))))))))))))) * * * * [misc]progress: [ 77 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* k (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 2) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n))))))))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* 2 PI)) (log (/ 1 n))))) (* (pow k 3) (exp (* 1/2 (* k (- (log (* 2 PI)) (log (/ 1 n)))))))))))))) * * * * [misc]progress: [ 78 / 78 ] simplifiying candidate # * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) k))) (- (* +nan.0 (/ (exp (* 1/2 (- (log (* -2 PI)) (log (/ -1 n))))) (* (exp (* 1/2 (* k (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))))))))) * * * [misc]progress: 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 (- 1/2) * * [misc]simplify: iters left: 2 (2 enodes) * [exit]simplify: Simplified to (- 1/2) * [exit]simplify: Simplified to (- 1/2) * * * * [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 6465 additional inputs, on iter 1 have 1535 / 8000 * * * * [misc]points: Computing exacts on every 404 of 6465 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 202 of 6465 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 6465 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 6465 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 6465 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 6465 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 6465 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 6465 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 6465 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 5257 additional inputs, on iter 2 have 2743 / 8000 * * * * [misc]points: Computing exacts on every 328 of 5257 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 164 of 5257 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 82 of 5257 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 41 of 5257 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 5257 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 5257 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 5257 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 5257 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 5257 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 4283 additional inputs, on iter 3 have 3717 / 8000 * * * * [misc]points: Computing exacts on every 267 of 4283 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 133 of 4283 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 66 of 4283 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 33 of 4283 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 4283 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 4283 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 4283 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 4283 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 4283 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 3483 additional inputs, on iter 4 have 4517 / 8000 * * * * [misc]points: Computing exacts on every 217 of 3483 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 108 of 3483 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 54 of 3483 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 27 of 3483 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 3483 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 3483 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 3483 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 3483 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 2840 additional inputs, on iter 5 have 5160 / 8000 * * * * [misc]points: Computing exacts on every 177 of 2840 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 88 of 2840 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 44 of 2840 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 22 of 2840 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 2840 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 2840 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 2840 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 2840 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 2318 additional inputs, on iter 6 have 5682 / 8000 * * * * [misc]points: Computing exacts on every 144 of 2318 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 72 of 2318 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 36 of 2318 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 2318 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 2318 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 2318 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 2318 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 2318 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 1916 additional inputs, on iter 7 have 6084 / 8000 * * * * [misc]points: Computing exacts on every 119 of 1916 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 59 of 1916 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 29 of 1916 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 1916 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 1916 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 1916 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 1916 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 1558 additional inputs, on iter 8 have 6442 / 8000 * * * * [misc]points: Computing exacts on every 97 of 1558 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 48 of 1558 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 24 of 1558 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 1558 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 1558 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 1558 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 1558 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 1261 additional inputs, on iter 9 have 6739 / 8000 * * * * [misc]points: Computing exacts on every 78 of 1261 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 39 of 1261 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 19 of 1261 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 1261 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 1261 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 1261 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 1261 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 1040 additional inputs, on iter 10 have 6960 / 8000 * * * * [misc]points: Computing exacts on every 65 of 1040 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 1040 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 1040 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 1040 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 1040 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 1040 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 1040 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 846 additional inputs, on iter 11 have 7154 / 8000 * * * * [misc]points: Computing exacts on every 52 of 846 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 846 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 846 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 846 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 846 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 846 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 679 additional inputs, on iter 12 have 7321 / 8000 * * * * [misc]points: Computing exacts on every 42 of 679 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 679 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 679 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 679 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 679 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 679 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 567 additional inputs, on iter 13 have 7433 / 8000 * * * * [misc]points: Computing exacts on every 35 of 567 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 567 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 567 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 567 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 567 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 567 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 457 additional inputs, on iter 14 have 7543 / 8000 * * * * [misc]points: Computing exacts on every 28 of 457 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 457 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 457 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 457 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 457 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 370 additional inputs, on iter 15 have 7630 / 8000 * * * * [misc]points: Computing exacts on every 23 of 370 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 370 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 370 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 370 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 370 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 298 additional inputs, on iter 16 have 7702 / 8000 * * * * [misc]points: Computing exacts on every 18 of 298 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 298 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 298 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 298 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 298 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 236 additional inputs, on iter 17 have 7764 / 8000 * * * * [misc]points: Computing exacts on every 14 of 236 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 236 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 236 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 236 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 190 additional inputs, on iter 18 have 7810 / 8000 * * * * [misc]points: Computing exacts on every 11 of 190 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 190 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 190 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 190 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 157 additional inputs, on iter 19 have 7843 / 8000 * * * * [misc]points: Computing exacts on every 9 of 157 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 157 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 157 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 157 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 129 additional inputs, on iter 20 have 7871 / 8000 * * * * [misc]points: Computing exacts on every 8 of 129 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 129 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 129 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 129 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 104 additional inputs, on iter 21 have 7896 / 8000 * * * * [misc]points: Computing exacts on every 6 of 104 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts on every 3 of 104 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 104 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 84 additional inputs, on iter 22 have 7916 / 8000 * * * * [misc]points: Computing exacts on every 5 of 84 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 84 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 84 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 69 additional inputs, on iter 23 have 7931 / 8000 * * * * [misc]points: Computing exacts on every 4 of 69 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 69 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 69 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 58 additional inputs, on iter 24 have 7942 / 8000 * * * * [misc]points: Computing exacts on every 3 of 58 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 58 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 51 additional inputs, on iter 25 have 7949 / 8000 * * * * [misc]points: Computing exacts on every 3 of 51 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 51 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 26 have 7958 / 8000 * * * * [misc]points: Computing exacts on every 2 of 42 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 42 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 35 additional inputs, on iter 27 have 7965 / 8000 * * * * [misc]points: Computing exacts on every 2 of 35 points to ramp up precision * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Computing exacts for 35 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 31 additional inputs, on iter 28 have 7969 / 8000 * * * * [misc]points: Computing exacts for 31 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 26 additional inputs, on iter 29 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 23 additional inputs, on iter 30 have 7977 / 8000 * * * * [misc]points: Computing exacts for 23 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 17 additional inputs, on iter 31 have 7983 / 8000 * * * * [misc]points: Computing exacts for 17 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 14 additional inputs, on iter 32 have 7986 / 8000 * * * * [misc]points: Computing exacts for 14 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 13 additional inputs, on iter 33 have 7987 / 8000 * * * * [misc]points: Computing exacts for 13 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 10 additional inputs, on iter 34 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 6 additional inputs, on iter 35 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 5 additional inputs, on iter 36 have 7995 / 8000 * * * * [misc]points: Computing exacts for 5 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 37 have 7996 / 8000 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 38 have 7997 / 8000 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 39 have 7997 / 8000 * * * * [misc]points: Computing exacts for 4 points * * * * [misc]points: Setting MPFR precision to 1088 * * * * [misc]points: Setting MPFR precision to 1344 * * * * [misc]points: Filtering points with unrepresentable outputs * * * * [misc]points: Sampling 4 additional inputs, on iter 40 have 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 41 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