58.972 * [progress]: [Phase 1 of 3] Setting up. 0.003 * * * [progress]: [1/2] Preparing points 0.178 * * * [progress]: [2/2] Setting up program. 0.184 * [progress]: [Phase 2 of 3] Improving. 0.184 * * * * [progress]: [ 1 / 1 ] simplifiying candidate # 0.185 * [simplify]: Simplifying: (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 0.185 * * [simplify]: iteration 0: 13 enodes 0.191 * * [simplify]: iteration 1: 31 enodes 0.203 * * [simplify]: iteration 2: 62 enodes 0.227 * * [simplify]: iteration 3: 124 enodes 0.655 * * [simplify]: iteration 4: 328 enodes 0.969 * * [simplify]: iteration 5: 970 enodes 2.029 * * [simplify]: iteration 6: 2753 enodes 3.175 * * [simplify]: iteration complete: 5000 enodes 3.175 * * [simplify]: Extracting #0: cost 1 inf + 0 3.176 * * [simplify]: Extracting #1: cost 218 inf + 0 3.180 * * [simplify]: Extracting #2: cost 583 inf + 1 3.186 * * [simplify]: Extracting #3: cost 872 inf + 91 3.195 * * [simplify]: Extracting #4: cost 882 inf + 7092 3.219 * * [simplify]: Extracting #5: cost 661 inf + 35266 3.260 * * [simplify]: Extracting #6: cost 372 inf + 225053 3.397 * * [simplify]: Extracting #7: cost 38 inf + 563892 3.535 * * [simplify]: Extracting #8: cost 0 inf + 582786 3.737 * * [simplify]: Extracting #9: cost 0 inf + 575286 3.919 * [simplify]: Simplified to: (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) 3.923 * * [progress]: iteration 1 / 4 3.923 * * * [progress]: picking best candidate 3.929 * * * * [pick]: Picked # 3.929 * * * [progress]: localizing error 3.958 * * * [progress]: generating rewritten candidates 3.958 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1 1) 3.977 * * * * [progress]: [ 2 / 3 ] rewriting at (2) 4.005 * * * * [progress]: [ 3 / 3 ] rewriting at (2 1) 4.061 * * * [progress]: generating series expansions 4.061 * * * * [progress]: [ 1 / 3 ] generating series at (2 1 1) 4.062 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI)) 4.062 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 4.062 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 4.062 * [taylor]: Taking taylor expansion of 2 in n 4.062 * [backup-simplify]: Simplify 2 into 2 4.062 * [taylor]: Taking taylor expansion of (* n PI) in n 4.062 * [taylor]: Taking taylor expansion of n in n 4.062 * [backup-simplify]: Simplify 0 into 0 4.062 * [backup-simplify]: Simplify 1 into 1 4.062 * [taylor]: Taking taylor expansion of PI in n 4.062 * [backup-simplify]: Simplify PI into PI 4.062 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 4.062 * [taylor]: Taking taylor expansion of 2 in n 4.062 * [backup-simplify]: Simplify 2 into 2 4.062 * [taylor]: Taking taylor expansion of (* n PI) in n 4.062 * [taylor]: Taking taylor expansion of n in n 4.062 * [backup-simplify]: Simplify 0 into 0 4.062 * [backup-simplify]: Simplify 1 into 1 4.062 * [taylor]: Taking taylor expansion of PI in n 4.062 * [backup-simplify]: Simplify PI into PI 4.062 * [backup-simplify]: Simplify (* 0 PI) into 0 4.063 * [backup-simplify]: Simplify (* 2 0) into 0 4.063 * [backup-simplify]: Simplify 0 into 0 4.064 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.065 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 4.065 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.066 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.067 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 4.067 * [backup-simplify]: Simplify 0 into 0 4.068 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.068 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.068 * [backup-simplify]: Simplify 0 into 0 4.070 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.070 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 4.071 * [backup-simplify]: Simplify 0 into 0 4.071 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.072 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 4.072 * [backup-simplify]: Simplify 0 into 0 4.073 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.074 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 4.074 * [backup-simplify]: Simplify 0 into 0 4.076 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 4.078 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 4.079 * [backup-simplify]: Simplify 0 into 0 4.079 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 4.079 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n)) 4.079 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 4.079 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 4.079 * [taylor]: Taking taylor expansion of 2 in n 4.079 * [backup-simplify]: Simplify 2 into 2 4.079 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.079 * [taylor]: Taking taylor expansion of PI in n 4.079 * [backup-simplify]: Simplify PI into PI 4.080 * [taylor]: Taking taylor expansion of n in n 4.080 * [backup-simplify]: Simplify 0 into 0 4.080 * [backup-simplify]: Simplify 1 into 1 4.080 * [backup-simplify]: Simplify (/ PI 1) into PI 4.080 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 4.080 * [taylor]: Taking taylor expansion of 2 in n 4.080 * [backup-simplify]: Simplify 2 into 2 4.080 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.080 * [taylor]: Taking taylor expansion of PI in n 4.080 * [backup-simplify]: Simplify PI into PI 4.080 * [taylor]: Taking taylor expansion of n in n 4.080 * [backup-simplify]: Simplify 0 into 0 4.080 * [backup-simplify]: Simplify 1 into 1 4.081 * [backup-simplify]: Simplify (/ PI 1) into PI 4.081 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.082 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.083 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.084 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 4.084 * [backup-simplify]: Simplify 0 into 0 4.085 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.086 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 4.086 * [backup-simplify]: Simplify 0 into 0 4.087 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.088 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.088 * [backup-simplify]: Simplify 0 into 0 4.090 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.091 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.091 * [backup-simplify]: Simplify 0 into 0 4.092 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.093 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.093 * [backup-simplify]: Simplify 0 into 0 4.093 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.095 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.095 * [backup-simplify]: Simplify 0 into 0 4.095 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 4.095 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n)) 4.095 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 4.095 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 4.095 * [taylor]: Taking taylor expansion of -2 in n 4.095 * [backup-simplify]: Simplify -2 into -2 4.095 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.095 * [taylor]: Taking taylor expansion of PI in n 4.095 * [backup-simplify]: Simplify PI into PI 4.095 * [taylor]: Taking taylor expansion of n in n 4.095 * [backup-simplify]: Simplify 0 into 0 4.095 * [backup-simplify]: Simplify 1 into 1 4.096 * [backup-simplify]: Simplify (/ PI 1) into PI 4.096 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 4.096 * [taylor]: Taking taylor expansion of -2 in n 4.096 * [backup-simplify]: Simplify -2 into -2 4.096 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.096 * [taylor]: Taking taylor expansion of PI in n 4.096 * [backup-simplify]: Simplify PI into PI 4.096 * [taylor]: Taking taylor expansion of n in n 4.096 * [backup-simplify]: Simplify 0 into 0 4.096 * [backup-simplify]: Simplify 1 into 1 4.096 * [backup-simplify]: Simplify (/ PI 1) into PI 4.096 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 4.097 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 4.097 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.098 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 4.098 * [backup-simplify]: Simplify 0 into 0 4.099 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.100 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 4.100 * [backup-simplify]: Simplify 0 into 0 4.100 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.101 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.101 * [backup-simplify]: Simplify 0 into 0 4.102 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.102 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.103 * [backup-simplify]: Simplify 0 into 0 4.103 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.104 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.104 * [backup-simplify]: Simplify 0 into 0 4.105 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.106 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.106 * [backup-simplify]: Simplify 0 into 0 4.106 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 4.106 * * * * [progress]: [ 2 / 3 ] generating series at (2) 4.106 * [backup-simplify]: Simplify (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 4.107 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 4.107 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 4.107 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.107 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.107 * [taylor]: Taking taylor expansion of k in k 4.107 * [backup-simplify]: Simplify 0 into 0 4.107 * [backup-simplify]: Simplify 1 into 1 4.107 * [backup-simplify]: Simplify (/ 1 1) into 1 4.107 * [backup-simplify]: Simplify (sqrt 0) into 0 4.108 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.108 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 4.108 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 4.108 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 4.108 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 4.108 * [taylor]: Taking taylor expansion of 1/2 in k 4.108 * [backup-simplify]: Simplify 1/2 into 1/2 4.108 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 4.108 * [taylor]: Taking taylor expansion of 1/2 in k 4.108 * [backup-simplify]: Simplify 1/2 into 1/2 4.108 * [taylor]: Taking taylor expansion of k in k 4.108 * [backup-simplify]: Simplify 0 into 0 4.108 * [backup-simplify]: Simplify 1 into 1 4.108 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 4.108 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 4.108 * [taylor]: Taking taylor expansion of 2 in k 4.108 * [backup-simplify]: Simplify 2 into 2 4.108 * [taylor]: Taking taylor expansion of (* n PI) in k 4.108 * [taylor]: Taking taylor expansion of n in k 4.108 * [backup-simplify]: Simplify n into n 4.108 * [taylor]: Taking taylor expansion of PI in k 4.108 * [backup-simplify]: Simplify PI into PI 4.108 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.108 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 4.108 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 4.109 * [backup-simplify]: Simplify (* 1/2 0) into 0 4.109 * [backup-simplify]: Simplify (- 0) into 0 4.109 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 4.109 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 4.109 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 4.109 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 4.109 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 4.109 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.109 * [taylor]: Taking taylor expansion of k in n 4.109 * [backup-simplify]: Simplify k into k 4.110 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.110 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 4.110 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.110 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 4.110 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 4.110 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 4.110 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 4.110 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 4.110 * [taylor]: Taking taylor expansion of 1/2 in n 4.110 * [backup-simplify]: Simplify 1/2 into 1/2 4.110 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 4.110 * [taylor]: Taking taylor expansion of 1/2 in n 4.110 * [backup-simplify]: Simplify 1/2 into 1/2 4.110 * [taylor]: Taking taylor expansion of k in n 4.110 * [backup-simplify]: Simplify k into k 4.110 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 4.110 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 4.110 * [taylor]: Taking taylor expansion of 2 in n 4.110 * [backup-simplify]: Simplify 2 into 2 4.110 * [taylor]: Taking taylor expansion of (* n PI) in n 4.110 * [taylor]: Taking taylor expansion of n in n 4.110 * [backup-simplify]: Simplify 0 into 0 4.110 * [backup-simplify]: Simplify 1 into 1 4.110 * [taylor]: Taking taylor expansion of PI in n 4.110 * [backup-simplify]: Simplify PI into PI 4.110 * [backup-simplify]: Simplify (* 0 PI) into 0 4.111 * [backup-simplify]: Simplify (* 2 0) into 0 4.112 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.113 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 4.113 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.113 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 4.113 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 4.113 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 4.114 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.115 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 4.116 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 4.116 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 4.116 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 4.116 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.116 * [taylor]: Taking taylor expansion of k in n 4.116 * [backup-simplify]: Simplify k into k 4.116 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.116 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 4.116 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.116 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 4.116 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 4.116 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 4.116 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 4.116 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 4.116 * [taylor]: Taking taylor expansion of 1/2 in n 4.116 * [backup-simplify]: Simplify 1/2 into 1/2 4.116 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 4.116 * [taylor]: Taking taylor expansion of 1/2 in n 4.116 * [backup-simplify]: Simplify 1/2 into 1/2 4.116 * [taylor]: Taking taylor expansion of k in n 4.116 * [backup-simplify]: Simplify k into k 4.116 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 4.116 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 4.116 * [taylor]: Taking taylor expansion of 2 in n 4.116 * [backup-simplify]: Simplify 2 into 2 4.116 * [taylor]: Taking taylor expansion of (* n PI) in n 4.116 * [taylor]: Taking taylor expansion of n in n 4.116 * [backup-simplify]: Simplify 0 into 0 4.116 * [backup-simplify]: Simplify 1 into 1 4.117 * [taylor]: Taking taylor expansion of PI in n 4.117 * [backup-simplify]: Simplify PI into PI 4.117 * [backup-simplify]: Simplify (* 0 PI) into 0 4.117 * [backup-simplify]: Simplify (* 2 0) into 0 4.118 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.119 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 4.120 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.120 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 4.120 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 4.120 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 4.121 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.122 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 4.122 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 4.123 * [backup-simplify]: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) 4.123 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 4.123 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 4.123 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 4.123 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 4.123 * [taylor]: Taking taylor expansion of 1/2 in k 4.123 * [backup-simplify]: Simplify 1/2 into 1/2 4.123 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 4.123 * [taylor]: Taking taylor expansion of 1/2 in k 4.123 * [backup-simplify]: Simplify 1/2 into 1/2 4.123 * [taylor]: Taking taylor expansion of k in k 4.123 * [backup-simplify]: Simplify 0 into 0 4.123 * [backup-simplify]: Simplify 1 into 1 4.123 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 4.123 * [taylor]: Taking taylor expansion of (log n) in k 4.123 * [taylor]: Taking taylor expansion of n in k 4.123 * [backup-simplify]: Simplify n into n 4.123 * [backup-simplify]: Simplify (log n) into (log n) 4.123 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 4.123 * [taylor]: Taking taylor expansion of (* 2 PI) in k 4.123 * [taylor]: Taking taylor expansion of 2 in k 4.123 * [backup-simplify]: Simplify 2 into 2 4.123 * [taylor]: Taking taylor expansion of PI in k 4.123 * [backup-simplify]: Simplify PI into PI 4.124 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.124 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.125 * [backup-simplify]: Simplify (* 1/2 0) into 0 4.125 * [backup-simplify]: Simplify (- 0) into 0 4.125 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 4.126 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.127 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 4.127 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 4.127 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.127 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.127 * [taylor]: Taking taylor expansion of k in k 4.127 * [backup-simplify]: Simplify 0 into 0 4.127 * [backup-simplify]: Simplify 1 into 1 4.128 * [backup-simplify]: Simplify (/ 1 1) into 1 4.128 * [backup-simplify]: Simplify (sqrt 0) into 0 4.129 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.130 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 4.130 * [backup-simplify]: Simplify 0 into 0 4.130 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.131 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 4.132 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 4.132 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 4.133 * [backup-simplify]: Simplify (- 0) into 0 4.133 * [backup-simplify]: Simplify (+ 0 0) into 0 4.134 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.135 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 4.136 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.137 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 4.137 * [taylor]: Taking taylor expansion of 0 in k 4.137 * [backup-simplify]: Simplify 0 into 0 4.137 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.138 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 4.139 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 4.139 * [backup-simplify]: Simplify (+ 0 0) into 0 4.140 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 4.140 * [backup-simplify]: Simplify (- 1/2) into -1/2 4.141 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 4.142 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 4.145 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 4.149 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 4.150 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 4.152 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.153 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.156 * [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 4.157 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 4.157 * [backup-simplify]: Simplify (- 0) into 0 4.157 * [backup-simplify]: Simplify (+ 0 0) into 0 4.159 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.160 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 4.162 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.163 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.163 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 4.169 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 4.169 * [taylor]: Taking taylor expansion of 0 in k 4.169 * [backup-simplify]: Simplify 0 into 0 4.169 * [backup-simplify]: Simplify 0 into 0 4.170 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.173 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.175 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.175 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 4.177 * [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 4.177 * [backup-simplify]: Simplify (+ 0 0) into 0 4.178 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 4.178 * [backup-simplify]: Simplify (- 0) into 0 4.178 * [backup-simplify]: Simplify (+ 0 0) into 0 4.180 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 4.182 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 4.188 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 4.191 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 4.192 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.193 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 4.196 * [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 4.197 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 4.197 * [backup-simplify]: Simplify (- 0) into 0 4.198 * [backup-simplify]: Simplify (+ 0 0) into 0 4.198 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.200 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 4.201 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.201 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.202 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 4.203 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 4.203 * [taylor]: Taking taylor expansion of 0 in k 4.203 * [backup-simplify]: Simplify 0 into 0 4.203 * [backup-simplify]: Simplify 0 into 0 4.203 * [backup-simplify]: Simplify 0 into 0 4.204 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.206 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.208 * [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 4.209 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.212 * [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 4.212 * [backup-simplify]: Simplify (+ 0 0) into 0 4.213 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 4.213 * [backup-simplify]: Simplify (- 0) into 0 4.214 * [backup-simplify]: Simplify (+ 0 0) into 0 4.215 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 4.220 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 4.238 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 4.251 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 4.271 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) 4.271 * [backup-simplify]: Simplify (/ (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 4.271 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 4.271 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 4.272 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.272 * [taylor]: Taking taylor expansion of k in k 4.272 * [backup-simplify]: Simplify 0 into 0 4.272 * [backup-simplify]: Simplify 1 into 1 4.272 * [backup-simplify]: Simplify (sqrt 0) into 0 4.274 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.274 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 4.274 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 4.274 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 4.274 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 4.274 * [taylor]: Taking taylor expansion of 1/2 in k 4.274 * [backup-simplify]: Simplify 1/2 into 1/2 4.274 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 4.274 * [taylor]: Taking taylor expansion of 1/2 in k 4.274 * [backup-simplify]: Simplify 1/2 into 1/2 4.274 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.274 * [taylor]: Taking taylor expansion of k in k 4.274 * [backup-simplify]: Simplify 0 into 0 4.274 * [backup-simplify]: Simplify 1 into 1 4.274 * [backup-simplify]: Simplify (/ 1 1) into 1 4.274 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 4.274 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 4.274 * [taylor]: Taking taylor expansion of 2 in k 4.274 * [backup-simplify]: Simplify 2 into 2 4.274 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.274 * [taylor]: Taking taylor expansion of PI in k 4.274 * [backup-simplify]: Simplify PI into PI 4.275 * [taylor]: Taking taylor expansion of n in k 4.275 * [backup-simplify]: Simplify n into n 4.275 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.275 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 4.275 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 4.275 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 4.276 * [backup-simplify]: Simplify (- 1/2) into -1/2 4.276 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 4.276 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 4.279 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 4.280 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 4.280 * [taylor]: Taking taylor expansion of (sqrt k) in n 4.280 * [taylor]: Taking taylor expansion of k in n 4.280 * [backup-simplify]: Simplify k into k 4.280 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 4.280 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 4.280 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 4.280 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 4.280 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 4.280 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 4.280 * [taylor]: Taking taylor expansion of 1/2 in n 4.280 * [backup-simplify]: Simplify 1/2 into 1/2 4.280 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 4.280 * [taylor]: Taking taylor expansion of 1/2 in n 4.280 * [backup-simplify]: Simplify 1/2 into 1/2 4.280 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.280 * [taylor]: Taking taylor expansion of k in n 4.280 * [backup-simplify]: Simplify k into k 4.280 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.280 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 4.280 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 4.280 * [taylor]: Taking taylor expansion of 2 in n 4.280 * [backup-simplify]: Simplify 2 into 2 4.280 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.280 * [taylor]: Taking taylor expansion of PI in n 4.280 * [backup-simplify]: Simplify PI into PI 4.280 * [taylor]: Taking taylor expansion of n in n 4.280 * [backup-simplify]: Simplify 0 into 0 4.280 * [backup-simplify]: Simplify 1 into 1 4.281 * [backup-simplify]: Simplify (/ PI 1) into PI 4.282 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.283 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.283 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 4.283 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 4.283 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 4.285 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.286 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 4.287 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 4.287 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 4.287 * [taylor]: Taking taylor expansion of (sqrt k) in n 4.287 * [taylor]: Taking taylor expansion of k in n 4.287 * [backup-simplify]: Simplify k into k 4.287 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 4.287 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 4.287 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 4.287 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 4.287 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 4.287 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 4.287 * [taylor]: Taking taylor expansion of 1/2 in n 4.287 * [backup-simplify]: Simplify 1/2 into 1/2 4.287 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 4.287 * [taylor]: Taking taylor expansion of 1/2 in n 4.287 * [backup-simplify]: Simplify 1/2 into 1/2 4.287 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.287 * [taylor]: Taking taylor expansion of k in n 4.287 * [backup-simplify]: Simplify k into k 4.287 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.288 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 4.288 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 4.288 * [taylor]: Taking taylor expansion of 2 in n 4.288 * [backup-simplify]: Simplify 2 into 2 4.288 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.288 * [taylor]: Taking taylor expansion of PI in n 4.288 * [backup-simplify]: Simplify PI into PI 4.288 * [taylor]: Taking taylor expansion of n in n 4.288 * [backup-simplify]: Simplify 0 into 0 4.288 * [backup-simplify]: Simplify 1 into 1 4.288 * [backup-simplify]: Simplify (/ PI 1) into PI 4.289 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.290 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.290 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 4.290 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 4.290 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 4.292 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.293 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 4.294 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 4.295 * [backup-simplify]: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) 4.295 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 4.295 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 4.295 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 4.296 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 4.296 * [taylor]: Taking taylor expansion of 1/2 in k 4.296 * [backup-simplify]: Simplify 1/2 into 1/2 4.296 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 4.296 * [taylor]: Taking taylor expansion of 1/2 in k 4.296 * [backup-simplify]: Simplify 1/2 into 1/2 4.296 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.296 * [taylor]: Taking taylor expansion of k in k 4.296 * [backup-simplify]: Simplify 0 into 0 4.296 * [backup-simplify]: Simplify 1 into 1 4.296 * [backup-simplify]: Simplify (/ 1 1) into 1 4.296 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 4.296 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 4.296 * [taylor]: Taking taylor expansion of (* 2 PI) in k 4.296 * [taylor]: Taking taylor expansion of 2 in k 4.296 * [backup-simplify]: Simplify 2 into 2 4.296 * [taylor]: Taking taylor expansion of PI in k 4.296 * [backup-simplify]: Simplify PI into PI 4.297 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.298 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.298 * [taylor]: Taking taylor expansion of (log n) in k 4.298 * [taylor]: Taking taylor expansion of n in k 4.298 * [backup-simplify]: Simplify n into n 4.298 * [backup-simplify]: Simplify (log n) into (log n) 4.298 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 4.299 * [backup-simplify]: Simplify (- 1/2) into -1/2 4.299 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 4.299 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.300 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 4.301 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 4.303 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 4.303 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.303 * [taylor]: Taking taylor expansion of k in k 4.303 * [backup-simplify]: Simplify 0 into 0 4.303 * [backup-simplify]: Simplify 1 into 1 4.303 * [backup-simplify]: Simplify (sqrt 0) into 0 4.305 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.306 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 4.306 * [backup-simplify]: Simplify 0 into 0 4.307 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.308 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 4.310 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 4.310 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.310 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 4.311 * [backup-simplify]: Simplify (- 0) into 0 4.311 * [backup-simplify]: Simplify (+ 0 0) into 0 4.313 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.314 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 4.316 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 4.317 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 4.317 * [taylor]: Taking taylor expansion of 0 in k 4.317 * [backup-simplify]: Simplify 0 into 0 4.317 * [backup-simplify]: Simplify 0 into 0 4.319 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 4.320 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 4.321 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.322 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 4.326 * [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 4.326 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.327 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 4.327 * [backup-simplify]: Simplify (- 0) into 0 4.328 * [backup-simplify]: Simplify (+ 0 0) into 0 4.329 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.331 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 4.333 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.334 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 4.335 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 4.335 * [taylor]: Taking taylor expansion of 0 in k 4.336 * [backup-simplify]: Simplify 0 into 0 4.336 * [backup-simplify]: Simplify 0 into 0 4.336 * [backup-simplify]: Simplify 0 into 0 4.339 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.340 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 4.341 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 4.341 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.342 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.345 * [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 4.346 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.346 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 4.347 * [backup-simplify]: Simplify (- 0) into 0 4.347 * [backup-simplify]: Simplify (+ 0 0) into 0 4.348 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.349 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 4.351 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.351 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 4.352 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 4.352 * [taylor]: Taking taylor expansion of 0 in k 4.353 * [backup-simplify]: Simplify 0 into 0 4.353 * [backup-simplify]: Simplify 0 into 0 4.353 * [backup-simplify]: Simplify 0 into 0 4.353 * [backup-simplify]: Simplify 0 into 0 4.355 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.356 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 4.357 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 4.360 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 4.360 * [backup-simplify]: Simplify (/ (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 4.360 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 4.360 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 4.360 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 4.360 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 4.360 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 4.360 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 4.360 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 4.360 * [taylor]: Taking taylor expansion of 1/2 in k 4.360 * [backup-simplify]: Simplify 1/2 into 1/2 4.360 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.360 * [taylor]: Taking taylor expansion of k in k 4.360 * [backup-simplify]: Simplify 0 into 0 4.360 * [backup-simplify]: Simplify 1 into 1 4.360 * [backup-simplify]: Simplify (/ 1 1) into 1 4.360 * [taylor]: Taking taylor expansion of 1/2 in k 4.360 * [backup-simplify]: Simplify 1/2 into 1/2 4.360 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 4.360 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 4.360 * [taylor]: Taking taylor expansion of -2 in k 4.360 * [backup-simplify]: Simplify -2 into -2 4.360 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.360 * [taylor]: Taking taylor expansion of PI in k 4.360 * [backup-simplify]: Simplify PI into PI 4.360 * [taylor]: Taking taylor expansion of n in k 4.360 * [backup-simplify]: Simplify n into n 4.361 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.361 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 4.361 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 4.361 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 4.361 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 4.361 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 4.361 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 4.361 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.361 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.361 * [taylor]: Taking taylor expansion of -1 in k 4.361 * [backup-simplify]: Simplify -1 into -1 4.361 * [taylor]: Taking taylor expansion of k in k 4.361 * [backup-simplify]: Simplify 0 into 0 4.361 * [backup-simplify]: Simplify 1 into 1 4.362 * [backup-simplify]: Simplify (/ -1 1) into -1 4.362 * [backup-simplify]: Simplify (sqrt 0) into 0 4.363 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.363 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 4.363 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 4.363 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 4.363 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 4.363 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 4.363 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 4.363 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 4.363 * [taylor]: Taking taylor expansion of 1/2 in n 4.363 * [backup-simplify]: Simplify 1/2 into 1/2 4.363 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.363 * [taylor]: Taking taylor expansion of k in n 4.363 * [backup-simplify]: Simplify k into k 4.363 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.363 * [taylor]: Taking taylor expansion of 1/2 in n 4.363 * [backup-simplify]: Simplify 1/2 into 1/2 4.363 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 4.363 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 4.363 * [taylor]: Taking taylor expansion of -2 in n 4.363 * [backup-simplify]: Simplify -2 into -2 4.363 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.363 * [taylor]: Taking taylor expansion of PI in n 4.363 * [backup-simplify]: Simplify PI into PI 4.363 * [taylor]: Taking taylor expansion of n in n 4.363 * [backup-simplify]: Simplify 0 into 0 4.363 * [backup-simplify]: Simplify 1 into 1 4.364 * [backup-simplify]: Simplify (/ PI 1) into PI 4.364 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 4.365 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 4.365 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 4.365 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 4.366 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.366 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 4.367 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 4.367 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 4.367 * [taylor]: Taking taylor expansion of (/ -1 k) in n 4.367 * [taylor]: Taking taylor expansion of -1 in n 4.367 * [backup-simplify]: Simplify -1 into -1 4.367 * [taylor]: Taking taylor expansion of k in n 4.368 * [backup-simplify]: Simplify k into k 4.368 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 4.368 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 4.368 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 4.368 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 4.369 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 4.369 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 4.369 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 4.369 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 4.369 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 4.369 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 4.369 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 4.369 * [taylor]: Taking taylor expansion of 1/2 in n 4.369 * [backup-simplify]: Simplify 1/2 into 1/2 4.369 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.369 * [taylor]: Taking taylor expansion of k in n 4.369 * [backup-simplify]: Simplify k into k 4.370 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.370 * [taylor]: Taking taylor expansion of 1/2 in n 4.370 * [backup-simplify]: Simplify 1/2 into 1/2 4.370 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 4.370 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 4.370 * [taylor]: Taking taylor expansion of -2 in n 4.370 * [backup-simplify]: Simplify -2 into -2 4.370 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.370 * [taylor]: Taking taylor expansion of PI in n 4.370 * [backup-simplify]: Simplify PI into PI 4.370 * [taylor]: Taking taylor expansion of n in n 4.370 * [backup-simplify]: Simplify 0 into 0 4.370 * [backup-simplify]: Simplify 1 into 1 4.370 * [backup-simplify]: Simplify (/ PI 1) into PI 4.371 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 4.372 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 4.372 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 4.372 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 4.374 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.375 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 4.376 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 4.376 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 4.376 * [taylor]: Taking taylor expansion of (/ -1 k) in n 4.376 * [taylor]: Taking taylor expansion of -1 in n 4.376 * [backup-simplify]: Simplify -1 into -1 4.376 * [taylor]: Taking taylor expansion of k in n 4.376 * [backup-simplify]: Simplify k into k 4.376 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 4.376 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 4.376 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 4.377 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 4.378 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 4.378 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 4.378 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 4.378 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 4.378 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 4.378 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 4.378 * [taylor]: Taking taylor expansion of 1/2 in k 4.378 * [backup-simplify]: Simplify 1/2 into 1/2 4.378 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.378 * [taylor]: Taking taylor expansion of k in k 4.378 * [backup-simplify]: Simplify 0 into 0 4.378 * [backup-simplify]: Simplify 1 into 1 4.379 * [backup-simplify]: Simplify (/ 1 1) into 1 4.379 * [taylor]: Taking taylor expansion of 1/2 in k 4.379 * [backup-simplify]: Simplify 1/2 into 1/2 4.379 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 4.379 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 4.379 * [taylor]: Taking taylor expansion of (* -2 PI) in k 4.379 * [taylor]: Taking taylor expansion of -2 in k 4.379 * [backup-simplify]: Simplify -2 into -2 4.379 * [taylor]: Taking taylor expansion of PI in k 4.379 * [backup-simplify]: Simplify PI into PI 4.379 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 4.380 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 4.380 * [taylor]: Taking taylor expansion of (log n) in k 4.380 * [taylor]: Taking taylor expansion of n in k 4.380 * [backup-simplify]: Simplify n into n 4.381 * [backup-simplify]: Simplify (log n) into (log n) 4.381 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 4.381 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 4.381 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.383 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 4.384 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 4.385 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 4.385 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.385 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.385 * [taylor]: Taking taylor expansion of -1 in k 4.385 * [backup-simplify]: Simplify -1 into -1 4.385 * [taylor]: Taking taylor expansion of k in k 4.385 * [backup-simplify]: Simplify 0 into 0 4.385 * [backup-simplify]: Simplify 1 into 1 4.386 * [backup-simplify]: Simplify (/ -1 1) into -1 4.386 * [backup-simplify]: Simplify (sqrt 0) into 0 4.388 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.389 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 4.390 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 4.391 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.392 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 4.394 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 4.394 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.395 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 4.395 * [backup-simplify]: Simplify (+ 0 0) into 0 4.397 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.398 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 4.400 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 4.401 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 4.401 * [taylor]: Taking taylor expansion of 0 in k 4.401 * [backup-simplify]: Simplify 0 into 0 4.401 * [backup-simplify]: Simplify 0 into 0 4.401 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.405 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.407 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 4.407 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 4.408 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.409 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 4.411 * [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 4.411 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.411 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 4.412 * [backup-simplify]: Simplify (+ 0 0) into 0 4.413 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.414 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 4.415 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.415 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.416 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 4.417 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 4.417 * [taylor]: Taking taylor expansion of 0 in k 4.417 * [backup-simplify]: Simplify 0 into 0 4.417 * [backup-simplify]: Simplify 0 into 0 4.417 * [backup-simplify]: Simplify 0 into 0 4.417 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.420 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.422 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 4.423 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 4.426 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 4.426 * * * * [progress]: [ 3 / 3 ] generating series at (2 1) 4.426 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 4.426 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 4.426 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 4.426 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 4.426 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 4.426 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 4.426 * [taylor]: Taking taylor expansion of 1/2 in k 4.426 * [backup-simplify]: Simplify 1/2 into 1/2 4.426 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 4.426 * [taylor]: Taking taylor expansion of 1/2 in k 4.426 * [backup-simplify]: Simplify 1/2 into 1/2 4.426 * [taylor]: Taking taylor expansion of k in k 4.426 * [backup-simplify]: Simplify 0 into 0 4.426 * [backup-simplify]: Simplify 1 into 1 4.426 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 4.426 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 4.426 * [taylor]: Taking taylor expansion of 2 in k 4.426 * [backup-simplify]: Simplify 2 into 2 4.426 * [taylor]: Taking taylor expansion of (* n PI) in k 4.426 * [taylor]: Taking taylor expansion of n in k 4.426 * [backup-simplify]: Simplify n into n 4.426 * [taylor]: Taking taylor expansion of PI in k 4.426 * [backup-simplify]: Simplify PI into PI 4.426 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.426 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 4.426 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 4.427 * [backup-simplify]: Simplify (* 1/2 0) into 0 4.427 * [backup-simplify]: Simplify (- 0) into 0 4.427 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 4.428 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 4.428 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 4.428 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 4.428 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 4.428 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 4.428 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 4.428 * [taylor]: Taking taylor expansion of 1/2 in n 4.428 * [backup-simplify]: Simplify 1/2 into 1/2 4.428 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 4.428 * [taylor]: Taking taylor expansion of 1/2 in n 4.428 * [backup-simplify]: Simplify 1/2 into 1/2 4.428 * [taylor]: Taking taylor expansion of k in n 4.428 * [backup-simplify]: Simplify k into k 4.428 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 4.428 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 4.428 * [taylor]: Taking taylor expansion of 2 in n 4.428 * [backup-simplify]: Simplify 2 into 2 4.428 * [taylor]: Taking taylor expansion of (* n PI) in n 4.428 * [taylor]: Taking taylor expansion of n in n 4.428 * [backup-simplify]: Simplify 0 into 0 4.428 * [backup-simplify]: Simplify 1 into 1 4.428 * [taylor]: Taking taylor expansion of PI in n 4.428 * [backup-simplify]: Simplify PI into PI 4.429 * [backup-simplify]: Simplify (* 0 PI) into 0 4.429 * [backup-simplify]: Simplify (* 2 0) into 0 4.431 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.432 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 4.433 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.433 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 4.433 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 4.434 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 4.435 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.436 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 4.437 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 4.437 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 4.437 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 4.438 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 4.438 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 4.438 * [taylor]: Taking taylor expansion of 1/2 in n 4.438 * [backup-simplify]: Simplify 1/2 into 1/2 4.438 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 4.438 * [taylor]: Taking taylor expansion of 1/2 in n 4.438 * [backup-simplify]: Simplify 1/2 into 1/2 4.438 * [taylor]: Taking taylor expansion of k in n 4.438 * [backup-simplify]: Simplify k into k 4.438 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 4.438 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 4.438 * [taylor]: Taking taylor expansion of 2 in n 4.438 * [backup-simplify]: Simplify 2 into 2 4.438 * [taylor]: Taking taylor expansion of (* n PI) in n 4.438 * [taylor]: Taking taylor expansion of n in n 4.438 * [backup-simplify]: Simplify 0 into 0 4.438 * [backup-simplify]: Simplify 1 into 1 4.438 * [taylor]: Taking taylor expansion of PI in n 4.438 * [backup-simplify]: Simplify PI into PI 4.439 * [backup-simplify]: Simplify (* 0 PI) into 0 4.439 * [backup-simplify]: Simplify (* 2 0) into 0 4.441 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.442 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 4.443 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.443 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 4.444 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 4.444 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 4.445 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.446 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 4.447 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 4.448 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 4.448 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 4.448 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 4.448 * [taylor]: Taking taylor expansion of 1/2 in k 4.448 * [backup-simplify]: Simplify 1/2 into 1/2 4.448 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 4.448 * [taylor]: Taking taylor expansion of 1/2 in k 4.448 * [backup-simplify]: Simplify 1/2 into 1/2 4.448 * [taylor]: Taking taylor expansion of k in k 4.448 * [backup-simplify]: Simplify 0 into 0 4.448 * [backup-simplify]: Simplify 1 into 1 4.448 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 4.448 * [taylor]: Taking taylor expansion of (log n) in k 4.448 * [taylor]: Taking taylor expansion of n in k 4.448 * [backup-simplify]: Simplify n into n 4.448 * [backup-simplify]: Simplify (log n) into (log n) 4.448 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 4.448 * [taylor]: Taking taylor expansion of (* 2 PI) in k 4.448 * [taylor]: Taking taylor expansion of 2 in k 4.448 * [backup-simplify]: Simplify 2 into 2 4.448 * [taylor]: Taking taylor expansion of PI in k 4.448 * [backup-simplify]: Simplify PI into PI 4.449 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.450 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.450 * [backup-simplify]: Simplify (* 1/2 0) into 0 4.451 * [backup-simplify]: Simplify (- 0) into 0 4.451 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 4.452 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.452 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 4.453 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 4.454 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 4.454 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.455 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 4.456 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 4.456 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 4.457 * [backup-simplify]: Simplify (- 0) into 0 4.457 * [backup-simplify]: Simplify (+ 0 0) into 0 4.458 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.459 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 4.460 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.460 * [taylor]: Taking taylor expansion of 0 in k 4.460 * [backup-simplify]: Simplify 0 into 0 4.460 * [backup-simplify]: Simplify 0 into 0 4.460 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.461 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 4.462 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 4.462 * [backup-simplify]: Simplify (+ 0 0) into 0 4.463 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 4.463 * [backup-simplify]: Simplify (- 1/2) into -1/2 4.463 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 4.464 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 4.466 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 4.468 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 4.469 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.470 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.471 * [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 4.472 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 4.472 * [backup-simplify]: Simplify (- 0) into 0 4.472 * [backup-simplify]: Simplify (+ 0 0) into 0 4.473 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.474 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 4.476 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.476 * [taylor]: Taking taylor expansion of 0 in k 4.476 * [backup-simplify]: Simplify 0 into 0 4.476 * [backup-simplify]: Simplify 0 into 0 4.476 * [backup-simplify]: Simplify 0 into 0 4.477 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.478 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 4.480 * [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 4.481 * [backup-simplify]: Simplify (+ 0 0) into 0 4.482 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 4.482 * [backup-simplify]: Simplify (- 0) into 0 4.483 * [backup-simplify]: Simplify (+ 0 0) into 0 4.485 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 4.489 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 4.495 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 4.501 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 4.501 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 4.501 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 4.501 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 4.501 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 4.501 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 4.501 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 4.501 * [taylor]: Taking taylor expansion of 1/2 in k 4.501 * [backup-simplify]: Simplify 1/2 into 1/2 4.501 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 4.501 * [taylor]: Taking taylor expansion of 1/2 in k 4.501 * [backup-simplify]: Simplify 1/2 into 1/2 4.501 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.501 * [taylor]: Taking taylor expansion of k in k 4.501 * [backup-simplify]: Simplify 0 into 0 4.501 * [backup-simplify]: Simplify 1 into 1 4.501 * [backup-simplify]: Simplify (/ 1 1) into 1 4.502 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 4.502 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 4.502 * [taylor]: Taking taylor expansion of 2 in k 4.502 * [backup-simplify]: Simplify 2 into 2 4.502 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.502 * [taylor]: Taking taylor expansion of PI in k 4.502 * [backup-simplify]: Simplify PI into PI 4.502 * [taylor]: Taking taylor expansion of n in k 4.502 * [backup-simplify]: Simplify n into n 4.502 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.502 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 4.502 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 4.502 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 4.502 * [backup-simplify]: Simplify (- 1/2) into -1/2 4.503 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 4.503 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 4.503 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 4.503 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 4.503 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 4.503 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 4.503 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 4.503 * [taylor]: Taking taylor expansion of 1/2 in n 4.503 * [backup-simplify]: Simplify 1/2 into 1/2 4.503 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 4.503 * [taylor]: Taking taylor expansion of 1/2 in n 4.503 * [backup-simplify]: Simplify 1/2 into 1/2 4.503 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.503 * [taylor]: Taking taylor expansion of k in n 4.503 * [backup-simplify]: Simplify k into k 4.503 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.503 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 4.503 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 4.503 * [taylor]: Taking taylor expansion of 2 in n 4.503 * [backup-simplify]: Simplify 2 into 2 4.503 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.503 * [taylor]: Taking taylor expansion of PI in n 4.503 * [backup-simplify]: Simplify PI into PI 4.503 * [taylor]: Taking taylor expansion of n in n 4.503 * [backup-simplify]: Simplify 0 into 0 4.503 * [backup-simplify]: Simplify 1 into 1 4.503 * [backup-simplify]: Simplify (/ PI 1) into PI 4.504 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.504 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.505 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 4.505 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 4.505 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 4.506 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.506 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 4.509 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 4.509 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 4.509 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 4.509 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 4.509 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 4.510 * [taylor]: Taking taylor expansion of 1/2 in n 4.510 * [backup-simplify]: Simplify 1/2 into 1/2 4.510 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 4.510 * [taylor]: Taking taylor expansion of 1/2 in n 4.510 * [backup-simplify]: Simplify 1/2 into 1/2 4.510 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.510 * [taylor]: Taking taylor expansion of k in n 4.510 * [backup-simplify]: Simplify k into k 4.510 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.510 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 4.510 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 4.510 * [taylor]: Taking taylor expansion of 2 in n 4.510 * [backup-simplify]: Simplify 2 into 2 4.510 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.510 * [taylor]: Taking taylor expansion of PI in n 4.510 * [backup-simplify]: Simplify PI into PI 4.510 * [taylor]: Taking taylor expansion of n in n 4.510 * [backup-simplify]: Simplify 0 into 0 4.510 * [backup-simplify]: Simplify 1 into 1 4.510 * [backup-simplify]: Simplify (/ PI 1) into PI 4.510 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.511 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.511 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 4.511 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 4.511 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 4.512 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.513 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 4.514 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 4.514 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 4.514 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 4.514 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 4.514 * [taylor]: Taking taylor expansion of 1/2 in k 4.514 * [backup-simplify]: Simplify 1/2 into 1/2 4.514 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 4.514 * [taylor]: Taking taylor expansion of 1/2 in k 4.514 * [backup-simplify]: Simplify 1/2 into 1/2 4.514 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.514 * [taylor]: Taking taylor expansion of k in k 4.514 * [backup-simplify]: Simplify 0 into 0 4.514 * [backup-simplify]: Simplify 1 into 1 4.514 * [backup-simplify]: Simplify (/ 1 1) into 1 4.514 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 4.514 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 4.514 * [taylor]: Taking taylor expansion of (* 2 PI) in k 4.514 * [taylor]: Taking taylor expansion of 2 in k 4.514 * [backup-simplify]: Simplify 2 into 2 4.514 * [taylor]: Taking taylor expansion of PI in k 4.514 * [backup-simplify]: Simplify PI into PI 4.515 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.515 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.515 * [taylor]: Taking taylor expansion of (log n) in k 4.515 * [taylor]: Taking taylor expansion of n in k 4.515 * [backup-simplify]: Simplify n into n 4.515 * [backup-simplify]: Simplify (log n) into (log n) 4.516 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 4.516 * [backup-simplify]: Simplify (- 1/2) into -1/2 4.516 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 4.516 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.517 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 4.518 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 4.518 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 4.519 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 4.520 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.520 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 4.521 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 4.521 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.522 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 4.522 * [backup-simplify]: Simplify (- 0) into 0 4.522 * [backup-simplify]: Simplify (+ 0 0) into 0 4.523 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.525 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 4.527 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 4.527 * [taylor]: Taking taylor expansion of 0 in k 4.527 * [backup-simplify]: Simplify 0 into 0 4.527 * [backup-simplify]: Simplify 0 into 0 4.527 * [backup-simplify]: Simplify 0 into 0 4.528 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.529 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 4.533 * [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 4.533 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.534 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 4.534 * [backup-simplify]: Simplify (- 0) into 0 4.535 * [backup-simplify]: Simplify (+ 0 0) into 0 4.536 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.538 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 4.540 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.540 * [taylor]: Taking taylor expansion of 0 in k 4.540 * [backup-simplify]: Simplify 0 into 0 4.540 * [backup-simplify]: Simplify 0 into 0 4.540 * [backup-simplify]: Simplify 0 into 0 4.540 * [backup-simplify]: Simplify 0 into 0 4.541 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.541 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.545 * [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 4.545 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.546 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 4.546 * [backup-simplify]: Simplify (- 0) into 0 4.546 * [backup-simplify]: Simplify (+ 0 0) into 0 4.547 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.548 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 4.550 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.550 * [taylor]: Taking taylor expansion of 0 in k 4.550 * [backup-simplify]: Simplify 0 into 0 4.550 * [backup-simplify]: Simplify 0 into 0 4.551 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 4.551 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 4.551 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 4.551 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 4.551 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 4.551 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 4.551 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 4.551 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 4.551 * [taylor]: Taking taylor expansion of 1/2 in k 4.551 * [backup-simplify]: Simplify 1/2 into 1/2 4.551 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.551 * [taylor]: Taking taylor expansion of k in k 4.551 * [backup-simplify]: Simplify 0 into 0 4.551 * [backup-simplify]: Simplify 1 into 1 4.551 * [backup-simplify]: Simplify (/ 1 1) into 1 4.551 * [taylor]: Taking taylor expansion of 1/2 in k 4.551 * [backup-simplify]: Simplify 1/2 into 1/2 4.551 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 4.551 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 4.551 * [taylor]: Taking taylor expansion of -2 in k 4.551 * [backup-simplify]: Simplify -2 into -2 4.551 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.551 * [taylor]: Taking taylor expansion of PI in k 4.551 * [backup-simplify]: Simplify PI into PI 4.551 * [taylor]: Taking taylor expansion of n in k 4.552 * [backup-simplify]: Simplify n into n 4.552 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.552 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 4.552 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 4.552 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 4.552 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 4.552 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 4.552 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 4.552 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 4.552 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 4.552 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 4.552 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 4.552 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 4.552 * [taylor]: Taking taylor expansion of 1/2 in n 4.553 * [backup-simplify]: Simplify 1/2 into 1/2 4.553 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.553 * [taylor]: Taking taylor expansion of k in n 4.553 * [backup-simplify]: Simplify k into k 4.553 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.553 * [taylor]: Taking taylor expansion of 1/2 in n 4.553 * [backup-simplify]: Simplify 1/2 into 1/2 4.553 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 4.553 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 4.553 * [taylor]: Taking taylor expansion of -2 in n 4.553 * [backup-simplify]: Simplify -2 into -2 4.553 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.553 * [taylor]: Taking taylor expansion of PI in n 4.553 * [backup-simplify]: Simplify PI into PI 4.553 * [taylor]: Taking taylor expansion of n in n 4.553 * [backup-simplify]: Simplify 0 into 0 4.553 * [backup-simplify]: Simplify 1 into 1 4.553 * [backup-simplify]: Simplify (/ PI 1) into PI 4.553 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 4.554 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 4.554 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 4.554 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 4.555 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.556 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 4.557 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 4.557 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 4.557 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 4.557 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 4.557 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 4.557 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 4.557 * [taylor]: Taking taylor expansion of 1/2 in n 4.557 * [backup-simplify]: Simplify 1/2 into 1/2 4.557 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.557 * [taylor]: Taking taylor expansion of k in n 4.557 * [backup-simplify]: Simplify k into k 4.557 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.557 * [taylor]: Taking taylor expansion of 1/2 in n 4.557 * [backup-simplify]: Simplify 1/2 into 1/2 4.557 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 4.557 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 4.557 * [taylor]: Taking taylor expansion of -2 in n 4.557 * [backup-simplify]: Simplify -2 into -2 4.557 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.557 * [taylor]: Taking taylor expansion of PI in n 4.557 * [backup-simplify]: Simplify PI into PI 4.557 * [taylor]: Taking taylor expansion of n in n 4.557 * [backup-simplify]: Simplify 0 into 0 4.557 * [backup-simplify]: Simplify 1 into 1 4.557 * [backup-simplify]: Simplify (/ PI 1) into PI 4.558 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 4.558 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 4.558 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 4.558 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 4.559 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.560 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 4.561 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 4.561 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 4.561 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 4.561 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 4.561 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 4.561 * [taylor]: Taking taylor expansion of 1/2 in k 4.561 * [backup-simplify]: Simplify 1/2 into 1/2 4.561 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.561 * [taylor]: Taking taylor expansion of k in k 4.561 * [backup-simplify]: Simplify 0 into 0 4.561 * [backup-simplify]: Simplify 1 into 1 4.561 * [backup-simplify]: Simplify (/ 1 1) into 1 4.561 * [taylor]: Taking taylor expansion of 1/2 in k 4.561 * [backup-simplify]: Simplify 1/2 into 1/2 4.561 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 4.561 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 4.561 * [taylor]: Taking taylor expansion of (* -2 PI) in k 4.561 * [taylor]: Taking taylor expansion of -2 in k 4.561 * [backup-simplify]: Simplify -2 into -2 4.561 * [taylor]: Taking taylor expansion of PI in k 4.561 * [backup-simplify]: Simplify PI into PI 4.562 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 4.562 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 4.562 * [taylor]: Taking taylor expansion of (log n) in k 4.562 * [taylor]: Taking taylor expansion of n in k 4.562 * [backup-simplify]: Simplify n into n 4.562 * [backup-simplify]: Simplify (log n) into (log n) 4.563 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 4.563 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 4.563 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.564 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 4.564 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 4.565 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 4.566 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 4.567 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.567 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 4.569 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 4.570 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.570 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 4.571 * [backup-simplify]: Simplify (+ 0 0) into 0 4.572 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.573 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 4.575 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 4.575 * [taylor]: Taking taylor expansion of 0 in k 4.575 * [backup-simplify]: Simplify 0 into 0 4.575 * [backup-simplify]: Simplify 0 into 0 4.575 * [backup-simplify]: Simplify 0 into 0 4.576 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.577 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 4.581 * [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 4.581 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.582 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 4.582 * [backup-simplify]: Simplify (+ 0 0) into 0 4.584 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.586 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 4.588 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.588 * [taylor]: Taking taylor expansion of 0 in k 4.588 * [backup-simplify]: Simplify 0 into 0 4.588 * [backup-simplify]: Simplify 0 into 0 4.588 * [backup-simplify]: Simplify 0 into 0 4.588 * [backup-simplify]: Simplify 0 into 0 4.589 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.591 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.597 * [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 4.597 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.599 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 4.599 * [backup-simplify]: Simplify (+ 0 0) into 0 4.601 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.603 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 4.606 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.606 * [taylor]: Taking taylor expansion of 0 in k 4.606 * [backup-simplify]: Simplify 0 into 0 4.606 * [backup-simplify]: Simplify 0 into 0 4.607 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 4.607 * * * [progress]: simplifying candidates 4.607 * * * * [progress]: [ 1 / 445 ] simplifiying candidate # 4.607 * * * * [progress]: [ 2 / 445 ] simplifiying candidate # 4.607 * * * * [progress]: [ 3 / 445 ] simplifiying candidate # 4.607 * * * * [progress]: [ 4 / 445 ] simplifiying candidate # 4.607 * * * * [progress]: [ 5 / 445 ] simplifiying candidate # 4.608 * * * * [progress]: [ 6 / 445 ] simplifiying candidate # 4.608 * * * * [progress]: [ 7 / 445 ] simplifiying candidate # 4.608 * * * * [progress]: [ 8 / 445 ] simplifiying candidate # 4.608 * * * * [progress]: [ 9 / 445 ] simplifiying candidate # 4.608 * * * * [progress]: [ 10 / 445 ] simplifiying candidate # 4.608 * * * * [progress]: [ 11 / 445 ] simplifiying candidate # 4.608 * * * * [progress]: [ 12 / 445 ] simplifiying candidate # 4.608 * * * * [progress]: [ 13 / 445 ] simplifiying candidate # 4.608 * * * * [progress]: [ 14 / 445 ] simplifiying candidate # 4.608 * * * * [progress]: [ 15 / 445 ] simplifiying candidate # 4.608 * * * * [progress]: [ 16 / 445 ] simplifiying candidate # 4.608 * * * * [progress]: [ 17 / 445 ] simplifiying candidate # 4.608 * * * * [progress]: [ 18 / 445 ] simplifiying candidate # 4.608 * * * * [progress]: [ 19 / 445 ] simplifiying candidate # 4.608 * * * * [progress]: [ 20 / 445 ] simplifiying candidate #real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))> 4.609 * * * * [progress]: [ 21 / 445 ] simplifiying candidate # 4.609 * * * * [progress]: [ 22 / 445 ] simplifiying candidate # 4.609 * * * * [progress]: [ 23 / 445 ] simplifiying candidate # 4.609 * * * * [progress]: [ 24 / 445 ] simplifiying candidate # 4.609 * * * * [progress]: [ 25 / 445 ] simplifiying candidate # 4.609 * * * * [progress]: [ 26 / 445 ] simplifiying candidate # 4.609 * * * * [progress]: [ 27 / 445 ] simplifiying 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candidate # 4.642 * * * * [progress]: [ 441 / 445 ] simplifiying candidate # 4.642 * * * * [progress]: [ 442 / 445 ] simplifiying candidate # 4.642 * * * * [progress]: [ 443 / 445 ] simplifiying candidate # 4.642 * * * * [progress]: [ 444 / 445 ] simplifiying candidate # 4.642 * * * * [progress]: [ 445 / 445 ] simplifiying candidate # 4.661 * [simplify]: Simplifying: (expm1 (* (* n 2) PI)) (log1p (* (* n 2) PI)) (* (* n 2) PI) (* (* n 2) PI) (+ (+ (log n) (log 2)) (log PI)) (+ (log (* n 2)) (log PI)) (log (* (* n 2) PI)) (exp (* (* n 2) PI)) (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI)) (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI)) (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI)) (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI)) (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI)) (* (* n 2) (* (cbrt PI) (cbrt PI))) (* (* n 2) (sqrt PI)) (* (* n 2) 1) (* 2 PI) (real->posit16 (* (* n 2) PI)) (expm1 (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (log1p (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (- (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))) (- (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))) (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k))) (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k))) (- (log (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (log (sqrt k))) (log (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (exp (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (* (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (- (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (- (sqrt k)) (/ (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (cbrt (sqrt k))) (/ (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt (cbrt k))) (/ (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt 1)) (/ (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt k)) (/ (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) 1) (/ (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt k)) (/ (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 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(log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 4.692 * * [simplify]: iteration 0: 699 enodes 4.899 * * [simplify]: iteration 1: 1539 enodes 5.492 * * [simplify]: iteration 2: 4186 enodes 6.538 * * [simplify]: iteration complete: 5000 enodes 6.539 * * [simplify]: Extracting #0: cost 219 inf + 0 6.541 * * [simplify]: Extracting #1: cost 794 inf + 1 6.545 * * [simplify]: Extracting #2: cost 1267 inf + 987 6.562 * * [simplify]: Extracting #3: cost 1372 inf + 41391 6.594 * * [simplify]: Extracting #4: cost 863 inf + 209716 6.707 * * [simplify]: Extracting #5: cost 537 inf + 364654 6.850 * * [simplify]: Extracting #6: cost 256 inf + 521341 7.071 * * [simplify]: Extracting #7: cost 42 inf + 672570 7.298 * * [simplify]: Extracting #8: cost 1 inf + 697089 7.516 * * [simplify]: Extracting #9: cost 0 inf + 696533 7.713 * * [simplify]: Extracting #10: cost 0 inf + 696518 7.920 * [simplify]: Simplified to: (expm1 (* n (* PI 2))) (log1p (* n (* PI 2))) (* n (* PI 2)) (* n (* PI 2)) (log (* n (* PI 2))) (log (* n (* PI 2))) (log (* n (* PI 2))) (* (exp (* PI n)) (exp (* PI n))) (* (* (* (* n (* n n)) 8) (* PI PI)) PI) (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2))) (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2))) (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2))) (sqrt (* n (* PI 2))) (sqrt (* n (* PI 2))) (* (* (* (cbrt PI) (cbrt PI)) 2) n) (* (sqrt PI) (* n 2)) (* n 2) (* PI 2) (real->posit16 (* n (* PI 2))) (expm1 (/ (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (sqrt k))) (log1p (/ (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (sqrt k))) (- (* (log (* n (* PI 2))) (- 1/2 (* k 1/2))) (log (sqrt k))) (- (* (log (* n (* PI 2))) (- 1/2 (* k 1/2))) (log (sqrt k))) (- (* (log (* n (* PI 2))) (- 1/2 (* k 1/2))) (log (sqrt k))) (- (* (log (* n (* PI 2))) (- 1/2 (* k 1/2))) (log (sqrt k))) (- (* (log (* n (* PI 2))) (- 1/2 (* k 1/2))) (log 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(* n (* PI 2)) (- 1/2 (/ (/ (cbrt k) (sqrt 2)) (/ (sqrt 2) (* (cbrt k) (cbrt k)))))) (pow (* n (* PI 2)) (* (/ (cbrt k) (sqrt 2)) (+ (- (/ (* (cbrt k) (cbrt k)) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* n (* PI 2)) (- 1/2 (/ (* (cbrt k) (* (cbrt k) (cbrt k))) 2))) (pow (* n (* PI 2)) (* (* (cbrt k) (cbrt k)) (+ (- (/ (cbrt k) 2)) (/ (cbrt k) 2)))) (pow (* n (* PI 2)) (- 1/2 (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2))))) (pow (* n (* PI 2)) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (+ (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (cbrt 2))))) (pow (* n (* PI 2)) (- 1/2 (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* n (* PI 2)) (+ (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2)))) (pow (* n (* PI 2)) (+ (- (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2))) (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2)))) (pow (* n (* PI 2)) (- 1/2 (/ (/ k (sqrt 2)) (sqrt 2)))) (pow (* n (* PI 2)) (fma (/ k (sqrt 2)) (/ -1 (sqrt 2)) (/ (/ k (sqrt 2)) (sqrt 2)))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))))) (pow (* n (* PI 2)) (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (+ (- (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2))))) (pow (* n (* PI 2)) (- 1/2 (/ (/ (cbrt k) (sqrt 2)) (/ (sqrt 2) (* (cbrt k) (cbrt k)))))) (pow (* n (* PI 2)) (* (/ (cbrt k) (sqrt 2)) (+ (- (/ (* (cbrt k) (cbrt k)) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* n (* PI 2)) (- 1/2 (/ (* (cbrt k) (* (cbrt k) (cbrt k))) 2))) (pow (* n (* PI 2)) (* (* (cbrt k) (cbrt k)) (+ (- (/ (cbrt k) 2)) (/ (cbrt k) 2)))) (pow (* n (* PI 2)) (- 1/2 (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2))))) (pow (* n (* PI 2)) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (+ (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (cbrt 2))))) (pow (* n (* PI 2)) (- 1/2 (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* n (* PI 2)) (+ (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2)))) (pow (* n (* PI 2)) (+ (- (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2))) (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2)))) (pow (* n (* PI 2)) (- 1/2 (/ (/ k (sqrt 2)) (sqrt 2)))) (pow (* n (* PI 2)) (fma (/ k (sqrt 2)) (/ -1 (sqrt 2)) (/ (/ k (sqrt 2)) (sqrt 2)))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (sqrt (* n (* PI 2))) (pow (* n (* PI 2)) (* -1/2 k)) (sqrt (* n (* PI 2))) (pow (* n (* PI 2)) (* -1/2 k)) (pow (* n 2) (- 1/2 (* k 1/2))) (pow PI (- 1/2 (* k 1/2))) (* (log (* n (* PI 2))) (- 1/2 (* k 1/2))) (exp (pow (* n (* PI 2)) (- 1/2 (* k 1/2)))) (* (cbrt (pow (* n (* PI 2)) (- 1/2 (* k 1/2)))) (cbrt (pow (* n (* PI 2)) (- 1/2 (* k 1/2))))) (cbrt (pow (* n (* PI 2)) (- 1/2 (* k 1/2)))) (* (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (* (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))))) (sqrt (pow (* n (* PI 2)) (- 1/2 (* k 1/2)))) (sqrt (pow (* n (* PI 2)) (- 1/2 (* k 1/2)))) (pow (* n (* PI 2)) (/ (- 1/2 (* k 1/2)) 2)) (pow (* n (* PI 2)) (/ (- 1/2 (* k 1/2)) 2)) (real->posit16 (pow (* n (* PI 2)) (- 1/2 (* k 1/2)))) (* n (* PI 2)) (* n (* PI 2)) (* n (* PI 2)) (- (fma (* (* +nan.0 (log (* PI 2))) (exp (* (log (* n (* PI 2))) 1/2))) (* (log n) (* k k)) (fma (- (* +nan.0 (log (* PI 2)))) (* (* k k) (exp (* (log (* n (* PI 2))) 1/2))) (fma (* +nan.0 (exp (* (log (* n (* PI 2))) 1/2))) (* (* k k) (* (log n) (log n))) (fma (- (* (exp (* (log (* n (* PI 2))) 1/2)) k)) +nan.0 (- (- (* +nan.0 (exp (* (log (* n (* PI 2))) 1/2))) (* (* (* k k) (exp (* (log (* n (* PI 2))) 1/2))) (* (* +nan.0 (log (* PI 2))) (log (* PI 2))))) (fma (* +nan.0 (exp (* (log (* n (* PI 2))) 1/2))) (- (* (log n) (* k k))) (fma (* k k) (* +nan.0 (exp (* (log (* n (* PI 2))) 1/2))) (fma (- (* +nan.0 (log (* PI 2)))) (* (exp (* (log (* n (* PI 2))) 1/2)) k) (* +nan.0 (* (log n) (* (exp (* (log (* n (* PI 2))) 1/2)) k)))))))))))) (fma (- (/ (exp (* (log (* n (* PI 2))) (- 1/2 (* k 1/2)))) (* (* k k) k))) +nan.0 (* +nan.0 (- (/ (exp (* (log (* n (* PI 2))) (- 1/2 (* k 1/2)))) k) (/ (exp (* (log (* n (* PI 2))) (- 1/2 (* k 1/2)))) (* k k))))) (fma (- +nan.0) (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* -2 PI)) (log (/ -1 n))))) k) (- (/ (* +nan.0 (exp (* (- 1/2 (* k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))))) (* k k)) (* +nan.0 (exp (* (- 1/2 (* k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))))))) (fma -1/2 (* k (fma (log n) (pow (* n (* PI 2)) 1/2) (* (log (* PI 2)) (pow (* n (* PI 2)) 1/2)))) (fma (* (* (pow (* n (* PI 2)) 1/2) (* (* k k) (log (* PI 2)))) (log n)) 1/4 (fma (* (log (* PI 2)) (* (pow (* n (* PI 2)) 1/2) (* (* k k) (log (* PI 2))))) 1/8 (fma (* (* k k) (* (log n) (log n))) (* (pow (* n (* PI 2)) 1/2) 1/8) (pow (* n (* PI 2)) 1/2))))) (exp (* (log (* n (* PI 2))) (- 1/2 (* k 1/2)))) (exp (* (- 1/2 (* k 1/2)) (- (log (* -2 PI)) (log (/ -1 n))))) 8.051 * * * [progress]: adding candidates to table 10.869 * * [progress]: iteration 2 / 4 10.869 * * * [progress]: picking best candidate 10.905 * * * * [pick]: Picked # 10.905 * * * [progress]: localizing error 10.947 * * * [progress]: generating rewritten candidates 10.947 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 1) 10.983 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2) 11.000 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2) 11.018 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 11.176 * * * [progress]: generating series expansions 11.176 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 1) 11.176 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI)) 11.176 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 11.176 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.176 * [taylor]: Taking taylor expansion of 2 in n 11.176 * [backup-simplify]: Simplify 2 into 2 11.176 * [taylor]: Taking taylor expansion of (* n PI) in n 11.176 * [taylor]: Taking taylor expansion of n in n 11.176 * [backup-simplify]: Simplify 0 into 0 11.176 * [backup-simplify]: Simplify 1 into 1 11.176 * [taylor]: Taking taylor expansion of PI in n 11.176 * [backup-simplify]: Simplify PI into PI 11.176 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.176 * [taylor]: Taking taylor expansion of 2 in n 11.176 * [backup-simplify]: Simplify 2 into 2 11.176 * [taylor]: Taking taylor expansion of (* n PI) in n 11.176 * [taylor]: Taking taylor expansion of n in n 11.176 * [backup-simplify]: Simplify 0 into 0 11.176 * [backup-simplify]: Simplify 1 into 1 11.176 * [taylor]: Taking taylor expansion of PI in n 11.176 * [backup-simplify]: Simplify PI into PI 11.177 * [backup-simplify]: Simplify (* 0 PI) into 0 11.177 * [backup-simplify]: Simplify (* 2 0) into 0 11.177 * [backup-simplify]: Simplify 0 into 0 11.178 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.179 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.180 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.180 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.181 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 11.181 * [backup-simplify]: Simplify 0 into 0 11.182 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.182 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.182 * [backup-simplify]: Simplify 0 into 0 11.183 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.184 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 11.184 * [backup-simplify]: Simplify 0 into 0 11.185 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.186 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 11.186 * [backup-simplify]: Simplify 0 into 0 11.187 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.188 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 11.188 * [backup-simplify]: Simplify 0 into 0 11.189 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 11.190 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 11.190 * [backup-simplify]: Simplify 0 into 0 11.190 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 11.191 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n)) 11.191 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 11.191 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.191 * [taylor]: Taking taylor expansion of 2 in n 11.191 * [backup-simplify]: Simplify 2 into 2 11.191 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.191 * [taylor]: Taking taylor expansion of PI in n 11.191 * [backup-simplify]: Simplify PI into PI 11.191 * [taylor]: Taking taylor expansion of n in n 11.191 * [backup-simplify]: Simplify 0 into 0 11.191 * [backup-simplify]: Simplify 1 into 1 11.191 * [backup-simplify]: Simplify (/ PI 1) into PI 11.191 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.191 * [taylor]: Taking taylor expansion of 2 in n 11.191 * [backup-simplify]: Simplify 2 into 2 11.191 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.191 * [taylor]: Taking taylor expansion of PI in n 11.191 * [backup-simplify]: Simplify PI into PI 11.191 * [taylor]: Taking taylor expansion of n in n 11.191 * [backup-simplify]: Simplify 0 into 0 11.191 * [backup-simplify]: Simplify 1 into 1 11.192 * [backup-simplify]: Simplify (/ PI 1) into PI 11.192 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.192 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.193 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.193 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.193 * [backup-simplify]: Simplify 0 into 0 11.194 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.195 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.195 * [backup-simplify]: Simplify 0 into 0 11.196 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.197 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.197 * [backup-simplify]: Simplify 0 into 0 11.198 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.200 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.200 * [backup-simplify]: Simplify 0 into 0 11.201 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.203 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.203 * [backup-simplify]: Simplify 0 into 0 11.204 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.206 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.206 * [backup-simplify]: Simplify 0 into 0 11.207 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 11.207 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n)) 11.207 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 11.207 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.207 * [taylor]: Taking taylor expansion of -2 in n 11.207 * [backup-simplify]: Simplify -2 into -2 11.207 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.207 * [taylor]: Taking taylor expansion of PI in n 11.207 * [backup-simplify]: Simplify PI into PI 11.207 * [taylor]: Taking taylor expansion of n in n 11.207 * [backup-simplify]: Simplify 0 into 0 11.207 * [backup-simplify]: Simplify 1 into 1 11.208 * [backup-simplify]: Simplify (/ PI 1) into PI 11.208 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.208 * [taylor]: Taking taylor expansion of -2 in n 11.208 * [backup-simplify]: Simplify -2 into -2 11.208 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.208 * [taylor]: Taking taylor expansion of PI in n 11.208 * [backup-simplify]: Simplify PI into PI 11.208 * [taylor]: Taking taylor expansion of n in n 11.208 * [backup-simplify]: Simplify 0 into 0 11.208 * [backup-simplify]: Simplify 1 into 1 11.208 * [backup-simplify]: Simplify (/ PI 1) into PI 11.209 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.209 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.210 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.211 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 11.211 * [backup-simplify]: Simplify 0 into 0 11.212 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.213 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 11.213 * [backup-simplify]: Simplify 0 into 0 11.214 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.216 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.216 * [backup-simplify]: Simplify 0 into 0 11.217 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.219 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.219 * [backup-simplify]: Simplify 0 into 0 11.219 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.220 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.220 * [backup-simplify]: Simplify 0 into 0 11.221 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.222 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.222 * [backup-simplify]: Simplify 0 into 0 11.222 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 11.222 * * * * [progress]: [ 2 / 4 ] generating series at (2 2) 11.223 * [backup-simplify]: Simplify (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) into (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) 11.223 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0 11.223 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in n 11.223 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 11.223 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 11.223 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 11.223 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 11.223 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 11.223 * [taylor]: Taking taylor expansion of 1/2 in n 11.223 * [backup-simplify]: Simplify 1/2 into 1/2 11.223 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 11.223 * [taylor]: Taking taylor expansion of 1/2 in n 11.223 * [backup-simplify]: Simplify 1/2 into 1/2 11.223 * [taylor]: Taking taylor expansion of k in n 11.223 * [backup-simplify]: Simplify k into k 11.223 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.223 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.223 * [taylor]: Taking taylor expansion of 2 in n 11.223 * [backup-simplify]: Simplify 2 into 2 11.223 * [taylor]: Taking taylor expansion of (* n PI) in n 11.223 * [taylor]: Taking taylor expansion of n in n 11.223 * [backup-simplify]: Simplify 0 into 0 11.223 * [backup-simplify]: Simplify 1 into 1 11.223 * [taylor]: Taking taylor expansion of PI in n 11.223 * [backup-simplify]: Simplify PI into PI 11.223 * [backup-simplify]: Simplify (* 0 PI) into 0 11.224 * [backup-simplify]: Simplify (* 2 0) into 0 11.225 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.225 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.226 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.226 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 11.226 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 11.226 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 11.227 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.228 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 11.229 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 11.229 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 11.229 * [taylor]: Taking taylor expansion of (sqrt k) in n 11.229 * [taylor]: Taking taylor expansion of k in n 11.229 * [backup-simplify]: Simplify k into k 11.229 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 11.230 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 11.230 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 11.230 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 11.230 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 11.230 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 11.230 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 11.230 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.230 * [taylor]: Taking taylor expansion of 1/2 in k 11.230 * [backup-simplify]: Simplify 1/2 into 1/2 11.230 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.230 * [taylor]: Taking taylor expansion of 1/2 in k 11.230 * [backup-simplify]: Simplify 1/2 into 1/2 11.230 * [taylor]: Taking taylor expansion of k in k 11.230 * [backup-simplify]: Simplify 0 into 0 11.230 * [backup-simplify]: Simplify 1 into 1 11.230 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.230 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.230 * [taylor]: Taking taylor expansion of 2 in k 11.230 * [backup-simplify]: Simplify 2 into 2 11.230 * [taylor]: Taking taylor expansion of (* n PI) in k 11.230 * [taylor]: Taking taylor expansion of n in k 11.230 * [backup-simplify]: Simplify n into n 11.230 * [taylor]: Taking taylor expansion of PI in k 11.230 * [backup-simplify]: Simplify PI into PI 11.230 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.230 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.230 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.240 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.240 * [backup-simplify]: Simplify (- 0) into 0 11.241 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.241 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.241 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.241 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 11.241 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.241 * [taylor]: Taking taylor expansion of k in k 11.241 * [backup-simplify]: Simplify 0 into 0 11.241 * [backup-simplify]: Simplify 1 into 1 11.241 * [backup-simplify]: Simplify (sqrt 0) into 0 11.242 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.242 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 11.242 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 11.242 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 11.242 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 11.242 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 11.242 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.242 * [taylor]: Taking taylor expansion of 1/2 in k 11.242 * [backup-simplify]: Simplify 1/2 into 1/2 11.242 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.242 * [taylor]: Taking taylor expansion of 1/2 in k 11.242 * [backup-simplify]: Simplify 1/2 into 1/2 11.242 * [taylor]: Taking taylor expansion of k in k 11.242 * [backup-simplify]: Simplify 0 into 0 11.242 * [backup-simplify]: Simplify 1 into 1 11.242 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.242 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.242 * [taylor]: Taking taylor expansion of 2 in k 11.242 * [backup-simplify]: Simplify 2 into 2 11.243 * [taylor]: Taking taylor expansion of (* n PI) in k 11.243 * [taylor]: Taking taylor expansion of n in k 11.243 * [backup-simplify]: Simplify n into n 11.243 * [taylor]: Taking taylor expansion of PI in k 11.243 * [backup-simplify]: Simplify PI into PI 11.243 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.243 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.243 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.243 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.243 * [backup-simplify]: Simplify (- 0) into 0 11.243 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.244 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.244 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.244 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 11.244 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.244 * [taylor]: Taking taylor expansion of k in k 11.244 * [backup-simplify]: Simplify 0 into 0 11.244 * [backup-simplify]: Simplify 1 into 1 11.244 * [backup-simplify]: Simplify (sqrt 0) into 0 11.245 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.245 * [backup-simplify]: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0 11.245 * [taylor]: Taking taylor expansion of 0 in n 11.245 * [backup-simplify]: Simplify 0 into 0 11.245 * [backup-simplify]: Simplify 0 into 0 11.245 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 11.246 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 11.246 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 11.247 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 11.247 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.247 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.248 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 11.248 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 11.248 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 11.249 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) 11.249 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 11.249 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 11.249 * [taylor]: Taking taylor expansion of +nan.0 in n 11.249 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.249 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 11.249 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 11.249 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 11.249 * [taylor]: Taking taylor expansion of (* n PI) in n 11.249 * [taylor]: Taking taylor expansion of n in n 11.250 * [backup-simplify]: Simplify 0 into 0 11.250 * [backup-simplify]: Simplify 1 into 1 11.250 * [taylor]: Taking taylor expansion of PI in n 11.250 * [backup-simplify]: Simplify PI into PI 11.250 * [backup-simplify]: Simplify (* 0 PI) into 0 11.251 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.251 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 11.251 * [backup-simplify]: Simplify (sqrt 0) into 0 11.253 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 11.253 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 11.253 * [taylor]: Taking taylor expansion of 1/2 in n 11.253 * [backup-simplify]: Simplify 1/2 into 1/2 11.253 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 11.253 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 11.256 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.256 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 11.263 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.267 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.268 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.268 * [backup-simplify]: Simplify 0 into 0 11.270 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.271 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 11.271 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 11.272 * [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 11.273 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 11.273 * [backup-simplify]: Simplify (- 0) into 0 11.273 * [backup-simplify]: Simplify (+ 0 0) into 0 11.274 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 11.275 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 11.276 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 11.280 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) 11.280 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n 11.280 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n 11.280 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n 11.280 * [taylor]: Taking taylor expansion of +nan.0 in n 11.280 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.280 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n 11.280 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n 11.280 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.280 * [taylor]: Taking taylor expansion of 2 in n 11.280 * [backup-simplify]: Simplify 2 into 2 11.281 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.281 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.281 * [taylor]: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n 11.281 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.281 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.281 * [taylor]: Taking taylor expansion of 2 in n 11.281 * [backup-simplify]: Simplify 2 into 2 11.281 * [taylor]: Taking taylor expansion of (* n PI) in n 11.281 * [taylor]: Taking taylor expansion of n in n 11.281 * [backup-simplify]: Simplify 0 into 0 11.281 * [backup-simplify]: Simplify 1 into 1 11.281 * [taylor]: Taking taylor expansion of PI in n 11.281 * [backup-simplify]: Simplify PI into PI 11.281 * [backup-simplify]: Simplify (* 0 PI) into 0 11.282 * [backup-simplify]: Simplify (* 2 0) into 0 11.283 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.284 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.284 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.284 * [taylor]: Taking taylor expansion of (pow (sqrt 1/2) 2) in n 11.285 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 11.285 * [taylor]: Taking taylor expansion of 1/2 in n 11.285 * [backup-simplify]: Simplify 1/2 into 1/2 11.285 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 11.285 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 11.285 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 11.285 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 11.285 * [taylor]: Taking taylor expansion of (* n PI) in n 11.285 * [taylor]: Taking taylor expansion of n in n 11.285 * [backup-simplify]: Simplify 0 into 0 11.285 * [backup-simplify]: Simplify 1 into 1 11.285 * [taylor]: Taking taylor expansion of PI in n 11.285 * [backup-simplify]: Simplify PI into PI 11.286 * [backup-simplify]: Simplify (* 0 PI) into 0 11.287 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.287 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 11.287 * [backup-simplify]: Simplify (sqrt 0) into 0 11.290 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 11.290 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 11.290 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 11.290 * [taylor]: Taking taylor expansion of +nan.0 in n 11.290 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.290 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 11.290 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 11.290 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 11.290 * [taylor]: Taking taylor expansion of (* n PI) in n 11.290 * [taylor]: Taking taylor expansion of n in n 11.290 * [backup-simplify]: Simplify 0 into 0 11.290 * [backup-simplify]: Simplify 1 into 1 11.290 * [taylor]: Taking taylor expansion of PI in n 11.290 * [backup-simplify]: Simplify PI into PI 11.290 * [backup-simplify]: Simplify (* 0 PI) into 0 11.292 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.293 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 11.293 * [backup-simplify]: Simplify (sqrt 0) into 0 11.295 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 11.295 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 11.295 * [taylor]: Taking taylor expansion of 1/2 in n 11.295 * [backup-simplify]: Simplify 1/2 into 1/2 11.295 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 11.296 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 11.297 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.299 * [backup-simplify]: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2) 11.301 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))) 11.303 * [backup-simplify]: Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 11.304 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.304 * [backup-simplify]: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0 11.305 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.306 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 11.307 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.308 * [backup-simplify]: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0 11.309 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0 11.312 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 11.313 * [backup-simplify]: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0 11.320 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 11.322 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.323 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 11.326 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.329 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.343 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 11.362 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 11.380 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 11.381 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0 11.382 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.383 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 11.385 * [backup-simplify]: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 11.389 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* (/ +nan.0 PI) 0) (* (/ +nan.0 (pow PI 2)) (sqrt 1/2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 11.395 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 11.398 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 11.400 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 11.419 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ (sqrt 1/2) PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 11.420 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 11.420 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0 11.420 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n 11.420 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 11.420 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.420 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.420 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.420 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.420 * [taylor]: Taking taylor expansion of 1/2 in n 11.420 * [backup-simplify]: Simplify 1/2 into 1/2 11.420 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.420 * [taylor]: Taking taylor expansion of 1/2 in n 11.420 * [backup-simplify]: Simplify 1/2 into 1/2 11.420 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.420 * [taylor]: Taking taylor expansion of k in n 11.420 * [backup-simplify]: Simplify k into k 11.420 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.420 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.420 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.420 * [taylor]: Taking taylor expansion of 2 in n 11.420 * [backup-simplify]: Simplify 2 into 2 11.420 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.420 * [taylor]: Taking taylor expansion of PI in n 11.420 * [backup-simplify]: Simplify PI into PI 11.420 * [taylor]: Taking taylor expansion of n in n 11.420 * [backup-simplify]: Simplify 0 into 0 11.420 * [backup-simplify]: Simplify 1 into 1 11.421 * [backup-simplify]: Simplify (/ PI 1) into PI 11.421 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.422 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.422 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.422 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.422 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.424 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.425 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 11.426 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 11.427 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 11.428 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 11.428 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.428 * [taylor]: Taking taylor expansion of k in n 11.428 * [backup-simplify]: Simplify k into k 11.428 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.428 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 11.428 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.428 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 11.428 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 11.428 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 11.428 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 11.428 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.428 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.428 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.428 * [taylor]: Taking taylor expansion of 1/2 in k 11.428 * [backup-simplify]: Simplify 1/2 into 1/2 11.428 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.428 * [taylor]: Taking taylor expansion of 1/2 in k 11.428 * [backup-simplify]: Simplify 1/2 into 1/2 11.428 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.428 * [taylor]: Taking taylor expansion of k in k 11.428 * [backup-simplify]: Simplify 0 into 0 11.428 * [backup-simplify]: Simplify 1 into 1 11.429 * [backup-simplify]: Simplify (/ 1 1) into 1 11.429 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.429 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.429 * [taylor]: Taking taylor expansion of 2 in k 11.429 * [backup-simplify]: Simplify 2 into 2 11.429 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.429 * [taylor]: Taking taylor expansion of PI in k 11.429 * [backup-simplify]: Simplify PI into PI 11.429 * [taylor]: Taking taylor expansion of n in k 11.429 * [backup-simplify]: Simplify n into n 11.429 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.429 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.429 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.429 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.430 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.430 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.430 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 11.430 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 11.431 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 11.431 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.431 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.431 * [taylor]: Taking taylor expansion of k in k 11.431 * [backup-simplify]: Simplify 0 into 0 11.431 * [backup-simplify]: Simplify 1 into 1 11.431 * [backup-simplify]: Simplify (/ 1 1) into 1 11.431 * [backup-simplify]: Simplify (sqrt 0) into 0 11.433 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.433 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 11.433 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 11.433 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 11.433 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.433 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.433 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.433 * [taylor]: Taking taylor expansion of 1/2 in k 11.433 * [backup-simplify]: Simplify 1/2 into 1/2 11.433 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.433 * [taylor]: Taking taylor expansion of 1/2 in k 11.433 * [backup-simplify]: Simplify 1/2 into 1/2 11.433 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.433 * [taylor]: Taking taylor expansion of k in k 11.433 * [backup-simplify]: Simplify 0 into 0 11.433 * [backup-simplify]: Simplify 1 into 1 11.434 * [backup-simplify]: Simplify (/ 1 1) into 1 11.434 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.434 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.434 * [taylor]: Taking taylor expansion of 2 in k 11.434 * [backup-simplify]: Simplify 2 into 2 11.434 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.434 * [taylor]: Taking taylor expansion of PI in k 11.434 * [backup-simplify]: Simplify PI into PI 11.434 * [taylor]: Taking taylor expansion of n in k 11.434 * [backup-simplify]: Simplify n into n 11.434 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.434 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.434 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.434 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.435 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.435 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.435 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 11.435 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 11.436 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 11.436 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.436 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.436 * [taylor]: Taking taylor expansion of k in k 11.436 * [backup-simplify]: Simplify 0 into 0 11.436 * [backup-simplify]: Simplify 1 into 1 11.436 * [backup-simplify]: Simplify (/ 1 1) into 1 11.436 * [backup-simplify]: Simplify (sqrt 0) into 0 11.437 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.438 * [backup-simplify]: Simplify (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 11.438 * [taylor]: Taking taylor expansion of 0 in n 11.438 * [backup-simplify]: Simplify 0 into 0 11.438 * [backup-simplify]: Simplify 0 into 0 11.438 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 11.439 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 11.439 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 11.439 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 11.439 * [taylor]: Taking taylor expansion of +nan.0 in n 11.439 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.439 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 11.439 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.439 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.439 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.439 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.439 * [taylor]: Taking taylor expansion of 1/2 in n 11.439 * [backup-simplify]: Simplify 1/2 into 1/2 11.439 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.439 * [taylor]: Taking taylor expansion of 1/2 in n 11.439 * [backup-simplify]: Simplify 1/2 into 1/2 11.439 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.439 * [taylor]: Taking taylor expansion of k in n 11.439 * [backup-simplify]: Simplify k into k 11.439 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.439 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.439 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.439 * [taylor]: Taking taylor expansion of 2 in n 11.439 * [backup-simplify]: Simplify 2 into 2 11.439 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.439 * [taylor]: Taking taylor expansion of PI in n 11.439 * [backup-simplify]: Simplify PI into PI 11.439 * [taylor]: Taking taylor expansion of n in n 11.439 * [backup-simplify]: Simplify 0 into 0 11.439 * [backup-simplify]: Simplify 1 into 1 11.440 * [backup-simplify]: Simplify (/ PI 1) into PI 11.440 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.441 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.441 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.441 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.442 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.443 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.444 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 11.445 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 11.446 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 11.447 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 11.448 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 11.449 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 11.449 * [backup-simplify]: Simplify 0 into 0 11.449 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.451 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.452 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 11.454 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 11.454 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 11.454 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 11.454 * [taylor]: Taking taylor expansion of +nan.0 in n 11.454 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.454 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 11.454 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.454 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.454 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.454 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.455 * [taylor]: Taking taylor expansion of 1/2 in n 11.455 * [backup-simplify]: Simplify 1/2 into 1/2 11.455 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.455 * [taylor]: Taking taylor expansion of 1/2 in n 11.455 * [backup-simplify]: Simplify 1/2 into 1/2 11.455 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.455 * [taylor]: Taking taylor expansion of k in n 11.455 * [backup-simplify]: Simplify k into k 11.455 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.455 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.455 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.455 * [taylor]: Taking taylor expansion of 2 in n 11.455 * [backup-simplify]: Simplify 2 into 2 11.455 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.455 * [taylor]: Taking taylor expansion of PI in n 11.455 * [backup-simplify]: Simplify PI into PI 11.455 * [taylor]: Taking taylor expansion of n in n 11.455 * [backup-simplify]: Simplify 0 into 0 11.455 * [backup-simplify]: Simplify 1 into 1 11.455 * [backup-simplify]: Simplify (/ PI 1) into PI 11.456 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.456 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.456 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.456 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.456 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.457 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.458 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 11.459 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 11.460 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 11.460 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 11.461 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 11.462 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 11.463 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.463 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.464 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.464 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.465 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 11.465 * [backup-simplify]: Simplify (- 0) into 0 11.465 * [backup-simplify]: Simplify (+ 0 0) into 0 11.466 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.467 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 11.468 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 11.469 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 11.470 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 11.471 * [backup-simplify]: Simplify (- 0) into 0 11.471 * [backup-simplify]: Simplify 0 into 0 11.471 * [backup-simplify]: Simplify 0 into 0 11.471 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.474 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.474 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 11.475 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 11.475 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 11.475 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 11.475 * [taylor]: Taking taylor expansion of +nan.0 in n 11.475 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.475 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 11.475 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.475 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.475 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.475 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.475 * [taylor]: Taking taylor expansion of 1/2 in n 11.475 * [backup-simplify]: Simplify 1/2 into 1/2 11.475 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.475 * [taylor]: Taking taylor expansion of 1/2 in n 11.475 * [backup-simplify]: Simplify 1/2 into 1/2 11.475 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.475 * [taylor]: Taking taylor expansion of k in n 11.475 * [backup-simplify]: Simplify k into k 11.475 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.475 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.475 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.475 * [taylor]: Taking taylor expansion of 2 in n 11.475 * [backup-simplify]: Simplify 2 into 2 11.475 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.475 * [taylor]: Taking taylor expansion of PI in n 11.475 * [backup-simplify]: Simplify PI into PI 11.475 * [taylor]: Taking taylor expansion of n in n 11.475 * [backup-simplify]: Simplify 0 into 0 11.475 * [backup-simplify]: Simplify 1 into 1 11.475 * [backup-simplify]: Simplify (/ PI 1) into PI 11.476 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.476 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.477 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.477 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.477 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.478 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.478 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 11.479 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 11.481 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 11.482 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 11.483 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 11.484 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 11.489 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 11.489 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 11.489 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 11.489 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 11.489 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 11.489 * [taylor]: Taking taylor expansion of (/ -1 k) in n 11.489 * [taylor]: Taking taylor expansion of -1 in n 11.489 * [backup-simplify]: Simplify -1 into -1 11.489 * [taylor]: Taking taylor expansion of k in n 11.489 * [backup-simplify]: Simplify k into k 11.489 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 11.489 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 11.490 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 11.490 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 11.490 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.490 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 11.490 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 11.490 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.490 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.490 * [taylor]: Taking taylor expansion of 1/2 in n 11.490 * [backup-simplify]: Simplify 1/2 into 1/2 11.490 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.490 * [taylor]: Taking taylor expansion of k in n 11.490 * [backup-simplify]: Simplify k into k 11.490 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.490 * [taylor]: Taking taylor expansion of 1/2 in n 11.490 * [backup-simplify]: Simplify 1/2 into 1/2 11.490 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.490 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.490 * [taylor]: Taking taylor expansion of -2 in n 11.490 * [backup-simplify]: Simplify -2 into -2 11.490 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.490 * [taylor]: Taking taylor expansion of PI in n 11.490 * [backup-simplify]: Simplify PI into PI 11.490 * [taylor]: Taking taylor expansion of n in n 11.490 * [backup-simplify]: Simplify 0 into 0 11.490 * [backup-simplify]: Simplify 1 into 1 11.491 * [backup-simplify]: Simplify (/ PI 1) into PI 11.491 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.492 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.492 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.492 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.494 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.495 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 11.496 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 11.498 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 11.498 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 11.498 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.498 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.498 * [taylor]: Taking taylor expansion of -1 in k 11.498 * [backup-simplify]: Simplify -1 into -1 11.498 * [taylor]: Taking taylor expansion of k in k 11.498 * [backup-simplify]: Simplify 0 into 0 11.498 * [backup-simplify]: Simplify 1 into 1 11.498 * [backup-simplify]: Simplify (/ -1 1) into -1 11.499 * [backup-simplify]: Simplify (sqrt 0) into 0 11.500 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.500 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 11.500 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 11.500 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 11.500 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 11.500 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.500 * [taylor]: Taking taylor expansion of 1/2 in k 11.500 * [backup-simplify]: Simplify 1/2 into 1/2 11.500 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.500 * [taylor]: Taking taylor expansion of k in k 11.500 * [backup-simplify]: Simplify 0 into 0 11.500 * [backup-simplify]: Simplify 1 into 1 11.501 * [backup-simplify]: Simplify (/ 1 1) into 1 11.501 * [taylor]: Taking taylor expansion of 1/2 in k 11.501 * [backup-simplify]: Simplify 1/2 into 1/2 11.501 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 11.501 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 11.501 * [taylor]: Taking taylor expansion of -2 in k 11.501 * [backup-simplify]: Simplify -2 into -2 11.501 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.501 * [taylor]: Taking taylor expansion of PI in k 11.501 * [backup-simplify]: Simplify PI into PI 11.501 * [taylor]: Taking taylor expansion of n in k 11.501 * [backup-simplify]: Simplify n into n 11.501 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.501 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 11.501 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 11.502 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.502 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.502 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 11.502 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 11.503 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 11.503 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 11.503 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.503 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.503 * [taylor]: Taking taylor expansion of -1 in k 11.503 * [backup-simplify]: Simplify -1 into -1 11.503 * [taylor]: Taking taylor expansion of k in k 11.503 * [backup-simplify]: Simplify 0 into 0 11.503 * [backup-simplify]: Simplify 1 into 1 11.503 * [backup-simplify]: Simplify (/ -1 1) into -1 11.504 * [backup-simplify]: Simplify (sqrt 0) into 0 11.505 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.505 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 11.505 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 11.505 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 11.505 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 11.505 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.505 * [taylor]: Taking taylor expansion of 1/2 in k 11.505 * [backup-simplify]: Simplify 1/2 into 1/2 11.505 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.505 * [taylor]: Taking taylor expansion of k in k 11.505 * [backup-simplify]: Simplify 0 into 0 11.505 * [backup-simplify]: Simplify 1 into 1 11.506 * [backup-simplify]: Simplify (/ 1 1) into 1 11.506 * [taylor]: Taking taylor expansion of 1/2 in k 11.506 * [backup-simplify]: Simplify 1/2 into 1/2 11.506 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 11.506 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 11.506 * [taylor]: Taking taylor expansion of -2 in k 11.506 * [backup-simplify]: Simplify -2 into -2 11.506 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.506 * [taylor]: Taking taylor expansion of PI in k 11.506 * [backup-simplify]: Simplify PI into PI 11.506 * [taylor]: Taking taylor expansion of n in k 11.506 * [backup-simplify]: Simplify n into n 11.506 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.506 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 11.506 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 11.507 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.507 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.507 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 11.507 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 11.508 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 11.508 * [taylor]: Taking taylor expansion of (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 11.508 * [taylor]: Taking taylor expansion of +nan.0 in n 11.508 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.508 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 11.508 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.508 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.508 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.508 * [taylor]: Taking taylor expansion of -2 in n 11.508 * [backup-simplify]: Simplify -2 into -2 11.508 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.508 * [taylor]: Taking taylor expansion of PI in n 11.508 * [backup-simplify]: Simplify PI into PI 11.508 * [taylor]: Taking taylor expansion of n in n 11.508 * [backup-simplify]: Simplify 0 into 0 11.508 * [backup-simplify]: Simplify 1 into 1 11.509 * [backup-simplify]: Simplify (/ PI 1) into PI 11.509 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.510 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.510 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.510 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.510 * [taylor]: Taking taylor expansion of 1/2 in n 11.510 * [backup-simplify]: Simplify 1/2 into 1/2 11.510 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.510 * [taylor]: Taking taylor expansion of k in n 11.510 * [backup-simplify]: Simplify k into k 11.510 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.510 * [taylor]: Taking taylor expansion of 1/2 in n 11.510 * [backup-simplify]: Simplify 1/2 into 1/2 11.512 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.512 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.512 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.514 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 11.515 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 11.516 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 11.517 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 11.518 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 11.521 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.522 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 11.522 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 11.522 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 11.522 * [taylor]: Taking taylor expansion of +nan.0 in n 11.522 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.522 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 11.522 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 11.522 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.522 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.522 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.522 * [taylor]: Taking taylor expansion of -2 in n 11.522 * [backup-simplify]: Simplify -2 into -2 11.522 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.522 * [taylor]: Taking taylor expansion of PI in n 11.522 * [backup-simplify]: Simplify PI into PI 11.522 * [taylor]: Taking taylor expansion of n in n 11.522 * [backup-simplify]: Simplify 0 into 0 11.522 * [backup-simplify]: Simplify 1 into 1 11.523 * [backup-simplify]: Simplify (/ PI 1) into PI 11.523 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.524 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.524 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.524 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.524 * [taylor]: Taking taylor expansion of 1/2 in n 11.524 * [backup-simplify]: Simplify 1/2 into 1/2 11.524 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.524 * [taylor]: Taking taylor expansion of k in n 11.524 * [backup-simplify]: Simplify k into k 11.524 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.524 * [taylor]: Taking taylor expansion of 1/2 in n 11.524 * [backup-simplify]: Simplify 1/2 into 1/2 11.526 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.526 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.526 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.527 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 11.529 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 11.530 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 11.531 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 11.532 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 11.534 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 11.535 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.535 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.536 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 11.536 * [backup-simplify]: Simplify (+ 0 0) into 0 11.537 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.538 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 11.540 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 11.541 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 11.543 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 11.547 * [backup-simplify]: Simplify (- (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 11.547 * [backup-simplify]: Simplify 0 into 0 11.548 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.552 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.554 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (* (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 11.554 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 11.554 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 11.554 * [taylor]: Taking taylor expansion of +nan.0 in n 11.554 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.554 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 11.554 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 11.554 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.554 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.554 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.554 * [taylor]: Taking taylor expansion of -2 in n 11.554 * [backup-simplify]: Simplify -2 into -2 11.554 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.554 * [taylor]: Taking taylor expansion of PI in n 11.554 * [backup-simplify]: Simplify PI into PI 11.554 * [taylor]: Taking taylor expansion of n in n 11.554 * [backup-simplify]: Simplify 0 into 0 11.554 * [backup-simplify]: Simplify 1 into 1 11.555 * [backup-simplify]: Simplify (/ PI 1) into PI 11.556 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.557 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.557 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.557 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.557 * [taylor]: Taking taylor expansion of 1/2 in n 11.557 * [backup-simplify]: Simplify 1/2 into 1/2 11.557 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.557 * [taylor]: Taking taylor expansion of k in n 11.557 * [backup-simplify]: Simplify k into k 11.557 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.557 * [taylor]: Taking taylor expansion of 1/2 in n 11.557 * [backup-simplify]: Simplify 1/2 into 1/2 11.559 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.559 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.559 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.560 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 11.562 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 11.563 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 11.564 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 11.565 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 11.566 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 11.571 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 11.571 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2) 11.571 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 11.571 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 11.571 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 11.571 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 11.571 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 11.571 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.571 * [taylor]: Taking taylor expansion of 1/2 in k 11.571 * [backup-simplify]: Simplify 1/2 into 1/2 11.571 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.571 * [taylor]: Taking taylor expansion of 1/2 in k 11.571 * [backup-simplify]: Simplify 1/2 into 1/2 11.571 * [taylor]: Taking taylor expansion of k in k 11.571 * [backup-simplify]: Simplify 0 into 0 11.571 * [backup-simplify]: Simplify 1 into 1 11.571 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.571 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.572 * [taylor]: Taking taylor expansion of 2 in k 11.572 * [backup-simplify]: Simplify 2 into 2 11.572 * [taylor]: Taking taylor expansion of (* n PI) in k 11.572 * [taylor]: Taking taylor expansion of n in k 11.572 * [backup-simplify]: Simplify n into n 11.572 * [taylor]: Taking taylor expansion of PI in k 11.572 * [backup-simplify]: Simplify PI into PI 11.572 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.572 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.572 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.572 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.573 * [backup-simplify]: Simplify (- 0) into 0 11.573 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.573 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.573 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.573 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 11.573 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 11.573 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 11.573 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 11.574 * [taylor]: Taking taylor expansion of 1/2 in n 11.574 * [backup-simplify]: Simplify 1/2 into 1/2 11.574 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 11.574 * [taylor]: Taking taylor expansion of 1/2 in n 11.574 * [backup-simplify]: Simplify 1/2 into 1/2 11.574 * [taylor]: Taking taylor expansion of k in n 11.574 * [backup-simplify]: Simplify k into k 11.574 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.574 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.574 * [taylor]: Taking taylor expansion of 2 in n 11.574 * [backup-simplify]: Simplify 2 into 2 11.574 * [taylor]: Taking taylor expansion of (* n PI) in n 11.574 * [taylor]: Taking taylor expansion of n in n 11.574 * [backup-simplify]: Simplify 0 into 0 11.574 * [backup-simplify]: Simplify 1 into 1 11.574 * [taylor]: Taking taylor expansion of PI in n 11.574 * [backup-simplify]: Simplify PI into PI 11.574 * [backup-simplify]: Simplify (* 0 PI) into 0 11.575 * [backup-simplify]: Simplify (* 2 0) into 0 11.576 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.578 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.579 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.580 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 11.580 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 11.580 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 11.581 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.586 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 11.587 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 11.587 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 11.587 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 11.587 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 11.587 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 11.587 * [taylor]: Taking taylor expansion of 1/2 in n 11.587 * [backup-simplify]: Simplify 1/2 into 1/2 11.587 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 11.587 * [taylor]: Taking taylor expansion of 1/2 in n 11.587 * [backup-simplify]: Simplify 1/2 into 1/2 11.587 * [taylor]: Taking taylor expansion of k in n 11.588 * [backup-simplify]: Simplify k into k 11.588 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.588 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.588 * [taylor]: Taking taylor expansion of 2 in n 11.588 * [backup-simplify]: Simplify 2 into 2 11.588 * [taylor]: Taking taylor expansion of (* n PI) in n 11.588 * [taylor]: Taking taylor expansion of n in n 11.588 * [backup-simplify]: Simplify 0 into 0 11.588 * [backup-simplify]: Simplify 1 into 1 11.588 * [taylor]: Taking taylor expansion of PI in n 11.588 * [backup-simplify]: Simplify PI into PI 11.588 * [backup-simplify]: Simplify (* 0 PI) into 0 11.589 * [backup-simplify]: Simplify (* 2 0) into 0 11.590 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.592 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.593 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.593 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 11.593 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 11.593 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 11.595 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.595 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 11.596 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 11.596 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 11.596 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 11.596 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.596 * [taylor]: Taking taylor expansion of 1/2 in k 11.596 * [backup-simplify]: Simplify 1/2 into 1/2 11.596 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.596 * [taylor]: Taking taylor expansion of 1/2 in k 11.596 * [backup-simplify]: Simplify 1/2 into 1/2 11.596 * [taylor]: Taking taylor expansion of k in k 11.596 * [backup-simplify]: Simplify 0 into 0 11.596 * [backup-simplify]: Simplify 1 into 1 11.596 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 11.596 * [taylor]: Taking taylor expansion of (log n) in k 11.596 * [taylor]: Taking taylor expansion of n in k 11.596 * [backup-simplify]: Simplify n into n 11.596 * [backup-simplify]: Simplify (log n) into (log n) 11.596 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.596 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.596 * [taylor]: Taking taylor expansion of 2 in k 11.596 * [backup-simplify]: Simplify 2 into 2 11.596 * [taylor]: Taking taylor expansion of PI in k 11.597 * [backup-simplify]: Simplify PI into PI 11.597 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.597 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.598 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.598 * [backup-simplify]: Simplify (- 0) into 0 11.598 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.599 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.600 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 11.601 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 11.601 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 11.602 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.603 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 11.604 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.604 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 11.604 * [backup-simplify]: Simplify (- 0) into 0 11.604 * [backup-simplify]: Simplify (+ 0 0) into 0 11.605 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.606 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 11.607 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.607 * [taylor]: Taking taylor expansion of 0 in k 11.607 * [backup-simplify]: Simplify 0 into 0 11.607 * [backup-simplify]: Simplify 0 into 0 11.608 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 11.608 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.610 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.610 * [backup-simplify]: Simplify (+ 0 0) into 0 11.610 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 11.610 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.611 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.612 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 11.614 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 11.616 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 11.616 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.617 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.619 * [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 11.620 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 11.620 * [backup-simplify]: Simplify (- 0) into 0 11.621 * [backup-simplify]: Simplify (+ 0 0) into 0 11.622 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.623 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 11.624 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.624 * [taylor]: Taking taylor expansion of 0 in k 11.624 * [backup-simplify]: Simplify 0 into 0 11.624 * [backup-simplify]: Simplify 0 into 0 11.625 * [backup-simplify]: Simplify 0 into 0 11.626 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 11.626 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.628 * [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 11.629 * [backup-simplify]: Simplify (+ 0 0) into 0 11.629 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 11.630 * [backup-simplify]: Simplify (- 0) into 0 11.630 * [backup-simplify]: Simplify (+ 0 0) into 0 11.631 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 11.635 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 11.640 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 11.651 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 11.651 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 11.651 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 11.651 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 11.651 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.651 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.651 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.651 * [taylor]: Taking taylor expansion of 1/2 in k 11.651 * [backup-simplify]: Simplify 1/2 into 1/2 11.651 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.651 * [taylor]: Taking taylor expansion of 1/2 in k 11.651 * [backup-simplify]: Simplify 1/2 into 1/2 11.651 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.651 * [taylor]: Taking taylor expansion of k in k 11.651 * [backup-simplify]: Simplify 0 into 0 11.651 * [backup-simplify]: Simplify 1 into 1 11.652 * [backup-simplify]: Simplify (/ 1 1) into 1 11.652 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.652 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.652 * [taylor]: Taking taylor expansion of 2 in k 11.652 * [backup-simplify]: Simplify 2 into 2 11.652 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.652 * [taylor]: Taking taylor expansion of PI in k 11.652 * [backup-simplify]: Simplify PI into PI 11.652 * [taylor]: Taking taylor expansion of n in k 11.652 * [backup-simplify]: Simplify n into n 11.652 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.652 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.652 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.653 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.653 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.654 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.654 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 11.654 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 11.654 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.654 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.654 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.654 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.654 * [taylor]: Taking taylor expansion of 1/2 in n 11.654 * [backup-simplify]: Simplify 1/2 into 1/2 11.654 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.654 * [taylor]: Taking taylor expansion of 1/2 in n 11.654 * [backup-simplify]: Simplify 1/2 into 1/2 11.654 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.654 * [taylor]: Taking taylor expansion of k in n 11.654 * [backup-simplify]: Simplify k into k 11.654 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.654 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.654 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.654 * [taylor]: Taking taylor expansion of 2 in n 11.654 * [backup-simplify]: Simplify 2 into 2 11.654 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.654 * [taylor]: Taking taylor expansion of PI in n 11.654 * [backup-simplify]: Simplify PI into PI 11.654 * [taylor]: Taking taylor expansion of n in n 11.654 * [backup-simplify]: Simplify 0 into 0 11.655 * [backup-simplify]: Simplify 1 into 1 11.655 * [backup-simplify]: Simplify (/ PI 1) into PI 11.655 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.657 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.657 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.657 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.657 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.658 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.659 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 11.661 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 11.661 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.661 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.661 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.661 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.661 * [taylor]: Taking taylor expansion of 1/2 in n 11.661 * [backup-simplify]: Simplify 1/2 into 1/2 11.661 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.661 * [taylor]: Taking taylor expansion of 1/2 in n 11.661 * [backup-simplify]: Simplify 1/2 into 1/2 11.661 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.661 * [taylor]: Taking taylor expansion of k in n 11.661 * [backup-simplify]: Simplify k into k 11.661 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.661 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.661 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.661 * [taylor]: Taking taylor expansion of 2 in n 11.661 * [backup-simplify]: Simplify 2 into 2 11.661 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.661 * [taylor]: Taking taylor expansion of PI in n 11.661 * [backup-simplify]: Simplify PI into PI 11.661 * [taylor]: Taking taylor expansion of n in n 11.661 * [backup-simplify]: Simplify 0 into 0 11.661 * [backup-simplify]: Simplify 1 into 1 11.662 * [backup-simplify]: Simplify (/ PI 1) into PI 11.662 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.663 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.663 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.663 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.663 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.665 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.666 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 11.667 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 11.667 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 11.667 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 11.667 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.667 * [taylor]: Taking taylor expansion of 1/2 in k 11.667 * [backup-simplify]: Simplify 1/2 into 1/2 11.667 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.667 * [taylor]: Taking taylor expansion of 1/2 in k 11.667 * [backup-simplify]: Simplify 1/2 into 1/2 11.667 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.667 * [taylor]: Taking taylor expansion of k in k 11.667 * [backup-simplify]: Simplify 0 into 0 11.667 * [backup-simplify]: Simplify 1 into 1 11.668 * [backup-simplify]: Simplify (/ 1 1) into 1 11.668 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 11.668 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.668 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.668 * [taylor]: Taking taylor expansion of 2 in k 11.668 * [backup-simplify]: Simplify 2 into 2 11.668 * [taylor]: Taking taylor expansion of PI in k 11.668 * [backup-simplify]: Simplify PI into PI 11.668 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.669 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.669 * [taylor]: Taking taylor expansion of (log n) in k 11.669 * [taylor]: Taking taylor expansion of n in k 11.670 * [backup-simplify]: Simplify n into n 11.670 * [backup-simplify]: Simplify (log n) into (log n) 11.670 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.670 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.671 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.671 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.672 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 11.673 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 11.674 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 11.675 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 11.676 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.677 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.679 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.679 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.680 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 11.680 * [backup-simplify]: Simplify (- 0) into 0 11.680 * [backup-simplify]: Simplify (+ 0 0) into 0 11.682 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.683 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 11.684 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 11.684 * [taylor]: Taking taylor expansion of 0 in k 11.684 * [backup-simplify]: Simplify 0 into 0 11.684 * [backup-simplify]: Simplify 0 into 0 11.684 * [backup-simplify]: Simplify 0 into 0 11.685 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.686 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.687 * [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 11.688 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.688 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 11.688 * [backup-simplify]: Simplify (- 0) into 0 11.689 * [backup-simplify]: Simplify (+ 0 0) into 0 11.690 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.690 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 11.692 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.692 * [taylor]: Taking taylor expansion of 0 in k 11.692 * [backup-simplify]: Simplify 0 into 0 11.692 * [backup-simplify]: Simplify 0 into 0 11.692 * [backup-simplify]: Simplify 0 into 0 11.692 * [backup-simplify]: Simplify 0 into 0 11.693 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.694 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.699 * [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 11.699 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.700 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 11.700 * [backup-simplify]: Simplify (- 0) into 0 11.701 * [backup-simplify]: Simplify (+ 0 0) into 0 11.702 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.703 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 11.704 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.704 * [taylor]: Taking taylor expansion of 0 in k 11.704 * [backup-simplify]: Simplify 0 into 0 11.704 * [backup-simplify]: Simplify 0 into 0 11.705 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 11.705 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 11.705 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 11.705 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 11.705 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 11.705 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 11.705 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 11.706 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.706 * [taylor]: Taking taylor expansion of 1/2 in k 11.706 * [backup-simplify]: Simplify 1/2 into 1/2 11.706 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.706 * [taylor]: Taking taylor expansion of k in k 11.706 * [backup-simplify]: Simplify 0 into 0 11.706 * [backup-simplify]: Simplify 1 into 1 11.706 * [backup-simplify]: Simplify (/ 1 1) into 1 11.706 * [taylor]: Taking taylor expansion of 1/2 in k 11.706 * [backup-simplify]: Simplify 1/2 into 1/2 11.706 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 11.706 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 11.706 * [taylor]: Taking taylor expansion of -2 in k 11.706 * [backup-simplify]: Simplify -2 into -2 11.706 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.706 * [taylor]: Taking taylor expansion of PI in k 11.706 * [backup-simplify]: Simplify PI into PI 11.706 * [taylor]: Taking taylor expansion of n in k 11.706 * [backup-simplify]: Simplify n into n 11.706 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.706 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 11.706 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 11.706 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.707 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.707 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 11.707 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 11.707 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.707 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 11.707 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 11.707 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.707 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.707 * [taylor]: Taking taylor expansion of 1/2 in n 11.707 * [backup-simplify]: Simplify 1/2 into 1/2 11.707 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.707 * [taylor]: Taking taylor expansion of k in n 11.707 * [backup-simplify]: Simplify k into k 11.707 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.707 * [taylor]: Taking taylor expansion of 1/2 in n 11.707 * [backup-simplify]: Simplify 1/2 into 1/2 11.707 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.707 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.707 * [taylor]: Taking taylor expansion of -2 in n 11.707 * [backup-simplify]: Simplify -2 into -2 11.707 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.707 * [taylor]: Taking taylor expansion of PI in n 11.707 * [backup-simplify]: Simplify PI into PI 11.707 * [taylor]: Taking taylor expansion of n in n 11.707 * [backup-simplify]: Simplify 0 into 0 11.707 * [backup-simplify]: Simplify 1 into 1 11.708 * [backup-simplify]: Simplify (/ PI 1) into PI 11.708 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.709 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.709 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.709 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.710 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.710 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 11.711 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 11.711 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.711 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 11.711 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 11.711 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.711 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.711 * [taylor]: Taking taylor expansion of 1/2 in n 11.711 * [backup-simplify]: Simplify 1/2 into 1/2 11.711 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.711 * [taylor]: Taking taylor expansion of k in n 11.711 * [backup-simplify]: Simplify k into k 11.711 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.711 * [taylor]: Taking taylor expansion of 1/2 in n 11.711 * [backup-simplify]: Simplify 1/2 into 1/2 11.711 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.711 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.711 * [taylor]: Taking taylor expansion of -2 in n 11.711 * [backup-simplify]: Simplify -2 into -2 11.711 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.711 * [taylor]: Taking taylor expansion of PI in n 11.711 * [backup-simplify]: Simplify PI into PI 11.712 * [taylor]: Taking taylor expansion of n in n 11.712 * [backup-simplify]: Simplify 0 into 0 11.712 * [backup-simplify]: Simplify 1 into 1 11.712 * [backup-simplify]: Simplify (/ PI 1) into PI 11.712 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.713 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.713 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.713 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.714 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.715 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 11.716 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 11.717 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 11.717 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 11.717 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 11.717 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.717 * [taylor]: Taking taylor expansion of 1/2 in k 11.717 * [backup-simplify]: Simplify 1/2 into 1/2 11.717 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.717 * [taylor]: Taking taylor expansion of k in k 11.717 * [backup-simplify]: Simplify 0 into 0 11.717 * [backup-simplify]: Simplify 1 into 1 11.717 * [backup-simplify]: Simplify (/ 1 1) into 1 11.717 * [taylor]: Taking taylor expansion of 1/2 in k 11.717 * [backup-simplify]: Simplify 1/2 into 1/2 11.717 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 11.717 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 11.717 * [taylor]: Taking taylor expansion of (* -2 PI) in k 11.717 * [taylor]: Taking taylor expansion of -2 in k 11.717 * [backup-simplify]: Simplify -2 into -2 11.717 * [taylor]: Taking taylor expansion of PI in k 11.717 * [backup-simplify]: Simplify PI into PI 11.718 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.719 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.719 * [taylor]: Taking taylor expansion of (log n) in k 11.719 * [taylor]: Taking taylor expansion of n in k 11.719 * [backup-simplify]: Simplify n into n 11.719 * [backup-simplify]: Simplify (log n) into (log n) 11.720 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.720 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.720 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.721 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 11.722 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 11.724 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 11.725 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 11.726 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.727 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 11.729 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 11.729 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.730 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 11.730 * [backup-simplify]: Simplify (+ 0 0) into 0 11.732 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.733 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 11.735 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 11.735 * [taylor]: Taking taylor expansion of 0 in k 11.735 * [backup-simplify]: Simplify 0 into 0 11.735 * [backup-simplify]: Simplify 0 into 0 11.735 * [backup-simplify]: Simplify 0 into 0 11.736 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.737 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 11.741 * [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 11.741 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.742 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 11.742 * [backup-simplify]: Simplify (+ 0 0) into 0 11.744 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.745 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 11.747 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.748 * [taylor]: Taking taylor expansion of 0 in k 11.748 * [backup-simplify]: Simplify 0 into 0 11.748 * [backup-simplify]: Simplify 0 into 0 11.748 * [backup-simplify]: Simplify 0 into 0 11.748 * [backup-simplify]: Simplify 0 into 0 11.748 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.749 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.753 * [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 11.753 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.754 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 11.754 * [backup-simplify]: Simplify (+ 0 0) into 0 11.755 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.756 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 11.758 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.758 * [taylor]: Taking taylor expansion of 0 in k 11.758 * [backup-simplify]: Simplify 0 into 0 11.758 * [backup-simplify]: Simplify 0 into 0 11.759 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 11.759 * * * * [progress]: [ 4 / 4 ] generating series at (2) 11.759 * [backup-simplify]: Simplify (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 11.759 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (k n) around 0 11.759 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 11.759 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 11.759 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.759 * [taylor]: Taking taylor expansion of k in n 11.759 * [backup-simplify]: Simplify k into k 11.759 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.759 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 11.759 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.759 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 11.759 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 11.759 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 11.759 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 11.759 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 11.759 * [taylor]: Taking taylor expansion of 1/2 in n 11.759 * [backup-simplify]: Simplify 1/2 into 1/2 11.759 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 11.759 * [taylor]: Taking taylor expansion of 1/2 in n 11.759 * [backup-simplify]: Simplify 1/2 into 1/2 11.759 * [taylor]: Taking taylor expansion of k in n 11.759 * [backup-simplify]: Simplify k into k 11.759 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.760 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.760 * [taylor]: Taking taylor expansion of 2 in n 11.760 * [backup-simplify]: Simplify 2 into 2 11.760 * [taylor]: Taking taylor expansion of (* n PI) in n 11.760 * [taylor]: Taking taylor expansion of n in n 11.760 * [backup-simplify]: Simplify 0 into 0 11.760 * [backup-simplify]: Simplify 1 into 1 11.760 * [taylor]: Taking taylor expansion of PI in n 11.760 * [backup-simplify]: Simplify PI into PI 11.760 * [backup-simplify]: Simplify (* 0 PI) into 0 11.760 * [backup-simplify]: Simplify (* 2 0) into 0 11.761 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.762 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.763 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.763 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 11.763 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 11.763 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 11.764 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.765 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 11.765 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 11.765 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 11.766 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.766 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.766 * [taylor]: Taking taylor expansion of k in k 11.766 * [backup-simplify]: Simplify 0 into 0 11.766 * [backup-simplify]: Simplify 1 into 1 11.766 * [backup-simplify]: Simplify (/ 1 1) into 1 11.766 * [backup-simplify]: Simplify (sqrt 0) into 0 11.767 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.767 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 11.767 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 11.767 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 11.767 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.767 * [taylor]: Taking taylor expansion of 1/2 in k 11.767 * [backup-simplify]: Simplify 1/2 into 1/2 11.767 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.767 * [taylor]: Taking taylor expansion of 1/2 in k 11.767 * [backup-simplify]: Simplify 1/2 into 1/2 11.767 * [taylor]: Taking taylor expansion of k in k 11.767 * [backup-simplify]: Simplify 0 into 0 11.767 * [backup-simplify]: Simplify 1 into 1 11.767 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.767 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.767 * [taylor]: Taking taylor expansion of 2 in k 11.767 * [backup-simplify]: Simplify 2 into 2 11.767 * [taylor]: Taking taylor expansion of (* n PI) in k 11.767 * [taylor]: Taking taylor expansion of n in k 11.767 * [backup-simplify]: Simplify n into n 11.767 * [taylor]: Taking taylor expansion of PI in k 11.767 * [backup-simplify]: Simplify PI into PI 11.767 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.767 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.768 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.768 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.768 * [backup-simplify]: Simplify (- 0) into 0 11.768 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.768 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.769 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.769 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 11.769 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.769 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.769 * [taylor]: Taking taylor expansion of k in k 11.769 * [backup-simplify]: Simplify 0 into 0 11.769 * [backup-simplify]: Simplify 1 into 1 11.769 * [backup-simplify]: Simplify (/ 1 1) into 1 11.769 * [backup-simplify]: Simplify (sqrt 0) into 0 11.770 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.770 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 11.770 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 11.770 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 11.770 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.770 * [taylor]: Taking taylor expansion of 1/2 in k 11.770 * [backup-simplify]: Simplify 1/2 into 1/2 11.770 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.770 * [taylor]: Taking taylor expansion of 1/2 in k 11.770 * [backup-simplify]: Simplify 1/2 into 1/2 11.770 * [taylor]: Taking taylor expansion of k in k 11.770 * [backup-simplify]: Simplify 0 into 0 11.770 * [backup-simplify]: Simplify 1 into 1 11.770 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.770 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.770 * [taylor]: Taking taylor expansion of 2 in k 11.770 * [backup-simplify]: Simplify 2 into 2 11.770 * [taylor]: Taking taylor expansion of (* n PI) in k 11.770 * [taylor]: Taking taylor expansion of n in k 11.770 * [backup-simplify]: Simplify n into n 11.770 * [taylor]: Taking taylor expansion of PI in k 11.770 * [backup-simplify]: Simplify PI into PI 11.770 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.770 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.771 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.771 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.771 * [backup-simplify]: Simplify (- 0) into 0 11.771 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.772 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.772 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.772 * [backup-simplify]: Simplify (* 0 (pow (* 2 (* n PI)) 1/2)) into 0 11.772 * [taylor]: Taking taylor expansion of 0 in n 11.772 * [backup-simplify]: Simplify 0 into 0 11.772 * [backup-simplify]: Simplify 0 into 0 11.772 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 11.773 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 11.773 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 11.774 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 11.774 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.774 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.775 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 11.775 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 11.775 * [backup-simplify]: Simplify (+ (* 0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 11.775 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 11.775 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 11.775 * [taylor]: Taking taylor expansion of +nan.0 in n 11.775 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.775 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 11.775 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.775 * [taylor]: Taking taylor expansion of 2 in n 11.775 * [backup-simplify]: Simplify 2 into 2 11.775 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.776 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.776 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.776 * [taylor]: Taking taylor expansion of (* n PI) in n 11.776 * [taylor]: Taking taylor expansion of n in n 11.776 * [backup-simplify]: Simplify 0 into 0 11.776 * [backup-simplify]: Simplify 1 into 1 11.776 * [taylor]: Taking taylor expansion of PI in n 11.776 * [backup-simplify]: Simplify PI into PI 11.776 * [backup-simplify]: Simplify (* 0 PI) into 0 11.777 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.778 * [backup-simplify]: Simplify (sqrt 0) into 0 11.778 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.779 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 11.779 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.779 * [backup-simplify]: Simplify (- 0) into 0 11.779 * [backup-simplify]: Simplify 0 into 0 11.779 * [backup-simplify]: Simplify 0 into 0 11.780 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 11.780 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 11.782 * [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 11.782 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 11.782 * [backup-simplify]: Simplify (- 0) into 0 11.783 * [backup-simplify]: Simplify (+ 0 0) into 0 11.783 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 11.784 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 11.784 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.786 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.787 * [backup-simplify]: Simplify (+ (* 0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 11.787 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 11.787 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 11.787 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 11.787 * [taylor]: Taking taylor expansion of +nan.0 in n 11.787 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.787 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 11.787 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 11.787 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.787 * [taylor]: Taking taylor expansion of 2 in n 11.787 * [backup-simplify]: Simplify 2 into 2 11.788 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.788 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.788 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.789 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.789 * [taylor]: Taking taylor expansion of 2 in n 11.789 * [backup-simplify]: Simplify 2 into 2 11.789 * [taylor]: Taking taylor expansion of (* n PI) in n 11.789 * [taylor]: Taking taylor expansion of n in n 11.789 * [backup-simplify]: Simplify 0 into 0 11.789 * [backup-simplify]: Simplify 1 into 1 11.789 * [taylor]: Taking taylor expansion of PI in n 11.789 * [backup-simplify]: Simplify PI into PI 11.790 * [backup-simplify]: Simplify (* 0 PI) into 0 11.790 * [backup-simplify]: Simplify (* 2 0) into 0 11.791 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.792 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.793 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.793 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.793 * [taylor]: Taking taylor expansion of (* n PI) in n 11.793 * [taylor]: Taking taylor expansion of n in n 11.793 * [backup-simplify]: Simplify 0 into 0 11.793 * [backup-simplify]: Simplify 1 into 1 11.793 * [taylor]: Taking taylor expansion of PI in n 11.793 * [backup-simplify]: Simplify PI into PI 11.793 * [backup-simplify]: Simplify (* 0 PI) into 0 11.794 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.795 * [backup-simplify]: Simplify (sqrt 0) into 0 11.796 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.796 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 11.796 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 11.796 * [taylor]: Taking taylor expansion of +nan.0 in n 11.796 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.796 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 11.796 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.796 * [taylor]: Taking taylor expansion of 2 in n 11.796 * [backup-simplify]: Simplify 2 into 2 11.796 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.797 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.797 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.797 * [taylor]: Taking taylor expansion of (* n PI) in n 11.797 * [taylor]: Taking taylor expansion of n in n 11.797 * [backup-simplify]: Simplify 0 into 0 11.797 * [backup-simplify]: Simplify 1 into 1 11.797 * [taylor]: Taking taylor expansion of PI in n 11.797 * [backup-simplify]: Simplify PI into PI 11.797 * [backup-simplify]: Simplify (* 0 PI) into 0 11.798 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.798 * [backup-simplify]: Simplify (sqrt 0) into 0 11.799 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.801 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.803 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 11.805 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 11.805 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.806 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 11.806 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.806 * [backup-simplify]: Simplify (- 0) into 0 11.807 * [backup-simplify]: Simplify (+ 0 0) into 0 11.807 * [backup-simplify]: Simplify (- 0) into 0 11.807 * [backup-simplify]: Simplify 0 into 0 11.814 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 11.819 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 11.823 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 11.826 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 11.826 * [backup-simplify]: Simplify 0 into 0 11.827 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.828 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 11.831 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0 11.832 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 11.832 * [backup-simplify]: Simplify (- 0) into 0 11.833 * [backup-simplify]: Simplify (+ 0 0) into 0 11.834 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 11.836 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 11.837 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.841 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.843 * [backup-simplify]: Simplify (+ (* 0 (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))) (+ (* +nan.0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) 11.843 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n 11.843 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n 11.843 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 11.843 * [taylor]: Taking taylor expansion of +nan.0 in n 11.843 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.843 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 11.843 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 11.843 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.844 * [taylor]: Taking taylor expansion of 2 in n 11.844 * [backup-simplify]: Simplify 2 into 2 11.844 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.845 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.845 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.845 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.845 * [taylor]: Taking taylor expansion of 2 in n 11.845 * [backup-simplify]: Simplify 2 into 2 11.845 * [taylor]: Taking taylor expansion of (* n PI) in n 11.845 * [taylor]: Taking taylor expansion of n in n 11.845 * [backup-simplify]: Simplify 0 into 0 11.845 * [backup-simplify]: Simplify 1 into 1 11.845 * [taylor]: Taking taylor expansion of PI in n 11.845 * [backup-simplify]: Simplify PI into PI 11.846 * [backup-simplify]: Simplify (* 0 PI) into 0 11.846 * [backup-simplify]: Simplify (* 2 0) into 0 11.848 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.850 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.851 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.851 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.851 * [taylor]: Taking taylor expansion of (* n PI) in n 11.851 * [taylor]: Taking taylor expansion of n in n 11.851 * [backup-simplify]: Simplify 0 into 0 11.851 * [backup-simplify]: Simplify 1 into 1 11.851 * [taylor]: Taking taylor expansion of PI in n 11.851 * [backup-simplify]: Simplify PI into PI 11.852 * [backup-simplify]: Simplify (* 0 PI) into 0 11.853 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.854 * [backup-simplify]: Simplify (sqrt 0) into 0 11.855 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.855 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 11.856 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 11.856 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 11.856 * [taylor]: Taking taylor expansion of +nan.0 in n 11.856 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.856 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 11.856 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 11.856 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.856 * [taylor]: Taking taylor expansion of 2 in n 11.856 * [backup-simplify]: Simplify 2 into 2 11.856 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.857 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.857 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 11.857 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.857 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.857 * [taylor]: Taking taylor expansion of 2 in n 11.857 * [backup-simplify]: Simplify 2 into 2 11.857 * [taylor]: Taking taylor expansion of (* n PI) in n 11.857 * [taylor]: Taking taylor expansion of n in n 11.857 * [backup-simplify]: Simplify 0 into 0 11.857 * [backup-simplify]: Simplify 1 into 1 11.857 * [taylor]: Taking taylor expansion of PI in n 11.857 * [backup-simplify]: Simplify PI into PI 11.858 * [backup-simplify]: Simplify (* 0 PI) into 0 11.858 * [backup-simplify]: Simplify (* 2 0) into 0 11.860 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.861 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.863 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.864 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.864 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.864 * [taylor]: Taking taylor expansion of (* n PI) in n 11.864 * [taylor]: Taking taylor expansion of n in n 11.864 * [backup-simplify]: Simplify 0 into 0 11.864 * [backup-simplify]: Simplify 1 into 1 11.864 * [taylor]: Taking taylor expansion of PI in n 11.864 * [backup-simplify]: Simplify PI into PI 11.865 * [backup-simplify]: Simplify (* 0 PI) into 0 11.866 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.867 * [backup-simplify]: Simplify (sqrt 0) into 0 11.868 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.868 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 11.868 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 11.868 * [taylor]: Taking taylor expansion of +nan.0 in n 11.868 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.868 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 11.869 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.869 * [taylor]: Taking taylor expansion of 2 in n 11.869 * [backup-simplify]: Simplify 2 into 2 11.869 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.870 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.870 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 11.870 * [taylor]: Taking taylor expansion of (* n PI) in n 11.870 * [taylor]: Taking taylor expansion of n in n 11.870 * [backup-simplify]: Simplify 0 into 0 11.870 * [backup-simplify]: Simplify 1 into 1 11.870 * [taylor]: Taking taylor expansion of PI in n 11.870 * [backup-simplify]: Simplify PI into PI 11.870 * [backup-simplify]: Simplify (* 0 PI) into 0 11.872 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.872 * [backup-simplify]: Simplify (sqrt 0) into 0 11.873 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 11.874 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.874 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 11.875 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 11.876 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.877 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.878 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.879 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 11.880 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 11.881 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 11.881 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.882 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 11.882 * [backup-simplify]: Simplify (* +nan.0 0) into 0 11.882 * [backup-simplify]: Simplify (- 0) into 0 11.882 * [backup-simplify]: Simplify (+ 0 0) into 0 11.883 * [backup-simplify]: Simplify (- 0) into 0 11.883 * [backup-simplify]: Simplify (+ 0 0) into 0 11.883 * [backup-simplify]: Simplify (- 0) into 0 11.883 * [backup-simplify]: Simplify 0 into 0 11.884 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.885 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 11.886 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.887 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.888 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 11.889 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 11.894 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 11.896 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 11.900 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 11.904 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 11.913 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) 11.921 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 11.930 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 11.931 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.936 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 11.937 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 11.948 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 11.957 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 11.962 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 11.966 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 11.982 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 11.982 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 k)) (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 11.983 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (k n) around 0 11.983 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 11.983 * [taylor]: Taking taylor expansion of (sqrt k) in n 11.983 * [taylor]: Taking taylor expansion of k in n 11.983 * [backup-simplify]: Simplify k into k 11.983 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 11.983 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 11.983 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.983 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.983 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.983 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.983 * [taylor]: Taking taylor expansion of 1/2 in n 11.983 * [backup-simplify]: Simplify 1/2 into 1/2 11.983 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.983 * [taylor]: Taking taylor expansion of 1/2 in n 11.983 * [backup-simplify]: Simplify 1/2 into 1/2 11.983 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.983 * [taylor]: Taking taylor expansion of k in n 11.983 * [backup-simplify]: Simplify k into k 11.983 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.983 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.983 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.983 * [taylor]: Taking taylor expansion of 2 in n 11.983 * [backup-simplify]: Simplify 2 into 2 11.983 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.983 * [taylor]: Taking taylor expansion of PI in n 11.983 * [backup-simplify]: Simplify PI into PI 11.983 * [taylor]: Taking taylor expansion of n in n 11.983 * [backup-simplify]: Simplify 0 into 0 11.983 * [backup-simplify]: Simplify 1 into 1 11.984 * [backup-simplify]: Simplify (/ PI 1) into PI 11.985 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.986 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.986 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.986 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.986 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.988 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.989 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 11.990 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 11.990 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 11.990 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.990 * [taylor]: Taking taylor expansion of k in k 11.990 * [backup-simplify]: Simplify 0 into 0 11.990 * [backup-simplify]: Simplify 1 into 1 11.991 * [backup-simplify]: Simplify (sqrt 0) into 0 11.992 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.992 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 11.992 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.992 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.992 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.992 * [taylor]: Taking taylor expansion of 1/2 in k 11.992 * [backup-simplify]: Simplify 1/2 into 1/2 11.992 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.992 * [taylor]: Taking taylor expansion of 1/2 in k 11.992 * [backup-simplify]: Simplify 1/2 into 1/2 11.993 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.993 * [taylor]: Taking taylor expansion of k in k 11.993 * [backup-simplify]: Simplify 0 into 0 11.993 * [backup-simplify]: Simplify 1 into 1 11.993 * [backup-simplify]: Simplify (/ 1 1) into 1 11.993 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.993 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.993 * [taylor]: Taking taylor expansion of 2 in k 11.993 * [backup-simplify]: Simplify 2 into 2 11.993 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.993 * [taylor]: Taking taylor expansion of PI in k 11.993 * [backup-simplify]: Simplify PI into PI 11.993 * [taylor]: Taking taylor expansion of n in k 11.993 * [backup-simplify]: Simplify n into n 11.993 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.994 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.994 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.994 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.995 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.995 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.995 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 11.995 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 11.995 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 11.995 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.995 * [taylor]: Taking taylor expansion of k in k 11.995 * [backup-simplify]: Simplify 0 into 0 11.995 * [backup-simplify]: Simplify 1 into 1 11.996 * [backup-simplify]: Simplify (sqrt 0) into 0 11.997 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.997 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 11.997 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.997 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.997 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.997 * [taylor]: Taking taylor expansion of 1/2 in k 11.997 * [backup-simplify]: Simplify 1/2 into 1/2 11.998 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.998 * [taylor]: Taking taylor expansion of 1/2 in k 11.998 * [backup-simplify]: Simplify 1/2 into 1/2 11.998 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.998 * [taylor]: Taking taylor expansion of k in k 11.998 * [backup-simplify]: Simplify 0 into 0 11.998 * [backup-simplify]: Simplify 1 into 1 11.998 * [backup-simplify]: Simplify (/ 1 1) into 1 11.998 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.998 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.998 * [taylor]: Taking taylor expansion of 2 in k 11.998 * [backup-simplify]: Simplify 2 into 2 11.998 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.998 * [taylor]: Taking taylor expansion of PI in k 11.998 * [backup-simplify]: Simplify PI into PI 11.998 * [taylor]: Taking taylor expansion of n in k 11.998 * [backup-simplify]: Simplify n into n 11.998 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.998 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.999 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.999 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.999 * [backup-simplify]: Simplify (- 1/2) into -1/2 12.000 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 12.000 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 12.000 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 12.000 * [backup-simplify]: Simplify (* 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into 0 12.000 * [taylor]: Taking taylor expansion of 0 in n 12.001 * [backup-simplify]: Simplify 0 into 0 12.001 * [backup-simplify]: Simplify 0 into 0 12.001 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 12.001 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 12.001 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 12.001 * [taylor]: Taking taylor expansion of +nan.0 in n 12.001 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.001 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 12.001 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 12.001 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 12.001 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 12.001 * [taylor]: Taking taylor expansion of 1/2 in n 12.002 * [backup-simplify]: Simplify 1/2 into 1/2 12.002 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.002 * [taylor]: Taking taylor expansion of 1/2 in n 12.002 * [backup-simplify]: Simplify 1/2 into 1/2 12.002 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.002 * [taylor]: Taking taylor expansion of k in n 12.002 * [backup-simplify]: Simplify k into k 12.002 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.002 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.002 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.002 * [taylor]: Taking taylor expansion of 2 in n 12.002 * [backup-simplify]: Simplify 2 into 2 12.002 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.002 * [taylor]: Taking taylor expansion of PI in n 12.002 * [backup-simplify]: Simplify PI into PI 12.002 * [taylor]: Taking taylor expansion of n in n 12.002 * [backup-simplify]: Simplify 0 into 0 12.002 * [backup-simplify]: Simplify 1 into 1 12.003 * [backup-simplify]: Simplify (/ PI 1) into PI 12.003 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.004 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.005 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.005 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 12.005 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 12.006 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.007 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 12.009 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 12.010 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 12.011 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 12.013 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 12.013 * [backup-simplify]: Simplify 0 into 0 12.016 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.017 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 12.017 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 12.017 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 12.017 * [taylor]: Taking taylor expansion of +nan.0 in n 12.017 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.017 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 12.017 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 12.017 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 12.017 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 12.017 * [taylor]: Taking taylor expansion of 1/2 in n 12.017 * [backup-simplify]: Simplify 1/2 into 1/2 12.017 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.017 * [taylor]: Taking taylor expansion of 1/2 in n 12.017 * [backup-simplify]: Simplify 1/2 into 1/2 12.017 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.017 * [taylor]: Taking taylor expansion of k in n 12.018 * [backup-simplify]: Simplify k into k 12.018 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.018 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.018 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.018 * [taylor]: Taking taylor expansion of 2 in n 12.018 * [backup-simplify]: Simplify 2 into 2 12.018 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.018 * [taylor]: Taking taylor expansion of PI in n 12.018 * [backup-simplify]: Simplify PI into PI 12.018 * [taylor]: Taking taylor expansion of n in n 12.018 * [backup-simplify]: Simplify 0 into 0 12.018 * [backup-simplify]: Simplify 1 into 1 12.019 * [backup-simplify]: Simplify (/ PI 1) into PI 12.019 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.020 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.021 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.021 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 12.021 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 12.022 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.024 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 12.025 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 12.026 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 12.028 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 12.029 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 12.030 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.031 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 12.033 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.033 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.033 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 12.034 * [backup-simplify]: Simplify (- 0) into 0 12.034 * [backup-simplify]: Simplify (+ 0 0) into 0 12.036 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.037 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 12.039 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.041 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 12.041 * [backup-simplify]: Simplify (- 0) into 0 12.041 * [backup-simplify]: Simplify 0 into 0 12.041 * [backup-simplify]: Simplify 0 into 0 12.045 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.047 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 12.047 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 12.047 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 12.047 * [taylor]: Taking taylor expansion of +nan.0 in n 12.047 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.047 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 12.047 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 12.047 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 12.047 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 12.047 * [taylor]: Taking taylor expansion of 1/2 in n 12.047 * [backup-simplify]: Simplify 1/2 into 1/2 12.047 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.047 * [taylor]: Taking taylor expansion of 1/2 in n 12.047 * [backup-simplify]: Simplify 1/2 into 1/2 12.047 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.047 * [taylor]: Taking taylor expansion of k in n 12.047 * [backup-simplify]: Simplify k into k 12.047 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.047 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.047 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.047 * [taylor]: Taking taylor expansion of 2 in n 12.047 * [backup-simplify]: Simplify 2 into 2 12.048 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.048 * [taylor]: Taking taylor expansion of PI in n 12.048 * [backup-simplify]: Simplify PI into PI 12.048 * [taylor]: Taking taylor expansion of n in n 12.048 * [backup-simplify]: Simplify 0 into 0 12.048 * [backup-simplify]: Simplify 1 into 1 12.048 * [backup-simplify]: Simplify (/ PI 1) into PI 12.049 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.050 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.050 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.050 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 12.050 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 12.052 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.053 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 12.054 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 12.056 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 12.057 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 12.058 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 12.063 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 12.064 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 12.064 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0 12.064 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 12.064 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.064 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 12.064 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 12.064 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.064 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.064 * [taylor]: Taking taylor expansion of 1/2 in n 12.064 * [backup-simplify]: Simplify 1/2 into 1/2 12.064 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.064 * [taylor]: Taking taylor expansion of k in n 12.064 * [backup-simplify]: Simplify k into k 12.064 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.064 * [taylor]: Taking taylor expansion of 1/2 in n 12.064 * [backup-simplify]: Simplify 1/2 into 1/2 12.064 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.064 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.064 * [taylor]: Taking taylor expansion of -2 in n 12.064 * [backup-simplify]: Simplify -2 into -2 12.064 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.064 * [taylor]: Taking taylor expansion of PI in n 12.065 * [backup-simplify]: Simplify PI into PI 12.065 * [taylor]: Taking taylor expansion of n in n 12.065 * [backup-simplify]: Simplify 0 into 0 12.065 * [backup-simplify]: Simplify 1 into 1 12.065 * [backup-simplify]: Simplify (/ PI 1) into PI 12.066 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.067 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.067 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.067 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.069 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.070 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 12.071 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 12.071 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 12.071 * [taylor]: Taking taylor expansion of (/ -1 k) in n 12.071 * [taylor]: Taking taylor expansion of -1 in n 12.071 * [backup-simplify]: Simplify -1 into -1 12.071 * [taylor]: Taking taylor expansion of k in n 12.071 * [backup-simplify]: Simplify k into k 12.071 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 12.071 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 12.071 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 12.071 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 12.072 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 12.072 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 12.072 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 12.072 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 12.072 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 12.072 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 12.072 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.072 * [taylor]: Taking taylor expansion of 1/2 in k 12.072 * [backup-simplify]: Simplify 1/2 into 1/2 12.072 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.072 * [taylor]: Taking taylor expansion of k in k 12.072 * [backup-simplify]: Simplify 0 into 0 12.072 * [backup-simplify]: Simplify 1 into 1 12.073 * [backup-simplify]: Simplify (/ 1 1) into 1 12.073 * [taylor]: Taking taylor expansion of 1/2 in k 12.073 * [backup-simplify]: Simplify 1/2 into 1/2 12.073 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 12.073 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 12.073 * [taylor]: Taking taylor expansion of -2 in k 12.073 * [backup-simplify]: Simplify -2 into -2 12.073 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.073 * [taylor]: Taking taylor expansion of PI in k 12.073 * [backup-simplify]: Simplify PI into PI 12.073 * [taylor]: Taking taylor expansion of n in k 12.073 * [backup-simplify]: Simplify n into n 12.073 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.073 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 12.073 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 12.073 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.074 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.074 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 12.074 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 12.074 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.074 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.074 * [taylor]: Taking taylor expansion of -1 in k 12.074 * [backup-simplify]: Simplify -1 into -1 12.074 * [taylor]: Taking taylor expansion of k in k 12.074 * [backup-simplify]: Simplify 0 into 0 12.074 * [backup-simplify]: Simplify 1 into 1 12.074 * [backup-simplify]: Simplify (/ -1 1) into -1 12.075 * [backup-simplify]: Simplify (sqrt 0) into 0 12.075 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.076 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 12.076 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 12.076 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 12.076 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 12.076 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 12.076 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 12.076 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.076 * [taylor]: Taking taylor expansion of 1/2 in k 12.076 * [backup-simplify]: Simplify 1/2 into 1/2 12.076 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.076 * [taylor]: Taking taylor expansion of k in k 12.076 * [backup-simplify]: Simplify 0 into 0 12.076 * [backup-simplify]: Simplify 1 into 1 12.076 * [backup-simplify]: Simplify (/ 1 1) into 1 12.076 * [taylor]: Taking taylor expansion of 1/2 in k 12.076 * [backup-simplify]: Simplify 1/2 into 1/2 12.076 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 12.076 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 12.076 * [taylor]: Taking taylor expansion of -2 in k 12.076 * [backup-simplify]: Simplify -2 into -2 12.076 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.076 * [taylor]: Taking taylor expansion of PI in k 12.076 * [backup-simplify]: Simplify PI into PI 12.076 * [taylor]: Taking taylor expansion of n in k 12.076 * [backup-simplify]: Simplify n into n 12.076 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.076 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 12.076 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 12.077 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.077 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.077 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 12.077 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 12.077 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.077 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.077 * [taylor]: Taking taylor expansion of -1 in k 12.077 * [backup-simplify]: Simplify -1 into -1 12.077 * [taylor]: Taking taylor expansion of k in k 12.077 * [backup-simplify]: Simplify 0 into 0 12.077 * [backup-simplify]: Simplify 1 into 1 12.078 * [backup-simplify]: Simplify (/ -1 1) into -1 12.078 * [backup-simplify]: Simplify (sqrt 0) into 0 12.079 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.079 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 12.079 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 12.079 * [taylor]: Taking taylor expansion of +nan.0 in n 12.079 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.079 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 12.079 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.079 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.079 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.079 * [taylor]: Taking taylor expansion of -2 in n 12.079 * [backup-simplify]: Simplify -2 into -2 12.079 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.079 * [taylor]: Taking taylor expansion of PI in n 12.079 * [backup-simplify]: Simplify PI into PI 12.079 * [taylor]: Taking taylor expansion of n in n 12.079 * [backup-simplify]: Simplify 0 into 0 12.079 * [backup-simplify]: Simplify 1 into 1 12.079 * [backup-simplify]: Simplify (/ PI 1) into PI 12.080 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.080 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.080 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.080 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.080 * [taylor]: Taking taylor expansion of 1/2 in n 12.080 * [backup-simplify]: Simplify 1/2 into 1/2 12.080 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.080 * [taylor]: Taking taylor expansion of k in n 12.080 * [backup-simplify]: Simplify k into k 12.080 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.081 * [taylor]: Taking taylor expansion of 1/2 in n 12.081 * [backup-simplify]: Simplify 1/2 into 1/2 12.081 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.082 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.082 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.082 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 12.083 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 12.084 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 12.085 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 12.085 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 12.090 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.091 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 12.091 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 12.091 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 12.091 * [taylor]: Taking taylor expansion of +nan.0 in n 12.091 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.091 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 12.091 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.091 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.091 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.091 * [taylor]: Taking taylor expansion of -2 in n 12.091 * [backup-simplify]: Simplify -2 into -2 12.091 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.091 * [taylor]: Taking taylor expansion of PI in n 12.091 * [backup-simplify]: Simplify PI into PI 12.091 * [taylor]: Taking taylor expansion of n in n 12.091 * [backup-simplify]: Simplify 0 into 0 12.091 * [backup-simplify]: Simplify 1 into 1 12.092 * [backup-simplify]: Simplify (/ PI 1) into PI 12.092 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.092 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.093 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.093 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.093 * [taylor]: Taking taylor expansion of 1/2 in n 12.093 * [backup-simplify]: Simplify 1/2 into 1/2 12.093 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.093 * [taylor]: Taking taylor expansion of k in n 12.093 * [backup-simplify]: Simplify k into k 12.093 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.093 * [taylor]: Taking taylor expansion of 1/2 in n 12.093 * [backup-simplify]: Simplify 1/2 into 1/2 12.094 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.094 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.094 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.095 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 12.096 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 12.096 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 12.097 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 12.098 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 12.099 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.099 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.099 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 12.099 * [backup-simplify]: Simplify (+ 0 0) into 0 12.100 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.100 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 12.102 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 12.102 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 12.103 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.105 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 12.105 * [backup-simplify]: Simplify 0 into 0 12.105 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.108 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.109 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 12.109 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 12.109 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 12.109 * [taylor]: Taking taylor expansion of +nan.0 in n 12.109 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.109 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 12.109 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.109 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.109 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.109 * [taylor]: Taking taylor expansion of -2 in n 12.109 * [backup-simplify]: Simplify -2 into -2 12.109 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.109 * [taylor]: Taking taylor expansion of PI in n 12.109 * [backup-simplify]: Simplify PI into PI 12.109 * [taylor]: Taking taylor expansion of n in n 12.109 * [backup-simplify]: Simplify 0 into 0 12.109 * [backup-simplify]: Simplify 1 into 1 12.110 * [backup-simplify]: Simplify (/ PI 1) into PI 12.110 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.111 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.111 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.111 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.111 * [taylor]: Taking taylor expansion of 1/2 in n 12.111 * [backup-simplify]: Simplify 1/2 into 1/2 12.111 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.111 * [taylor]: Taking taylor expansion of k in n 12.111 * [backup-simplify]: Simplify k into k 12.111 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.111 * [taylor]: Taking taylor expansion of 1/2 in n 12.111 * [backup-simplify]: Simplify 1/2 into 1/2 12.112 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.112 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.112 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.113 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 12.114 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 12.115 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 12.116 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 12.116 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 12.119 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 12.119 * * * [progress]: simplifying candidates 12.119 * * * * [progress]: [ 1 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 2 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 3 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 4 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 5 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 6 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 7 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 8 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 9 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 10 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 11 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 12 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 13 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 14 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 15 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 16 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 17 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 18 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 19 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 20 / 1611 ] simplifiying candidate #real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))))))> 12.120 * * * * [progress]: [ 21 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 22 / 1611 ] simplifiying candidate # 12.120 * * * * [progress]: [ 23 / 1611 ] simplifiying candidate # 12.121 * * * * [progress]: [ 24 / 1611 ] simplifiying candidate # 12.121 * * * * [progress]: [ 25 / 1611 ] simplifiying candidate # 12.121 * * * * [progress]: [ 26 / 1611 ] simplifiying candidate # 12.121 * * * * [progress]: [ 27 / 1611 ] simplifiying candidate # 12.121 * * * * [progress]: [ 28 / 1611 ] simplifiying candidate # 12.121 * * * * [progress]: [ 29 / 1611 ] simplifiying candidate # 12.121 * * * * [progress]: [ 30 / 1611 ] simplifiying candidate # 12.121 * * * * [progress]: [ 31 / 1611 ] simplifiying candidate # 12.121 * * * * [progress]: [ 32 / 1611 ] simplifiying candidate # 12.121 * * * * [progress]: [ 33 / 1611 ] simplifiying candidate # 12.121 * * * * [progress]: [ 34 / 1611 ] simplifiying candidate # 12.121 * * * * [progress]: [ 35 / 1611 ] simplifiying candidate # 12.121 * * * * [progress]: [ 36 / 1611 ] 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2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI)) (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI)) (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI)) (* (* n 2) (* (cbrt PI) (cbrt PI))) (* (* n 2) (sqrt PI)) (* (* n 2) 1) (* 2 PI) (real->posit16 (* (* n 2) PI)) (expm1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (log1p (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (- (log (sqrt k)) (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))) (- (log (sqrt k)) (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))) (- (log (sqrt k)) (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (- (log (sqrt k)) (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (- (log (sqrt k)) (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (log (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (exp (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (cbrt (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))) (cbrt (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (* (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (- (sqrt k)) (- (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))))) (/ (cbrt (sqrt k)) (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2))))))) (/ (cbrt (sqrt k)) (pow (* (* n 2) PI) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))))) (/ (cbrt (sqrt k)) (pow (* (* n 2) PI) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))))) (/ (cbrt (sqrt k)) (pow (* (* n 2) PI) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))))) (/ (cbrt (sqrt k)) (pow (* (* n 2) PI) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 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+nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 12.381 * * [simplify]: iteration 0: 1732 enodes 14.600 * * [simplify]: iteration 1: 4740 enodes 16.466 * * [simplify]: iteration complete: 5000 enodes 16.467 * * [simplify]: Extracting #0: cost 589 inf + 0 16.471 * * [simplify]: Extracting #1: cost 1720 inf + 2 16.481 * * [simplify]: Extracting #2: cost 1771 inf + 7270 16.500 * * [simplify]: Extracting #3: cost 1647 inf + 33395 16.529 * * [simplify]: Extracting #4: cost 1052 inf + 186706 16.591 * * [simplify]: Extracting #5: cost 692 inf + 370492 16.727 * * [simplify]: Extracting #6: cost 367 inf + 579831 16.883 * * [simplify]: Extracting #7: cost 140 inf + 746083 17.081 * * [simplify]: Extracting #8: cost 40 inf + 813250 17.307 * * [simplify]: Extracting #9: cost 8 inf + 836345 17.501 * * [simplify]: Extracting #10: cost 0 inf + 843681 17.726 * * [simplify]: Extracting #11: cost 0 inf + 843338 17.959 * * [simplify]: Extracting #12: cost 0 inf + 843293 18.188 * [simplify]: Simplified to: (expm1 (* n (* PI 2))) (log1p (* n (* PI 2))) (* n (* PI 2)) (* n (* PI 2)) (log (* n (* PI 2))) (log (* n (* PI 2))) (log (* n (* PI 2))) (* (exp (* PI n)) (exp (* PI n))) (* (* PI (* PI PI)) (* (* n (* n n)) 8)) (* (* (* 2 n) (* (* 2 n) (* 2 n))) (* PI (* PI PI))) (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2))) (* (* n (* PI 2)) (* (* n (* PI 2)) (* n (* PI 2)))) (sqrt (* n (* PI 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(cbrt (/ k 2))))))) (pow (* n (* PI 2)) (+ 1/2 (- (/ k 2)))) (pow (* n (* PI 2)) (+ 1/2 (* (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* n (* PI 2)) (+ 1/2 (* (/ (cbrt k) (sqrt 2)) (- (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n (* PI 2)) (+ 1/2 (* (/ (cbrt k) 2) (- (* (cbrt k) (cbrt k)))))) (pow (* n (* PI 2)) (+ 1/2 (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)))))) (pow (* n (* PI 2)) (+ 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* PI 2)) (+ 1/2 (* (/ (sqrt k) 2) (- (sqrt k))))) (pow (* n (* PI 2)) (+ 1/2 (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n (* PI 2)) (+ 1/2 (* (- (/ k (sqrt 2))) (/ 1 (sqrt 2))))) (pow (* n (* PI 2)) (+ 1/2 (- (/ k 2)))) (pow (* n (* PI 2)) (+ 1/2 (- (/ k 2)))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (sqrt (* n (* PI 2))) (sqrt (* n (* PI 2))) (pow (* 2 n) (- 1/2 (/ k 2))) (* (cbrt (pow (* n (* PI 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* PI 2)) (- 1/2 (/ k 2))))) (sqrt (pow (* n (* PI 2)) (- 1/2 (/ k 2)))) 1 (pow (* n (* PI 2)) (/ (- 1/2 (/ k 2)) 2)) 1 (/ 1 (sqrt k)) (/ 1 (/ (sqrt k) (sqrt (* n (* PI 2))))) (/ (sqrt k) (pow (* n (* PI 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n (* PI 2)) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* n (* PI 2)) (- 1/2 (/ k 2)))) (/ 1 (sqrt k)) (real->posit16 (* (/ 1 (sqrt k)) (pow (* n (* PI 2)) (- 1/2 (/ k 2))))) (* n (* PI 2)) (* n (* PI 2)) (* n (* PI 2)) (- (- (* (/ (* (* (* (* (sqrt 1/2) (sqrt 1/2)) (log (* PI 2))) (* k k)) (sqrt 2)) PI) +nan.0) (- (* +nan.0 (/ (* (* k k) (sqrt 1/2)) PI)) (- (* (/ (* (* k (sqrt 1/2)) n) (* PI PI)) +nan.0) (- (* +nan.0 (/ (log n) (/ PI (* (* (* k k) (* (sqrt 1/2) (sqrt 1/2))) (sqrt 2))))) (/ (* +nan.0 (* k (sqrt 1/2))) PI)))))) (- (- (* (/ (exp (- (* (- 1/2 (* k 1/2)) (- (log (* PI 2)) (- (log n)))))) k) +nan.0) (- (* +nan.0 (/ (exp (- (* (- 1/2 (* k 1/2)) (- (log (* PI 2)) (- (log n)))))) (* k k))) (* +nan.0 (exp (- (* (- 1/2 (* k 1/2)) (- (log (* PI 2)) (- (log n)))))))))) (- (- (* +nan.0 (/ (exp (- (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2))))) (* k k))) (- (* +nan.0 (/ (exp (- (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2))))) k)) (* +nan.0 (exp (- (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2))))))))) (- (fma (* 1/4 (log (* PI 2))) (* (* (log n) (* k k)) (exp (* (log (* n (* PI 2))) 1/2))) (fma 1/8 (* (exp (* (log (* n (* PI 2))) 1/2)) (* (* k k) (* (log n) (log n)))) (fma (* 1/8 (* (log (* PI 2)) (log (* PI 2)))) (* (exp (* (log (* n (* PI 2))) 1/2)) (* k k)) (exp (* (log (* n (* PI 2))) 1/2))))) (* 1/2 (fma (* k (log n)) (exp (* (log (* n (* PI 2))) 1/2)) (* (log (* PI 2)) (* (exp (* (log (* n (* PI 2))) 1/2)) k))))) (exp (* (- 1/2 (* k 1/2)) (- (log (* PI 2)) (- (log n))))) (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (- (fma (* (* (sqrt 2) n) (* k PI)) +nan.0 (- (fma (* +nan.0 (sqrt 2)) (* PI n) (- (- (* (* (log (* PI 2)) (* (* (sqrt 2) n) (* k PI))) +nan.0) (fma (* +nan.0 (sqrt 2)) (* (* PI n) (* k (log n))) (- (* (* +nan.0 (sqrt 2)) (* (* PI PI) (* n n))))))))))) (- (- (* +nan.0 (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* PI 2)) (- (log n))))) (* k (* k k)))) (- (* +nan.0 (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* PI 2)) (- (log n))))) k)) (* (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* PI 2)) (- (log n))))) (* k k)) +nan.0)))) (- (- (* (/ (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) k) +nan.0) (- (* +nan.0 (/ (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (* k k))) (* +nan.0 (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2)))))))) 18.679 * * * [progress]: adding candidates to table 29.838 * * [progress]: iteration 3 / 4 29.838 * * * [progress]: picking best candidate 29.898 * * * * [pick]: Picked # 29.898 * * * [progress]: localizing error 29.939 * * * [progress]: generating rewritten candidates 29.939 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1) 29.950 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 29.979 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 30.033 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2) 30.869 * * * [progress]: generating series expansions 30.869 * * * * [progress]: [ 1 / 4 ] generating series at (2 1) 30.869 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k)) 30.870 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0 30.870 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 30.870 * [taylor]: Taking taylor expansion of (/ 1 k) in k 30.870 * [taylor]: Taking taylor expansion of k in k 30.870 * [backup-simplify]: Simplify 0 into 0 30.870 * [backup-simplify]: Simplify 1 into 1 30.870 * [backup-simplify]: Simplify (/ 1 1) into 1 30.870 * [backup-simplify]: Simplify (sqrt 0) into 0 30.872 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 30.872 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 30.872 * [taylor]: Taking taylor expansion of (/ 1 k) in k 30.872 * [taylor]: Taking taylor expansion of k in k 30.872 * [backup-simplify]: Simplify 0 into 0 30.872 * [backup-simplify]: Simplify 1 into 1 30.872 * [backup-simplify]: Simplify (/ 1 1) into 1 30.872 * [backup-simplify]: Simplify (sqrt 0) into 0 30.873 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 30.873 * [backup-simplify]: Simplify 0 into 0 30.873 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.874 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 30.876 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 30.876 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.876 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.879 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 30.880 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.880 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 30.880 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k) 30.880 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0 30.880 * [taylor]: Taking taylor expansion of (sqrt k) in k 30.880 * [taylor]: Taking taylor expansion of k in k 30.880 * [backup-simplify]: Simplify 0 into 0 30.880 * [backup-simplify]: Simplify 1 into 1 30.880 * [backup-simplify]: Simplify (sqrt 0) into 0 30.881 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 30.881 * [taylor]: Taking taylor expansion of (sqrt k) in k 30.881 * [taylor]: Taking taylor expansion of k in k 30.881 * [backup-simplify]: Simplify 0 into 0 30.881 * [backup-simplify]: Simplify 1 into 1 30.882 * [backup-simplify]: Simplify (sqrt 0) into 0 30.883 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 30.883 * [backup-simplify]: Simplify 0 into 0 30.883 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.885 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 30.885 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.887 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 30.887 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.887 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (/ 1 k) 3)) (+ (* +nan.0 (pow (/ 1 k) 2)) (* +nan.0 (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 30.887 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k))) 30.887 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0 30.887 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 30.887 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 30.887 * [taylor]: Taking taylor expansion of (/ -1 k) in k 30.887 * [taylor]: Taking taylor expansion of -1 in k 30.887 * [backup-simplify]: Simplify -1 into -1 30.888 * [taylor]: Taking taylor expansion of k in k 30.888 * [backup-simplify]: Simplify 0 into 0 30.888 * [backup-simplify]: Simplify 1 into 1 30.888 * [backup-simplify]: Simplify (/ -1 1) into -1 30.888 * [backup-simplify]: Simplify (sqrt 0) into 0 30.889 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 30.889 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 30.889 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 30.889 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 30.889 * [taylor]: Taking taylor expansion of (/ -1 k) in k 30.889 * [taylor]: Taking taylor expansion of -1 in k 30.889 * [backup-simplify]: Simplify -1 into -1 30.889 * [taylor]: Taking taylor expansion of k in k 30.889 * [backup-simplify]: Simplify 0 into 0 30.889 * [backup-simplify]: Simplify 1 into 1 30.890 * [backup-simplify]: Simplify (/ -1 1) into -1 30.890 * [backup-simplify]: Simplify (sqrt 0) into 0 30.891 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 30.891 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 30.891 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.892 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 30.893 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 30.895 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 30.895 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 30.896 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.898 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 30.900 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 30.901 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 30.901 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 30.901 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 30.902 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI)) 30.902 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 30.902 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 30.902 * [taylor]: Taking taylor expansion of 2 in n 30.902 * [backup-simplify]: Simplify 2 into 2 30.902 * [taylor]: Taking taylor expansion of (* n PI) in n 30.902 * [taylor]: Taking taylor expansion of n in n 30.902 * [backup-simplify]: Simplify 0 into 0 30.902 * [backup-simplify]: Simplify 1 into 1 30.902 * [taylor]: Taking taylor expansion of PI in n 30.902 * [backup-simplify]: Simplify PI into PI 30.902 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 30.902 * [taylor]: Taking taylor expansion of 2 in n 30.902 * [backup-simplify]: Simplify 2 into 2 30.902 * [taylor]: Taking taylor expansion of (* n PI) in n 30.902 * [taylor]: Taking taylor expansion of n in n 30.902 * [backup-simplify]: Simplify 0 into 0 30.902 * [backup-simplify]: Simplify 1 into 1 30.902 * [taylor]: Taking taylor expansion of PI in n 30.902 * [backup-simplify]: Simplify PI into PI 30.902 * [backup-simplify]: Simplify (* 0 PI) into 0 30.902 * [backup-simplify]: Simplify (* 2 0) into 0 30.902 * [backup-simplify]: Simplify 0 into 0 30.904 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 30.906 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 30.906 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 30.907 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 30.908 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 30.909 * [backup-simplify]: Simplify 0 into 0 30.910 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 30.911 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 30.911 * [backup-simplify]: Simplify 0 into 0 30.913 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 30.914 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 30.914 * [backup-simplify]: Simplify 0 into 0 30.916 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 30.917 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 30.918 * [backup-simplify]: Simplify 0 into 0 30.919 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 30.922 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 30.922 * [backup-simplify]: Simplify 0 into 0 30.924 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 30.926 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 30.926 * [backup-simplify]: Simplify 0 into 0 30.926 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 30.926 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n)) 30.927 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 30.927 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 30.927 * [taylor]: Taking taylor expansion of 2 in n 30.927 * [backup-simplify]: Simplify 2 into 2 30.927 * [taylor]: Taking taylor expansion of (/ PI n) in n 30.927 * [taylor]: Taking taylor expansion of PI in n 30.927 * [backup-simplify]: Simplify PI into PI 30.927 * [taylor]: Taking taylor expansion of n in n 30.927 * [backup-simplify]: Simplify 0 into 0 30.927 * [backup-simplify]: Simplify 1 into 1 30.927 * [backup-simplify]: Simplify (/ PI 1) into PI 30.927 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 30.927 * [taylor]: Taking taylor expansion of 2 in n 30.927 * [backup-simplify]: Simplify 2 into 2 30.927 * [taylor]: Taking taylor expansion of (/ PI n) in n 30.927 * [taylor]: Taking taylor expansion of PI in n 30.927 * [backup-simplify]: Simplify PI into PI 30.927 * [taylor]: Taking taylor expansion of n in n 30.928 * [backup-simplify]: Simplify 0 into 0 30.928 * [backup-simplify]: Simplify 1 into 1 30.928 * [backup-simplify]: Simplify (/ PI 1) into PI 30.929 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 30.929 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 30.930 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 30.931 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 30.931 * [backup-simplify]: Simplify 0 into 0 30.932 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.933 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 30.933 * [backup-simplify]: Simplify 0 into 0 30.934 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.936 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 30.936 * [backup-simplify]: Simplify 0 into 0 30.937 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.938 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 30.938 * [backup-simplify]: Simplify 0 into 0 30.940 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.941 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 30.941 * [backup-simplify]: Simplify 0 into 0 30.942 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.944 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 30.944 * [backup-simplify]: Simplify 0 into 0 30.945 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 30.945 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n)) 30.945 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 30.945 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 30.945 * [taylor]: Taking taylor expansion of -2 in n 30.945 * [backup-simplify]: Simplify -2 into -2 30.945 * [taylor]: Taking taylor expansion of (/ PI n) in n 30.945 * [taylor]: Taking taylor expansion of PI in n 30.945 * [backup-simplify]: Simplify PI into PI 30.945 * [taylor]: Taking taylor expansion of n in n 30.945 * [backup-simplify]: Simplify 0 into 0 30.945 * [backup-simplify]: Simplify 1 into 1 30.946 * [backup-simplify]: Simplify (/ PI 1) into PI 30.946 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 30.946 * [taylor]: Taking taylor expansion of -2 in n 30.946 * [backup-simplify]: Simplify -2 into -2 30.946 * [taylor]: Taking taylor expansion of (/ PI n) in n 30.946 * [taylor]: Taking taylor expansion of PI in n 30.946 * [backup-simplify]: Simplify PI into PI 30.946 * [taylor]: Taking taylor expansion of n in n 30.946 * [backup-simplify]: Simplify 0 into 0 30.946 * [backup-simplify]: Simplify 1 into 1 30.947 * [backup-simplify]: Simplify (/ PI 1) into PI 30.947 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 30.948 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 30.949 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 30.950 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 30.950 * [backup-simplify]: Simplify 0 into 0 30.951 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.952 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 30.952 * [backup-simplify]: Simplify 0 into 0 30.953 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.955 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 30.955 * [backup-simplify]: Simplify 0 into 0 30.956 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.957 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 30.957 * [backup-simplify]: Simplify 0 into 0 30.959 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.960 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 30.960 * [backup-simplify]: Simplify 0 into 0 30.962 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.963 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 30.963 * [backup-simplify]: Simplify 0 into 0 30.964 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 30.964 * * * * [progress]: [ 3 / 4 ] generating series at (2) 30.964 * [backup-simplify]: Simplify (/ (/ 1 (sqrt k)) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) into (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) 30.973 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in (k n) around 0 30.973 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 30.973 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 30.973 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 30.973 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 30.973 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 30.973 * [taylor]: Taking taylor expansion of 1/2 in n 30.973 * [backup-simplify]: Simplify 1/2 into 1/2 30.973 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 30.973 * [taylor]: Taking taylor expansion of 1/2 in n 30.973 * [backup-simplify]: Simplify 1/2 into 1/2 30.973 * [taylor]: Taking taylor expansion of k in n 30.973 * [backup-simplify]: Simplify k into k 30.973 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 30.973 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 30.973 * [taylor]: Taking taylor expansion of 2 in n 30.973 * [backup-simplify]: Simplify 2 into 2 30.973 * [taylor]: Taking taylor expansion of (* n PI) in n 30.973 * [taylor]: Taking taylor expansion of n in n 30.973 * [backup-simplify]: Simplify 0 into 0 30.973 * [backup-simplify]: Simplify 1 into 1 30.973 * [taylor]: Taking taylor expansion of PI in n 30.974 * [backup-simplify]: Simplify PI into PI 30.974 * [backup-simplify]: Simplify (* 0 PI) into 0 30.975 * [backup-simplify]: Simplify (* 2 0) into 0 30.977 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 30.978 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 30.979 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 30.980 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 30.980 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 30.980 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 30.981 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 30.982 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 30.984 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 30.984 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 30.984 * [taylor]: Taking taylor expansion of (/ 1 k) in n 30.984 * [taylor]: Taking taylor expansion of k in n 30.984 * [backup-simplify]: Simplify k into k 30.984 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 30.984 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 30.984 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 30.984 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 30.984 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 30.984 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 30.984 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 30.984 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 30.984 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 30.984 * [taylor]: Taking taylor expansion of 1/2 in k 30.984 * [backup-simplify]: Simplify 1/2 into 1/2 30.984 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 30.984 * [taylor]: Taking taylor expansion of 1/2 in k 30.984 * [backup-simplify]: Simplify 1/2 into 1/2 30.984 * [taylor]: Taking taylor expansion of k in k 30.984 * [backup-simplify]: Simplify 0 into 0 30.984 * [backup-simplify]: Simplify 1 into 1 30.984 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 30.984 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 30.985 * [taylor]: Taking taylor expansion of 2 in k 30.985 * [backup-simplify]: Simplify 2 into 2 30.985 * [taylor]: Taking taylor expansion of (* n PI) in k 30.985 * [taylor]: Taking taylor expansion of n in k 30.985 * [backup-simplify]: Simplify n into n 30.985 * [taylor]: Taking taylor expansion of PI in k 30.985 * [backup-simplify]: Simplify PI into PI 30.985 * [backup-simplify]: Simplify (* n PI) into (* n PI) 30.985 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 30.985 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 30.985 * [backup-simplify]: Simplify (* 1/2 0) into 0 30.986 * [backup-simplify]: Simplify (- 0) into 0 30.986 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 30.986 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 30.986 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 30.987 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 30.987 * [taylor]: Taking taylor expansion of (/ 1 k) in k 30.987 * [taylor]: Taking taylor expansion of k in k 30.987 * [backup-simplify]: Simplify 0 into 0 30.987 * [backup-simplify]: Simplify 1 into 1 30.987 * [backup-simplify]: Simplify (/ 1 1) into 1 30.987 * [backup-simplify]: Simplify (sqrt 0) into 0 30.989 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 30.989 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 30.989 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 30.989 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 30.989 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 30.989 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 30.989 * [taylor]: Taking taylor expansion of 1/2 in k 30.989 * [backup-simplify]: Simplify 1/2 into 1/2 30.989 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 30.989 * [taylor]: Taking taylor expansion of 1/2 in k 30.989 * [backup-simplify]: Simplify 1/2 into 1/2 30.989 * [taylor]: Taking taylor expansion of k in k 30.989 * [backup-simplify]: Simplify 0 into 0 30.989 * [backup-simplify]: Simplify 1 into 1 30.989 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 30.989 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 30.989 * [taylor]: Taking taylor expansion of 2 in k 30.990 * [backup-simplify]: Simplify 2 into 2 30.990 * [taylor]: Taking taylor expansion of (* n PI) in k 30.990 * [taylor]: Taking taylor expansion of n in k 30.990 * [backup-simplify]: Simplify n into n 30.990 * [taylor]: Taking taylor expansion of PI in k 30.990 * [backup-simplify]: Simplify PI into PI 30.990 * [backup-simplify]: Simplify (* n PI) into (* n PI) 30.990 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 30.990 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 30.991 * [backup-simplify]: Simplify (* 1/2 0) into 0 30.991 * [backup-simplify]: Simplify (- 0) into 0 30.991 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 30.992 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 30.992 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 30.992 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 30.992 * [taylor]: Taking taylor expansion of (/ 1 k) in k 30.992 * [taylor]: Taking taylor expansion of k in k 30.992 * [backup-simplify]: Simplify 0 into 0 30.992 * [backup-simplify]: Simplify 1 into 1 30.992 * [backup-simplify]: Simplify (/ 1 1) into 1 30.993 * [backup-simplify]: Simplify (sqrt 0) into 0 30.994 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 30.994 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0 30.995 * [taylor]: Taking taylor expansion of 0 in n 30.995 * [backup-simplify]: Simplify 0 into 0 30.995 * [backup-simplify]: Simplify 0 into 0 30.995 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 30.996 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 30.997 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 30.997 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 30.998 * [backup-simplify]: Simplify (- 1/2) into -1/2 30.998 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 30.999 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 30.999 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 31.000 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 31.000 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 31.000 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 31.000 * [taylor]: Taking taylor expansion of +nan.0 in n 31.000 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.000 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 31.000 * [taylor]: Taking taylor expansion of (sqrt 2) in n 31.000 * [taylor]: Taking taylor expansion of 2 in n 31.000 * [backup-simplify]: Simplify 2 into 2 31.000 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 31.001 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 31.001 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 31.001 * [taylor]: Taking taylor expansion of (* n PI) in n 31.001 * [taylor]: Taking taylor expansion of n in n 31.001 * [backup-simplify]: Simplify 0 into 0 31.001 * [backup-simplify]: Simplify 1 into 1 31.001 * [taylor]: Taking taylor expansion of PI in n 31.001 * [backup-simplify]: Simplify PI into PI 31.002 * [backup-simplify]: Simplify (* 0 PI) into 0 31.004 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 31.004 * [backup-simplify]: Simplify (sqrt 0) into 0 31.006 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 31.006 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 31.007 * [backup-simplify]: Simplify (* +nan.0 0) into 0 31.007 * [backup-simplify]: Simplify (- 0) into 0 31.007 * [backup-simplify]: Simplify 0 into 0 31.007 * [backup-simplify]: Simplify 0 into 0 31.008 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 31.011 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 31.012 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 31.013 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 31.015 * [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 31.016 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 31.017 * [backup-simplify]: Simplify (- 0) into 0 31.017 * [backup-simplify]: Simplify (+ 0 0) into 0 31.019 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 31.020 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 31.021 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 31.021 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 31.021 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 31.021 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 31.021 * [taylor]: Taking taylor expansion of +nan.0 in n 31.021 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.021 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 31.022 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 31.022 * [taylor]: Taking taylor expansion of (sqrt 2) in n 31.022 * [taylor]: Taking taylor expansion of 2 in n 31.022 * [backup-simplify]: Simplify 2 into 2 31.022 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 31.023 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 31.023 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 31.023 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 31.023 * [taylor]: Taking taylor expansion of 2 in n 31.023 * [backup-simplify]: Simplify 2 into 2 31.023 * [taylor]: Taking taylor expansion of (* n PI) in n 31.023 * [taylor]: Taking taylor expansion of n in n 31.023 * [backup-simplify]: Simplify 0 into 0 31.023 * [backup-simplify]: Simplify 1 into 1 31.023 * [taylor]: Taking taylor expansion of PI in n 31.023 * [backup-simplify]: Simplify PI into PI 31.023 * [backup-simplify]: Simplify (* 0 PI) into 0 31.024 * [backup-simplify]: Simplify (* 2 0) into 0 31.025 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 31.026 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 31.026 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.026 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 31.026 * [taylor]: Taking taylor expansion of (* n PI) in n 31.026 * [taylor]: Taking taylor expansion of n in n 31.026 * [backup-simplify]: Simplify 0 into 0 31.026 * [backup-simplify]: Simplify 1 into 1 31.027 * [taylor]: Taking taylor expansion of PI in n 31.027 * [backup-simplify]: Simplify PI into PI 31.027 * [backup-simplify]: Simplify (* 0 PI) into 0 31.028 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 31.028 * [backup-simplify]: Simplify (sqrt 0) into 0 31.029 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 31.029 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 31.029 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 31.029 * [taylor]: Taking taylor expansion of +nan.0 in n 31.029 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.029 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 31.029 * [taylor]: Taking taylor expansion of (sqrt 2) in n 31.029 * [taylor]: Taking taylor expansion of 2 in n 31.029 * [backup-simplify]: Simplify 2 into 2 31.029 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 31.030 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 31.030 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 31.030 * [taylor]: Taking taylor expansion of (* n PI) in n 31.030 * [taylor]: Taking taylor expansion of n in n 31.030 * [backup-simplify]: Simplify 0 into 0 31.030 * [backup-simplify]: Simplify 1 into 1 31.030 * [taylor]: Taking taylor expansion of PI in n 31.030 * [backup-simplify]: Simplify PI into PI 31.030 * [backup-simplify]: Simplify (* 0 PI) into 0 31.031 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 31.031 * [backup-simplify]: Simplify (sqrt 0) into 0 31.032 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 31.033 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 31.034 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 31.035 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 31.035 * [backup-simplify]: Simplify (* +nan.0 0) into 0 31.036 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 31.036 * [backup-simplify]: Simplify (* +nan.0 0) into 0 31.036 * [backup-simplify]: Simplify (- 0) into 0 31.037 * [backup-simplify]: Simplify (+ 0 0) into 0 31.037 * [backup-simplify]: Simplify (- 0) into 0 31.037 * [backup-simplify]: Simplify 0 into 0 31.039 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 31.042 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 31.045 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 31.046 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 31.046 * [backup-simplify]: Simplify 0 into 0 31.047 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 31.049 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 31.050 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 31.051 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 31.053 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0 31.055 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 31.055 * [backup-simplify]: Simplify (- 0) into 0 31.055 * [backup-simplify]: Simplify (+ 0 0) into 0 31.057 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 31.058 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 31.060 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) 31.060 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n 31.060 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n 31.060 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 31.060 * [taylor]: Taking taylor expansion of +nan.0 in n 31.060 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.060 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 31.060 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 31.060 * [taylor]: Taking taylor expansion of (sqrt 2) in n 31.060 * [taylor]: Taking taylor expansion of 2 in n 31.060 * [backup-simplify]: Simplify 2 into 2 31.061 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 31.061 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 31.061 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 31.061 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 31.061 * [taylor]: Taking taylor expansion of 2 in n 31.061 * [backup-simplify]: Simplify 2 into 2 31.061 * [taylor]: Taking taylor expansion of (* n PI) in n 31.061 * [taylor]: Taking taylor expansion of n in n 31.061 * [backup-simplify]: Simplify 0 into 0 31.061 * [backup-simplify]: Simplify 1 into 1 31.061 * [taylor]: Taking taylor expansion of PI in n 31.061 * [backup-simplify]: Simplify PI into PI 31.062 * [backup-simplify]: Simplify (* 0 PI) into 0 31.062 * [backup-simplify]: Simplify (* 2 0) into 0 31.064 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 31.066 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 31.067 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.067 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 31.067 * [taylor]: Taking taylor expansion of (* n PI) in n 31.067 * [taylor]: Taking taylor expansion of n in n 31.067 * [backup-simplify]: Simplify 0 into 0 31.067 * [backup-simplify]: Simplify 1 into 1 31.067 * [taylor]: Taking taylor expansion of PI in n 31.067 * [backup-simplify]: Simplify PI into PI 31.068 * [backup-simplify]: Simplify (* 0 PI) into 0 31.069 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 31.070 * [backup-simplify]: Simplify (sqrt 0) into 0 31.072 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 31.072 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n 31.072 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n 31.072 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 31.072 * [taylor]: Taking taylor expansion of +nan.0 in n 31.072 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.072 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 31.072 * [taylor]: Taking taylor expansion of (sqrt 2) in n 31.072 * [taylor]: Taking taylor expansion of 2 in n 31.072 * [backup-simplify]: Simplify 2 into 2 31.073 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 31.074 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 31.074 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 31.074 * [taylor]: Taking taylor expansion of (* n PI) in n 31.074 * [taylor]: Taking taylor expansion of n in n 31.074 * [backup-simplify]: Simplify 0 into 0 31.074 * [backup-simplify]: Simplify 1 into 1 31.074 * [taylor]: Taking taylor expansion of PI in n 31.074 * [backup-simplify]: Simplify PI into PI 31.074 * [backup-simplify]: Simplify (* 0 PI) into 0 31.076 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 31.077 * [backup-simplify]: Simplify (sqrt 0) into 0 31.078 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 31.078 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n 31.078 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 31.078 * [taylor]: Taking taylor expansion of +nan.0 in n 31.078 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.078 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 31.078 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 31.078 * [taylor]: Taking taylor expansion of (sqrt 2) in n 31.078 * [taylor]: Taking taylor expansion of 2 in n 31.078 * [backup-simplify]: Simplify 2 into 2 31.079 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 31.080 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 31.080 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 31.080 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 31.080 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 31.080 * [taylor]: Taking taylor expansion of 2 in n 31.080 * [backup-simplify]: Simplify 2 into 2 31.080 * [taylor]: Taking taylor expansion of (* n PI) in n 31.080 * [taylor]: Taking taylor expansion of n in n 31.080 * [backup-simplify]: Simplify 0 into 0 31.080 * [backup-simplify]: Simplify 1 into 1 31.080 * [taylor]: Taking taylor expansion of PI in n 31.080 * [backup-simplify]: Simplify PI into PI 31.080 * [backup-simplify]: Simplify (* 0 PI) into 0 31.081 * [backup-simplify]: Simplify (* 2 0) into 0 31.083 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 31.084 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 31.086 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.087 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 31.087 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 31.087 * [taylor]: Taking taylor expansion of (* n PI) in n 31.087 * [taylor]: Taking taylor expansion of n in n 31.087 * [backup-simplify]: Simplify 0 into 0 31.087 * [backup-simplify]: Simplify 1 into 1 31.087 * [taylor]: Taking taylor expansion of PI in n 31.087 * [backup-simplify]: Simplify PI into PI 31.088 * [backup-simplify]: Simplify (* 0 PI) into 0 31.089 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 31.090 * [backup-simplify]: Simplify (sqrt 0) into 0 31.091 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 31.093 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 31.094 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 31.096 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 31.096 * [backup-simplify]: Simplify (* +nan.0 0) into 0 31.097 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 31.097 * [backup-simplify]: Simplify (* +nan.0 0) into 0 31.099 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 31.100 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 31.103 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 31.104 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 31.106 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 31.106 * [backup-simplify]: Simplify (* +nan.0 0) into 0 31.110 * [backup-simplify]: Simplify (- 0) into 0 31.110 * [backup-simplify]: Simplify (+ 0 0) into 0 31.111 * [backup-simplify]: Simplify (- 0) into 0 31.111 * [backup-simplify]: Simplify (+ 0 0) into 0 31.111 * [backup-simplify]: Simplify (- 0) into 0 31.112 * [backup-simplify]: Simplify 0 into 0 31.113 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 31.114 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 31.116 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 31.118 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 31.120 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 31.122 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 31.129 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 31.133 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 31.139 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 31.143 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 31.152 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) 31.161 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 31.169 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 31.170 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 31.175 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 31.176 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 31.181 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 31.189 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 31.192 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 31.195 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 31.203 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 31.204 * [backup-simplify]: Simplify (/ (/ 1 (sqrt (/ 1 k))) (/ 1 (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))))) into (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 31.204 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (k n) around 0 31.204 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 31.204 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 31.204 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 31.204 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 31.204 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 31.204 * [taylor]: Taking taylor expansion of 1/2 in n 31.204 * [backup-simplify]: Simplify 1/2 into 1/2 31.204 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.204 * [taylor]: Taking taylor expansion of 1/2 in n 31.204 * [backup-simplify]: Simplify 1/2 into 1/2 31.204 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.204 * [taylor]: Taking taylor expansion of k in n 31.204 * [backup-simplify]: Simplify k into k 31.204 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.204 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 31.204 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 31.204 * [taylor]: Taking taylor expansion of 2 in n 31.204 * [backup-simplify]: Simplify 2 into 2 31.204 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.204 * [taylor]: Taking taylor expansion of PI in n 31.204 * [backup-simplify]: Simplify PI into PI 31.204 * [taylor]: Taking taylor expansion of n in n 31.204 * [backup-simplify]: Simplify 0 into 0 31.204 * [backup-simplify]: Simplify 1 into 1 31.204 * [backup-simplify]: Simplify (/ PI 1) into PI 31.205 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 31.205 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.206 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.206 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 31.206 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 31.207 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.207 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 31.208 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 31.208 * [taylor]: Taking taylor expansion of (sqrt k) in n 31.208 * [taylor]: Taking taylor expansion of k in n 31.208 * [backup-simplify]: Simplify k into k 31.208 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 31.208 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 31.208 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 31.208 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 31.208 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 31.208 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 31.208 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 31.208 * [taylor]: Taking taylor expansion of 1/2 in k 31.208 * [backup-simplify]: Simplify 1/2 into 1/2 31.208 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 31.208 * [taylor]: Taking taylor expansion of 1/2 in k 31.208 * [backup-simplify]: Simplify 1/2 into 1/2 31.208 * [taylor]: Taking taylor expansion of (/ 1 k) in k 31.208 * [taylor]: Taking taylor expansion of k in k 31.208 * [backup-simplify]: Simplify 0 into 0 31.208 * [backup-simplify]: Simplify 1 into 1 31.209 * [backup-simplify]: Simplify (/ 1 1) into 1 31.209 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 31.209 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 31.209 * [taylor]: Taking taylor expansion of 2 in k 31.209 * [backup-simplify]: Simplify 2 into 2 31.209 * [taylor]: Taking taylor expansion of (/ PI n) in k 31.209 * [taylor]: Taking taylor expansion of PI in k 31.209 * [backup-simplify]: Simplify PI into PI 31.209 * [taylor]: Taking taylor expansion of n in k 31.209 * [backup-simplify]: Simplify n into n 31.209 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 31.209 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 31.209 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 31.209 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 31.210 * [backup-simplify]: Simplify (- 1/2) into -1/2 31.210 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 31.210 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 31.210 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 31.210 * [taylor]: Taking taylor expansion of (sqrt k) in k 31.210 * [taylor]: Taking taylor expansion of k in k 31.210 * [backup-simplify]: Simplify 0 into 0 31.210 * [backup-simplify]: Simplify 1 into 1 31.211 * [backup-simplify]: Simplify (sqrt 0) into 0 31.212 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 31.212 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 31.212 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 31.212 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 31.212 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 31.212 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 31.212 * [taylor]: Taking taylor expansion of 1/2 in k 31.212 * [backup-simplify]: Simplify 1/2 into 1/2 31.212 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 31.212 * [taylor]: Taking taylor expansion of 1/2 in k 31.212 * [backup-simplify]: Simplify 1/2 into 1/2 31.212 * [taylor]: Taking taylor expansion of (/ 1 k) in k 31.212 * [taylor]: Taking taylor expansion of k in k 31.212 * [backup-simplify]: Simplify 0 into 0 31.212 * [backup-simplify]: Simplify 1 into 1 31.212 * [backup-simplify]: Simplify (/ 1 1) into 1 31.212 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 31.212 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 31.212 * [taylor]: Taking taylor expansion of 2 in k 31.212 * [backup-simplify]: Simplify 2 into 2 31.212 * [taylor]: Taking taylor expansion of (/ PI n) in k 31.212 * [taylor]: Taking taylor expansion of PI in k 31.212 * [backup-simplify]: Simplify PI into PI 31.212 * [taylor]: Taking taylor expansion of n in k 31.212 * [backup-simplify]: Simplify n into n 31.212 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 31.212 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 31.212 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 31.213 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 31.213 * [backup-simplify]: Simplify (- 1/2) into -1/2 31.213 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 31.213 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 31.213 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 31.213 * [taylor]: Taking taylor expansion of (sqrt k) in k 31.213 * [taylor]: Taking taylor expansion of k in k 31.213 * [backup-simplify]: Simplify 0 into 0 31.213 * [backup-simplify]: Simplify 1 into 1 31.214 * [backup-simplify]: Simplify (sqrt 0) into 0 31.214 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 31.215 * [backup-simplify]: Simplify (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 0) into 0 31.215 * [taylor]: Taking taylor expansion of 0 in n 31.215 * [backup-simplify]: Simplify 0 into 0 31.215 * [backup-simplify]: Simplify 0 into 0 31.215 * [backup-simplify]: Simplify (+ (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 31.215 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 31.215 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 31.215 * [taylor]: Taking taylor expansion of +nan.0 in n 31.215 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.215 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 31.215 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 31.215 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 31.216 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 31.216 * [taylor]: Taking taylor expansion of 1/2 in n 31.216 * [backup-simplify]: Simplify 1/2 into 1/2 31.216 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.216 * [taylor]: Taking taylor expansion of 1/2 in n 31.216 * [backup-simplify]: Simplify 1/2 into 1/2 31.216 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.216 * [taylor]: Taking taylor expansion of k in n 31.216 * [backup-simplify]: Simplify k into k 31.216 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.216 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 31.216 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 31.216 * [taylor]: Taking taylor expansion of 2 in n 31.216 * [backup-simplify]: Simplify 2 into 2 31.216 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.216 * [taylor]: Taking taylor expansion of PI in n 31.216 * [backup-simplify]: Simplify PI into PI 31.216 * [taylor]: Taking taylor expansion of n in n 31.216 * [backup-simplify]: Simplify 0 into 0 31.216 * [backup-simplify]: Simplify 1 into 1 31.217 * [backup-simplify]: Simplify (/ PI 1) into PI 31.217 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 31.218 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.218 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.218 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 31.218 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 31.220 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.221 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 31.222 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 31.224 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 31.225 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 31.226 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 31.226 * [backup-simplify]: Simplify 0 into 0 31.229 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 31.230 * [backup-simplify]: Simplify (+ (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 31.230 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 31.230 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 31.230 * [taylor]: Taking taylor expansion of +nan.0 in n 31.231 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.231 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 31.231 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 31.231 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 31.231 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 31.231 * [taylor]: Taking taylor expansion of 1/2 in n 31.231 * [backup-simplify]: Simplify 1/2 into 1/2 31.231 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.231 * [taylor]: Taking taylor expansion of 1/2 in n 31.231 * [backup-simplify]: Simplify 1/2 into 1/2 31.231 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.231 * [taylor]: Taking taylor expansion of k in n 31.231 * [backup-simplify]: Simplify k into k 31.231 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.231 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 31.231 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 31.231 * [taylor]: Taking taylor expansion of 2 in n 31.231 * [backup-simplify]: Simplify 2 into 2 31.231 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.231 * [taylor]: Taking taylor expansion of PI in n 31.231 * [backup-simplify]: Simplify PI into PI 31.231 * [taylor]: Taking taylor expansion of n in n 31.231 * [backup-simplify]: Simplify 0 into 0 31.231 * [backup-simplify]: Simplify 1 into 1 31.232 * [backup-simplify]: Simplify (/ PI 1) into PI 31.232 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 31.233 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.234 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.234 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 31.234 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 31.235 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.240 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 31.241 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 31.242 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 31.243 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 31.244 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 31.244 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 31.245 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 31.246 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 31.246 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 31.246 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 31.247 * [backup-simplify]: Simplify (- 0) into 0 31.247 * [backup-simplify]: Simplify (+ 0 0) into 0 31.248 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.249 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 31.250 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 31.251 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 31.252 * [backup-simplify]: Simplify (- 0) into 0 31.252 * [backup-simplify]: Simplify 0 into 0 31.252 * [backup-simplify]: Simplify 0 into 0 31.254 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 31.255 * [backup-simplify]: Simplify (+ (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 31.255 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 31.255 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 31.255 * [taylor]: Taking taylor expansion of +nan.0 in n 31.255 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.255 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 31.255 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 31.255 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 31.255 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 31.255 * [taylor]: Taking taylor expansion of 1/2 in n 31.255 * [backup-simplify]: Simplify 1/2 into 1/2 31.255 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.255 * [taylor]: Taking taylor expansion of 1/2 in n 31.255 * [backup-simplify]: Simplify 1/2 into 1/2 31.256 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.256 * [taylor]: Taking taylor expansion of k in n 31.256 * [backup-simplify]: Simplify k into k 31.256 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.256 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 31.256 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 31.256 * [taylor]: Taking taylor expansion of 2 in n 31.256 * [backup-simplify]: Simplify 2 into 2 31.256 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.256 * [taylor]: Taking taylor expansion of PI in n 31.256 * [backup-simplify]: Simplify PI into PI 31.256 * [taylor]: Taking taylor expansion of n in n 31.256 * [backup-simplify]: Simplify 0 into 0 31.256 * [backup-simplify]: Simplify 1 into 1 31.256 * [backup-simplify]: Simplify (/ PI 1) into PI 31.256 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 31.257 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.257 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.257 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 31.257 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 31.258 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.259 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 31.260 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 31.261 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 31.262 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 31.262 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 31.265 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 31.266 * [backup-simplify]: Simplify (/ (/ 1 (sqrt (/ 1 (- k)))) (/ 1 (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 31.266 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0 31.266 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 31.266 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 31.266 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 31.266 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 31.266 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 31.266 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.266 * [taylor]: Taking taylor expansion of 1/2 in n 31.266 * [backup-simplify]: Simplify 1/2 into 1/2 31.266 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.266 * [taylor]: Taking taylor expansion of k in n 31.266 * [backup-simplify]: Simplify k into k 31.266 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.266 * [taylor]: Taking taylor expansion of 1/2 in n 31.266 * [backup-simplify]: Simplify 1/2 into 1/2 31.266 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 31.266 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 31.266 * [taylor]: Taking taylor expansion of -2 in n 31.266 * [backup-simplify]: Simplify -2 into -2 31.266 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.266 * [taylor]: Taking taylor expansion of PI in n 31.266 * [backup-simplify]: Simplify PI into PI 31.266 * [taylor]: Taking taylor expansion of n in n 31.266 * [backup-simplify]: Simplify 0 into 0 31.266 * [backup-simplify]: Simplify 1 into 1 31.267 * [backup-simplify]: Simplify (/ PI 1) into PI 31.267 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 31.268 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 31.268 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.268 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 31.270 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.272 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 31.273 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 31.273 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 31.273 * [taylor]: Taking taylor expansion of (/ -1 k) in n 31.273 * [taylor]: Taking taylor expansion of -1 in n 31.273 * [backup-simplify]: Simplify -1 into -1 31.273 * [taylor]: Taking taylor expansion of k in n 31.273 * [backup-simplify]: Simplify k into k 31.273 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 31.274 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 31.274 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 31.274 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 31.275 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 31.275 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 31.275 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 31.276 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 31.276 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 31.276 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 31.276 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 31.276 * [taylor]: Taking taylor expansion of 1/2 in k 31.276 * [backup-simplify]: Simplify 1/2 into 1/2 31.276 * [taylor]: Taking taylor expansion of (/ 1 k) in k 31.276 * [taylor]: Taking taylor expansion of k in k 31.276 * [backup-simplify]: Simplify 0 into 0 31.276 * [backup-simplify]: Simplify 1 into 1 31.276 * [backup-simplify]: Simplify (/ 1 1) into 1 31.276 * [taylor]: Taking taylor expansion of 1/2 in k 31.276 * [backup-simplify]: Simplify 1/2 into 1/2 31.276 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 31.276 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 31.276 * [taylor]: Taking taylor expansion of -2 in k 31.277 * [backup-simplify]: Simplify -2 into -2 31.277 * [taylor]: Taking taylor expansion of (/ PI n) in k 31.277 * [taylor]: Taking taylor expansion of PI in k 31.277 * [backup-simplify]: Simplify PI into PI 31.277 * [taylor]: Taking taylor expansion of n in k 31.277 * [backup-simplify]: Simplify n into n 31.277 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 31.277 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 31.277 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 31.277 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 31.278 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 31.278 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 31.278 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 31.278 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 31.278 * [taylor]: Taking taylor expansion of (/ -1 k) in k 31.278 * [taylor]: Taking taylor expansion of -1 in k 31.278 * [backup-simplify]: Simplify -1 into -1 31.278 * [taylor]: Taking taylor expansion of k in k 31.278 * [backup-simplify]: Simplify 0 into 0 31.279 * [backup-simplify]: Simplify 1 into 1 31.279 * [backup-simplify]: Simplify (/ -1 1) into -1 31.279 * [backup-simplify]: Simplify (sqrt 0) into 0 31.281 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 31.281 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 31.281 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 31.281 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 31.281 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 31.281 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 31.282 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 31.282 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 31.282 * [taylor]: Taking taylor expansion of 1/2 in k 31.282 * [backup-simplify]: Simplify 1/2 into 1/2 31.282 * [taylor]: Taking taylor expansion of (/ 1 k) in k 31.282 * [taylor]: Taking taylor expansion of k in k 31.282 * [backup-simplify]: Simplify 0 into 0 31.282 * [backup-simplify]: Simplify 1 into 1 31.282 * [backup-simplify]: Simplify (/ 1 1) into 1 31.282 * [taylor]: Taking taylor expansion of 1/2 in k 31.282 * [backup-simplify]: Simplify 1/2 into 1/2 31.282 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 31.282 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 31.282 * [taylor]: Taking taylor expansion of -2 in k 31.282 * [backup-simplify]: Simplify -2 into -2 31.282 * [taylor]: Taking taylor expansion of (/ PI n) in k 31.282 * [taylor]: Taking taylor expansion of PI in k 31.282 * [backup-simplify]: Simplify PI into PI 31.282 * [taylor]: Taking taylor expansion of n in k 31.282 * [backup-simplify]: Simplify n into n 31.283 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 31.283 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 31.283 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 31.283 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 31.284 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 31.284 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 31.284 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 31.284 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 31.284 * [taylor]: Taking taylor expansion of (/ -1 k) in k 31.284 * [taylor]: Taking taylor expansion of -1 in k 31.284 * [backup-simplify]: Simplify -1 into -1 31.284 * [taylor]: Taking taylor expansion of k in k 31.284 * [backup-simplify]: Simplify 0 into 0 31.284 * [backup-simplify]: Simplify 1 into 1 31.285 * [backup-simplify]: Simplify (/ -1 1) into -1 31.285 * [backup-simplify]: Simplify (sqrt 0) into 0 31.287 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 31.288 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 31.288 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 31.288 * [taylor]: Taking taylor expansion of +nan.0 in n 31.288 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.288 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 31.288 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 31.288 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 31.288 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 31.288 * [taylor]: Taking taylor expansion of -2 in n 31.288 * [backup-simplify]: Simplify -2 into -2 31.288 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.288 * [taylor]: Taking taylor expansion of PI in n 31.288 * [backup-simplify]: Simplify PI into PI 31.288 * [taylor]: Taking taylor expansion of n in n 31.288 * [backup-simplify]: Simplify 0 into 0 31.288 * [backup-simplify]: Simplify 1 into 1 31.289 * [backup-simplify]: Simplify (/ PI 1) into PI 31.289 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 31.290 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 31.290 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 31.290 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.290 * [taylor]: Taking taylor expansion of 1/2 in n 31.290 * [backup-simplify]: Simplify 1/2 into 1/2 31.290 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.290 * [taylor]: Taking taylor expansion of k in n 31.290 * [backup-simplify]: Simplify k into k 31.290 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.290 * [taylor]: Taking taylor expansion of 1/2 in n 31.290 * [backup-simplify]: Simplify 1/2 into 1/2 31.291 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.291 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.291 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 31.292 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 31.293 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 31.294 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 31.295 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 31.296 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 31.298 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 31.299 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 31.299 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 31.299 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 31.299 * [taylor]: Taking taylor expansion of +nan.0 in n 31.299 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.299 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 31.299 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 31.299 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 31.299 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 31.299 * [taylor]: Taking taylor expansion of -2 in n 31.299 * [backup-simplify]: Simplify -2 into -2 31.299 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.299 * [taylor]: Taking taylor expansion of PI in n 31.299 * [backup-simplify]: Simplify PI into PI 31.299 * [taylor]: Taking taylor expansion of n in n 31.299 * [backup-simplify]: Simplify 0 into 0 31.299 * [backup-simplify]: Simplify 1 into 1 31.299 * [backup-simplify]: Simplify (/ PI 1) into PI 31.300 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 31.300 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 31.300 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 31.300 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.300 * [taylor]: Taking taylor expansion of 1/2 in n 31.300 * [backup-simplify]: Simplify 1/2 into 1/2 31.300 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.300 * [taylor]: Taking taylor expansion of k in n 31.300 * [backup-simplify]: Simplify k into k 31.300 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.300 * [taylor]: Taking taylor expansion of 1/2 in n 31.300 * [backup-simplify]: Simplify 1/2 into 1/2 31.301 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.301 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.301 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 31.302 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 31.303 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 31.304 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 31.305 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 31.305 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 31.306 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.306 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 31.307 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 31.307 * [backup-simplify]: Simplify (+ 0 0) into 0 31.308 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 31.308 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 31.309 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 31.310 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 31.311 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 31.312 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 31.312 * [backup-simplify]: Simplify 0 into 0 31.313 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 31.315 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 31.316 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 31.316 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 31.316 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 31.316 * [taylor]: Taking taylor expansion of +nan.0 in n 31.316 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.316 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 31.316 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 31.316 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 31.316 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 31.316 * [taylor]: Taking taylor expansion of -2 in n 31.316 * [backup-simplify]: Simplify -2 into -2 31.316 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.316 * [taylor]: Taking taylor expansion of PI in n 31.317 * [backup-simplify]: Simplify PI into PI 31.317 * [taylor]: Taking taylor expansion of n in n 31.317 * [backup-simplify]: Simplify 0 into 0 31.317 * [backup-simplify]: Simplify 1 into 1 31.317 * [backup-simplify]: Simplify (/ PI 1) into PI 31.317 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 31.318 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 31.318 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 31.318 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.318 * [taylor]: Taking taylor expansion of 1/2 in n 31.318 * [backup-simplify]: Simplify 1/2 into 1/2 31.318 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.318 * [taylor]: Taking taylor expansion of k in n 31.318 * [backup-simplify]: Simplify k into k 31.318 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.318 * [taylor]: Taking taylor expansion of 1/2 in n 31.318 * [backup-simplify]: Simplify 1/2 into 1/2 31.319 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.319 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.319 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 31.320 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 31.321 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 31.322 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 31.324 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 31.325 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 31.328 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 31.329 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2) 31.329 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 31.329 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 31.329 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 31.329 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 31.329 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 31.329 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 31.329 * [taylor]: Taking taylor expansion of 1/2 in k 31.329 * [backup-simplify]: Simplify 1/2 into 1/2 31.329 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 31.329 * [taylor]: Taking taylor expansion of 1/2 in k 31.329 * [backup-simplify]: Simplify 1/2 into 1/2 31.329 * [taylor]: Taking taylor expansion of k in k 31.329 * [backup-simplify]: Simplify 0 into 0 31.329 * [backup-simplify]: Simplify 1 into 1 31.329 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 31.329 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 31.329 * [taylor]: Taking taylor expansion of 2 in k 31.329 * [backup-simplify]: Simplify 2 into 2 31.329 * [taylor]: Taking taylor expansion of (* n PI) in k 31.329 * [taylor]: Taking taylor expansion of n in k 31.329 * [backup-simplify]: Simplify n into n 31.329 * [taylor]: Taking taylor expansion of PI in k 31.329 * [backup-simplify]: Simplify PI into PI 31.329 * [backup-simplify]: Simplify (* n PI) into (* n PI) 31.329 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 31.330 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 31.330 * [backup-simplify]: Simplify (* 1/2 0) into 0 31.330 * [backup-simplify]: Simplify (- 0) into 0 31.331 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 31.331 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 31.331 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 31.331 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 31.331 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 31.331 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 31.331 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 31.331 * [taylor]: Taking taylor expansion of 1/2 in n 31.331 * [backup-simplify]: Simplify 1/2 into 1/2 31.331 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 31.331 * [taylor]: Taking taylor expansion of 1/2 in n 31.331 * [backup-simplify]: Simplify 1/2 into 1/2 31.331 * [taylor]: Taking taylor expansion of k in n 31.331 * [backup-simplify]: Simplify k into k 31.331 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 31.331 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 31.331 * [taylor]: Taking taylor expansion of 2 in n 31.331 * [backup-simplify]: Simplify 2 into 2 31.331 * [taylor]: Taking taylor expansion of (* n PI) in n 31.331 * [taylor]: Taking taylor expansion of n in n 31.331 * [backup-simplify]: Simplify 0 into 0 31.331 * [backup-simplify]: Simplify 1 into 1 31.331 * [taylor]: Taking taylor expansion of PI in n 31.331 * [backup-simplify]: Simplify PI into PI 31.332 * [backup-simplify]: Simplify (* 0 PI) into 0 31.332 * [backup-simplify]: Simplify (* 2 0) into 0 31.334 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 31.335 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 31.336 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.336 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 31.336 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 31.336 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 31.338 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 31.339 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 31.340 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 31.340 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 31.340 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 31.341 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 31.341 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 31.341 * [taylor]: Taking taylor expansion of 1/2 in n 31.341 * [backup-simplify]: Simplify 1/2 into 1/2 31.341 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 31.341 * [taylor]: Taking taylor expansion of 1/2 in n 31.341 * [backup-simplify]: Simplify 1/2 into 1/2 31.341 * [taylor]: Taking taylor expansion of k in n 31.341 * [backup-simplify]: Simplify k into k 31.341 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 31.341 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 31.341 * [taylor]: Taking taylor expansion of 2 in n 31.341 * [backup-simplify]: Simplify 2 into 2 31.341 * [taylor]: Taking taylor expansion of (* n PI) in n 31.341 * [taylor]: Taking taylor expansion of n in n 31.341 * [backup-simplify]: Simplify 0 into 0 31.341 * [backup-simplify]: Simplify 1 into 1 31.341 * [taylor]: Taking taylor expansion of PI in n 31.341 * [backup-simplify]: Simplify PI into PI 31.341 * [backup-simplify]: Simplify (* 0 PI) into 0 31.342 * [backup-simplify]: Simplify (* 2 0) into 0 31.344 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 31.346 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 31.347 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.347 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 31.347 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 31.347 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 31.348 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 31.349 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 31.351 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 31.351 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 31.351 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 31.351 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 31.351 * [taylor]: Taking taylor expansion of 1/2 in k 31.351 * [backup-simplify]: Simplify 1/2 into 1/2 31.351 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 31.351 * [taylor]: Taking taylor expansion of 1/2 in k 31.351 * [backup-simplify]: Simplify 1/2 into 1/2 31.351 * [taylor]: Taking taylor expansion of k in k 31.351 * [backup-simplify]: Simplify 0 into 0 31.351 * [backup-simplify]: Simplify 1 into 1 31.351 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 31.351 * [taylor]: Taking taylor expansion of (log n) in k 31.351 * [taylor]: Taking taylor expansion of n in k 31.351 * [backup-simplify]: Simplify n into n 31.351 * [backup-simplify]: Simplify (log n) into (log n) 31.351 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 31.351 * [taylor]: Taking taylor expansion of (* 2 PI) in k 31.351 * [taylor]: Taking taylor expansion of 2 in k 31.351 * [backup-simplify]: Simplify 2 into 2 31.351 * [taylor]: Taking taylor expansion of PI in k 31.351 * [backup-simplify]: Simplify PI into PI 31.352 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 31.353 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.353 * [backup-simplify]: Simplify (* 1/2 0) into 0 31.354 * [backup-simplify]: Simplify (- 0) into 0 31.354 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 31.355 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 31.360 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 31.361 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 31.362 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 31.364 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 31.365 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 31.367 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 31.367 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 31.368 * [backup-simplify]: Simplify (- 0) into 0 31.368 * [backup-simplify]: Simplify (+ 0 0) into 0 31.370 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 31.371 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 31.373 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 31.373 * [taylor]: Taking taylor expansion of 0 in k 31.373 * [backup-simplify]: Simplify 0 into 0 31.373 * [backup-simplify]: Simplify 0 into 0 31.374 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 31.375 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 31.376 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 31.377 * [backup-simplify]: Simplify (+ 0 0) into 0 31.378 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 31.378 * [backup-simplify]: Simplify (- 1/2) into -1/2 31.378 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 31.380 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 31.381 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 31.383 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 31.384 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 31.385 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 31.387 * [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 31.387 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 31.388 * [backup-simplify]: Simplify (- 0) into 0 31.388 * [backup-simplify]: Simplify (+ 0 0) into 0 31.389 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 31.390 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 31.391 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 31.391 * [taylor]: Taking taylor expansion of 0 in k 31.391 * [backup-simplify]: Simplify 0 into 0 31.391 * [backup-simplify]: Simplify 0 into 0 31.391 * [backup-simplify]: Simplify 0 into 0 31.392 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 31.393 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 31.395 * [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 31.395 * [backup-simplify]: Simplify (+ 0 0) into 0 31.396 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 31.396 * [backup-simplify]: Simplify (- 0) into 0 31.396 * [backup-simplify]: Simplify (+ 0 0) into 0 31.397 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 31.400 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 31.403 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 31.409 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 31.409 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 31.409 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 31.409 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 31.409 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 31.409 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 31.409 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 31.409 * [taylor]: Taking taylor expansion of 1/2 in k 31.409 * [backup-simplify]: Simplify 1/2 into 1/2 31.409 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 31.409 * [taylor]: Taking taylor expansion of 1/2 in k 31.409 * [backup-simplify]: Simplify 1/2 into 1/2 31.409 * [taylor]: Taking taylor expansion of (/ 1 k) in k 31.409 * [taylor]: Taking taylor expansion of k in k 31.410 * [backup-simplify]: Simplify 0 into 0 31.410 * [backup-simplify]: Simplify 1 into 1 31.410 * [backup-simplify]: Simplify (/ 1 1) into 1 31.410 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 31.410 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 31.410 * [taylor]: Taking taylor expansion of 2 in k 31.410 * [backup-simplify]: Simplify 2 into 2 31.410 * [taylor]: Taking taylor expansion of (/ PI n) in k 31.410 * [taylor]: Taking taylor expansion of PI in k 31.410 * [backup-simplify]: Simplify PI into PI 31.410 * [taylor]: Taking taylor expansion of n in k 31.410 * [backup-simplify]: Simplify n into n 31.410 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 31.410 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 31.410 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 31.410 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 31.411 * [backup-simplify]: Simplify (- 1/2) into -1/2 31.411 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 31.411 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 31.411 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 31.411 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 31.411 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 31.411 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 31.411 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 31.411 * [taylor]: Taking taylor expansion of 1/2 in n 31.411 * [backup-simplify]: Simplify 1/2 into 1/2 31.411 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.412 * [taylor]: Taking taylor expansion of 1/2 in n 31.412 * [backup-simplify]: Simplify 1/2 into 1/2 31.412 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.412 * [taylor]: Taking taylor expansion of k in n 31.412 * [backup-simplify]: Simplify k into k 31.412 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.412 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 31.412 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 31.412 * [taylor]: Taking taylor expansion of 2 in n 31.412 * [backup-simplify]: Simplify 2 into 2 31.412 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.412 * [taylor]: Taking taylor expansion of PI in n 31.412 * [backup-simplify]: Simplify PI into PI 31.412 * [taylor]: Taking taylor expansion of n in n 31.412 * [backup-simplify]: Simplify 0 into 0 31.412 * [backup-simplify]: Simplify 1 into 1 31.412 * [backup-simplify]: Simplify (/ PI 1) into PI 31.413 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 31.414 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.414 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.414 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 31.414 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 31.416 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.417 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 31.419 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 31.419 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 31.419 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 31.419 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 31.419 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 31.419 * [taylor]: Taking taylor expansion of 1/2 in n 31.419 * [backup-simplify]: Simplify 1/2 into 1/2 31.419 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.420 * [taylor]: Taking taylor expansion of 1/2 in n 31.420 * [backup-simplify]: Simplify 1/2 into 1/2 31.420 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.420 * [taylor]: Taking taylor expansion of k in n 31.420 * [backup-simplify]: Simplify k into k 31.420 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.420 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 31.420 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 31.420 * [taylor]: Taking taylor expansion of 2 in n 31.420 * [backup-simplify]: Simplify 2 into 2 31.420 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.420 * [taylor]: Taking taylor expansion of PI in n 31.420 * [backup-simplify]: Simplify PI into PI 31.420 * [taylor]: Taking taylor expansion of n in n 31.420 * [backup-simplify]: Simplify 0 into 0 31.420 * [backup-simplify]: Simplify 1 into 1 31.421 * [backup-simplify]: Simplify (/ PI 1) into PI 31.422 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 31.423 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.423 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.423 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 31.424 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 31.425 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.426 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 31.428 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 31.428 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 31.428 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 31.428 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 31.428 * [taylor]: Taking taylor expansion of 1/2 in k 31.428 * [backup-simplify]: Simplify 1/2 into 1/2 31.428 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 31.428 * [taylor]: Taking taylor expansion of 1/2 in k 31.428 * [backup-simplify]: Simplify 1/2 into 1/2 31.428 * [taylor]: Taking taylor expansion of (/ 1 k) in k 31.428 * [taylor]: Taking taylor expansion of k in k 31.428 * [backup-simplify]: Simplify 0 into 0 31.428 * [backup-simplify]: Simplify 1 into 1 31.429 * [backup-simplify]: Simplify (/ 1 1) into 1 31.429 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 31.429 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 31.429 * [taylor]: Taking taylor expansion of (* 2 PI) in k 31.429 * [taylor]: Taking taylor expansion of 2 in k 31.429 * [backup-simplify]: Simplify 2 into 2 31.429 * [taylor]: Taking taylor expansion of PI in k 31.429 * [backup-simplify]: Simplify PI into PI 31.429 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 31.430 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.431 * [taylor]: Taking taylor expansion of (log n) in k 31.431 * [taylor]: Taking taylor expansion of n in k 31.431 * [backup-simplify]: Simplify n into n 31.431 * [backup-simplify]: Simplify (log n) into (log n) 31.431 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 31.431 * [backup-simplify]: Simplify (- 1/2) into -1/2 31.432 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 31.432 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 31.433 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 31.434 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 31.435 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 31.437 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 31.438 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 31.439 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 31.440 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 31.440 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 31.440 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 31.440 * [backup-simplify]: Simplify (- 0) into 0 31.441 * [backup-simplify]: Simplify (+ 0 0) into 0 31.442 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.442 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 31.443 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 31.444 * [taylor]: Taking taylor expansion of 0 in k 31.444 * [backup-simplify]: Simplify 0 into 0 31.444 * [backup-simplify]: Simplify 0 into 0 31.444 * [backup-simplify]: Simplify 0 into 0 31.444 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 31.445 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 31.447 * [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 31.447 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 31.448 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 31.448 * [backup-simplify]: Simplify (- 0) into 0 31.448 * [backup-simplify]: Simplify (+ 0 0) into 0 31.449 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.450 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 31.451 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 31.452 * [taylor]: Taking taylor expansion of 0 in k 31.452 * [backup-simplify]: Simplify 0 into 0 31.452 * [backup-simplify]: Simplify 0 into 0 31.452 * [backup-simplify]: Simplify 0 into 0 31.452 * [backup-simplify]: Simplify 0 into 0 31.452 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 31.453 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 31.457 * [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 31.457 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 31.458 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 31.458 * [backup-simplify]: Simplify (- 0) into 0 31.458 * [backup-simplify]: Simplify (+ 0 0) into 0 31.459 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.460 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 31.462 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 31.462 * [taylor]: Taking taylor expansion of 0 in k 31.462 * [backup-simplify]: Simplify 0 into 0 31.462 * [backup-simplify]: Simplify 0 into 0 31.463 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 31.463 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 31.463 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 31.463 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 31.463 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 31.463 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 31.463 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 31.463 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 31.463 * [taylor]: Taking taylor expansion of 1/2 in k 31.463 * [backup-simplify]: Simplify 1/2 into 1/2 31.463 * [taylor]: Taking taylor expansion of (/ 1 k) in k 31.463 * [taylor]: Taking taylor expansion of k in k 31.463 * [backup-simplify]: Simplify 0 into 0 31.463 * [backup-simplify]: Simplify 1 into 1 31.463 * [backup-simplify]: Simplify (/ 1 1) into 1 31.463 * [taylor]: Taking taylor expansion of 1/2 in k 31.463 * [backup-simplify]: Simplify 1/2 into 1/2 31.463 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 31.463 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 31.463 * [taylor]: Taking taylor expansion of -2 in k 31.463 * [backup-simplify]: Simplify -2 into -2 31.463 * [taylor]: Taking taylor expansion of (/ PI n) in k 31.463 * [taylor]: Taking taylor expansion of PI in k 31.463 * [backup-simplify]: Simplify PI into PI 31.463 * [taylor]: Taking taylor expansion of n in k 31.464 * [backup-simplify]: Simplify n into n 31.464 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 31.464 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 31.464 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 31.464 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 31.464 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 31.464 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 31.464 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 31.464 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 31.464 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 31.464 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 31.464 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 31.464 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.465 * [taylor]: Taking taylor expansion of 1/2 in n 31.465 * [backup-simplify]: Simplify 1/2 into 1/2 31.465 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.465 * [taylor]: Taking taylor expansion of k in n 31.465 * [backup-simplify]: Simplify k into k 31.465 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.465 * [taylor]: Taking taylor expansion of 1/2 in n 31.465 * [backup-simplify]: Simplify 1/2 into 1/2 31.465 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 31.465 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 31.465 * [taylor]: Taking taylor expansion of -2 in n 31.465 * [backup-simplify]: Simplify -2 into -2 31.465 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.465 * [taylor]: Taking taylor expansion of PI in n 31.465 * [backup-simplify]: Simplify PI into PI 31.465 * [taylor]: Taking taylor expansion of n in n 31.465 * [backup-simplify]: Simplify 0 into 0 31.465 * [backup-simplify]: Simplify 1 into 1 31.465 * [backup-simplify]: Simplify (/ PI 1) into PI 31.465 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 31.468 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 31.468 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.468 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 31.470 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.470 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 31.471 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 31.471 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 31.471 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 31.471 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 31.471 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 31.471 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.471 * [taylor]: Taking taylor expansion of 1/2 in n 31.471 * [backup-simplify]: Simplify 1/2 into 1/2 31.471 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.471 * [taylor]: Taking taylor expansion of k in n 31.471 * [backup-simplify]: Simplify k into k 31.472 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.472 * [taylor]: Taking taylor expansion of 1/2 in n 31.472 * [backup-simplify]: Simplify 1/2 into 1/2 31.472 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 31.472 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 31.472 * [taylor]: Taking taylor expansion of -2 in n 31.472 * [backup-simplify]: Simplify -2 into -2 31.472 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.472 * [taylor]: Taking taylor expansion of PI in n 31.472 * [backup-simplify]: Simplify PI into PI 31.472 * [taylor]: Taking taylor expansion of n in n 31.472 * [backup-simplify]: Simplify 0 into 0 31.472 * [backup-simplify]: Simplify 1 into 1 31.472 * [backup-simplify]: Simplify (/ PI 1) into PI 31.473 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 31.474 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 31.474 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.474 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 31.475 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.477 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 31.478 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 31.478 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 31.478 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 31.478 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 31.478 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 31.478 * [taylor]: Taking taylor expansion of 1/2 in k 31.478 * [backup-simplify]: Simplify 1/2 into 1/2 31.478 * [taylor]: Taking taylor expansion of (/ 1 k) in k 31.478 * [taylor]: Taking taylor expansion of k in k 31.478 * [backup-simplify]: Simplify 0 into 0 31.478 * [backup-simplify]: Simplify 1 into 1 31.478 * [backup-simplify]: Simplify (/ 1 1) into 1 31.479 * [taylor]: Taking taylor expansion of 1/2 in k 31.479 * [backup-simplify]: Simplify 1/2 into 1/2 31.479 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 31.479 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 31.479 * [taylor]: Taking taylor expansion of (* -2 PI) in k 31.479 * [taylor]: Taking taylor expansion of -2 in k 31.479 * [backup-simplify]: Simplify -2 into -2 31.479 * [taylor]: Taking taylor expansion of PI in k 31.479 * [backup-simplify]: Simplify PI into PI 31.479 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 31.480 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 31.480 * [taylor]: Taking taylor expansion of (log n) in k 31.480 * [taylor]: Taking taylor expansion of n in k 31.480 * [backup-simplify]: Simplify n into n 31.480 * [backup-simplify]: Simplify (log n) into (log n) 31.481 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 31.481 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 31.481 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 31.482 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 31.484 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 31.485 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 31.486 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 31.487 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 31.488 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 31.490 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 31.490 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 31.490 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 31.491 * [backup-simplify]: Simplify (+ 0 0) into 0 31.492 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.494 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 31.496 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 31.496 * [taylor]: Taking taylor expansion of 0 in k 31.496 * [backup-simplify]: Simplify 0 into 0 31.496 * [backup-simplify]: Simplify 0 into 0 31.496 * [backup-simplify]: Simplify 0 into 0 31.497 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 31.498 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 31.500 * [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 31.501 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 31.501 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 31.501 * [backup-simplify]: Simplify (+ 0 0) into 0 31.502 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.503 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 31.505 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 31.505 * [taylor]: Taking taylor expansion of 0 in k 31.505 * [backup-simplify]: Simplify 0 into 0 31.505 * [backup-simplify]: Simplify 0 into 0 31.505 * [backup-simplify]: Simplify 0 into 0 31.505 * [backup-simplify]: Simplify 0 into 0 31.506 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 31.507 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 31.510 * [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 31.510 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 31.511 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 31.512 * [backup-simplify]: Simplify (+ 0 0) into 0 31.513 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.514 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 31.516 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 31.516 * [taylor]: Taking taylor expansion of 0 in k 31.517 * [backup-simplify]: Simplify 0 into 0 31.517 * [backup-simplify]: Simplify 0 into 0 31.518 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 31.518 * * * [progress]: simplifying candidates 31.518 * * * * [progress]: [ 1 / 3542 ] simplifiying candidate # 31.518 * * * * [progress]: [ 2 / 3542 ] simplifiying candidate # 31.518 * * * * [progress]: [ 3 / 3542 ] simplifiying candidate # 31.519 * * * * [progress]: [ 4 / 3542 ] simplifiying candidate # 31.519 * * * * [progress]: [ 5 / 3542 ] simplifiying candidate # 31.519 * * * * [progress]: [ 6 / 3542 ] simplifiying candidate # 31.519 * * * * [progress]: [ 7 / 3542 ] simplifiying candidate # 31.519 * * * * [progress]: [ 8 / 3542 ] simplifiying candidate # 31.519 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[progress]: [ 39 / 3542 ] simplifiying candidate # 31.521 * * * * [progress]: [ 40 / 3542 ] simplifiying candidate # 31.522 * * * * [progress]: [ 41 / 3542 ] simplifiying candidate # 31.522 * * * * [progress]: [ 42 / 3542 ] simplifiying candidate # 31.522 * * * * [progress]: [ 43 / 3542 ] simplifiying candidate # 31.522 * * * * [progress]: [ 44 / 3542 ] simplifiying candidate # 31.522 * * * * [progress]: [ 45 / 3542 ] simplifiying candidate # 31.522 * * * * [progress]: [ 46 / 3542 ] simplifiying candidate # 31.522 * * * * [progress]: [ 47 / 3542 ] simplifiying candidate # 31.522 * * * * [progress]: [ 48 / 3542 ] simplifiying candidate #real (real->posit16 (/ 1 (sqrt k)))) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))> 31.522 * * * * [progress]: [ 49 / 3542 ] simplifiying candidate # 31.522 * * * * [progress]: [ 50 / 3542 ] simplifiying candidate # 31.522 * * * * [progress]: [ 51 / 3542 ] simplifiying candidate # 31.522 * * * * [progress]: [ 52 / 3542 ] simplifiying candidate # 31.522 * 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[progress]: [ 68 / 3542 ] simplifiying candidate #real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))))))> 31.524 * * * * [progress]: [ 69 / 3542 ] simplifiying candidate # 31.524 * * * * [progress]: [ 70 / 3542 ] simplifiying candidate # 31.524 * * * * [progress]: [ 71 / 3542 ] simplifiying candidate # 31.524 * * * * [progress]: [ 72 / 3542 ] simplifiying candidate # 31.524 * * * * [progress]: [ 73 / 3542 ] simplifiying candidate # 31.524 * * * * [progress]: [ 74 / 3542 ] simplifiying candidate # 31.524 * * * * [progress]: [ 75 / 3542 ] simplifiying candidate # 31.524 * * * * [progress]: [ 76 / 3542 ] simplifiying candidate # 31.524 * * * * [progress]: [ 77 / 3542 ] simplifiying candidate # 31.524 * * * * [progress]: [ 78 / 3542 ] simplifiying candidate # 31.524 * * * * [progress]: [ 79 / 3542 ] simplifiying candidate # 31.525 * * * * [progress]: [ 80 / 3542 ] simplifiying candidate # 31.525 * * * * [progress]: [ 81 / 3542 ] simplifiying candidate # 31.525 * * * * [progress]: [ 82 / 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[progress]: [ 3526 / 3542 ] simplifiying candidate # 31.817 * * * * [progress]: [ 3527 / 3542 ] simplifiying candidate # 31.818 * * * * [progress]: [ 3528 / 3542 ] simplifiying candidate # 31.818 * * * * [progress]: [ 3529 / 3542 ] simplifiying candidate # 31.818 * * * * [progress]: [ 3530 / 3542 ] simplifiying candidate #real (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))))> 31.818 * * * * [progress]: [ 3531 / 3542 ] simplifiying candidate # 31.818 * * * * [progress]: [ 3532 / 3542 ] simplifiying candidate # 31.818 * * * * [progress]: [ 3533 / 3542 ] simplifiying candidate # 31.818 * * * * [progress]: [ 3534 / 3542 ] simplifiying candidate # 31.818 * * * * [progress]: [ 3535 / 3542 ] simplifiying candidate # 31.818 * * * * [progress]: [ 3536 / 3542 ] simplifiying candidate # 31.818 * * * * [progress]: [ 3537 / 3542 ] simplifiying candidate # 31.818 * * * * [progress]: [ 3538 / 3542 ] simplifiying candidate # 31.818 * * * * [progress]: [ 3539 / 3542 ] simplifiying candidate # 31.818 * * * * [progress]: [ 3540 / 3542 ] simplifiying candidate # 31.819 * * * * [progress]: [ 3541 / 3542 ] simplifiying candidate # 31.819 * * * * [progress]: [ 3542 / 3542 ] simplifiying candidate # 31.979 * [simplify]: Simplifying: (expm1 (/ 1 (sqrt k))) (log1p (/ 1 (sqrt k))) (- 1/2) (- 1) (- (/ 1 2)) (- (log (sqrt k))) (- 0 (log (sqrt k))) (- (log 1) (log (sqrt k))) (log (/ 1 (sqrt k))) (exp (/ 1 (sqrt k))) (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k))) (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))) (- 1) (- (sqrt k)) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1) (cbrt (sqrt k))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1) (sqrt (cbrt k))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k))) (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (/ (cbrt 1) (sqrt k)) (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k))) (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sqrt k)) (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1) (cbrt (sqrt k))) (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1) (sqrt (cbrt k))) (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt 1)) (/ (sqrt 1) (sqrt k)) (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) 1) (/ (sqrt 1) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) (/ 1 1) (/ 1 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1 (sqrt (sqrt k))) (/ 1 1) (/ (sqrt k) (cbrt 1)) (/ (sqrt k) (sqrt 1)) (/ (sqrt k) 1) (real->posit16 (/ 1 (sqrt k))) (expm1 (* (* n 2) PI)) (log1p (* (* n 2) PI)) (* (* n 2) PI) (* (* n 2) PI) (+ (+ (log n) (log 2)) (log PI)) (+ (log (* n 2)) (log PI)) (log (* (* n 2) PI)) (exp (* (* n 2) PI)) (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI)) (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI)) (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI)) (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI)) (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI)) (* (* n 2) (* (cbrt PI) (cbrt PI))) (* (* n 2) (sqrt PI)) (* (* n 2) 1) (* 2 PI) (real->posit16 (* (* n 2) PI)) (expm1 (/ (/ 1 (sqrt k)) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))) (log1p (/ (/ 1 (sqrt k)) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))) (- (- (log (sqrt k))) (- (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2))))) (- (- (log (sqrt k))) (- (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2))))) (- (- (log (sqrt k))) (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))))) (- (- (log (sqrt k))) (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))))) (- (- (log (sqrt k))) (- (log (pow (* (* n 2) 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1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 32.184 * * [simplify]: iteration 0: 4156 enodes 34.261 * * [simplify]: iteration complete: 5001 enodes 34.265 * * [simplify]: Extracting #0: cost 2908 inf + 0 34.281 * * [simplify]: Extracting #1: cost 3398 inf + 1 34.299 * * [simplify]: Extracting #2: cost 3570 inf + 1090 34.321 * * [simplify]: Extracting #3: cost 3540 inf + 18390 34.360 * * [simplify]: Extracting #4: cost 3276 inf + 120727 34.488 * * [simplify]: Extracting #5: cost 2478 inf + 632723 34.695 * * [simplify]: Extracting #6: cost 1517 inf + 1351569 34.990 * * [simplify]: Extracting #7: cost 680 inf + 2071837 35.335 * * [simplify]: Extracting #8: cost 274 inf + 2438713 35.684 * * [simplify]: Extracting #9: cost 38 inf + 2670024 36.115 * * [simplify]: Extracting #10: cost 21 inf + 2687755 36.556 * * [simplify]: Extracting #11: cost 13 inf + 2689430 36.933 * * [simplify]: Extracting #12: cost 10 inf + 2690894 37.361 * * [simplify]: Extracting #13: cost 6 inf + 2693843 37.716 * * [simplify]: Extracting #14: cost 3 inf + 2697168 38.102 * * [simplify]: Extracting #15: cost 1 inf + 2699418 38.446 * * [simplify]: Extracting #16: cost 0 inf + 2700558 38.842 * * [simplify]: Extracting #17: cost 0 inf + 2700493 39.297 * [simplify]: Simplified to: (expm1 (/ 1 (sqrt k))) (log1p (/ 1 (sqrt k))) (- 1/2) (- 1) (- (/ 1 2)) (- (log (sqrt k))) (- (log (sqrt k))) (- (log (sqrt k))) (- (log (sqrt k))) (exp (/ 1 (sqrt k))) (/ (/ 1 k) (sqrt k)) (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k))) (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))) (- 1) (- (sqrt k)) (* (/ (cbrt 1) (cbrt (sqrt k))) (/ (cbrt 1) (cbrt (sqrt k)))) (/ (cbrt 1) (cbrt (sqrt k))) (/ (* (cbrt 1) (cbrt 1)) (fabs (cbrt k))) (/ (cbrt 1) (sqrt (cbrt k))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k))) (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (/ (cbrt 1) (sqrt k)) (/ (* 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(* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (- (fma +nan.0 (* k k) (+ (- +nan.0) (- (* (- +nan.0) k))))) (- (fma +nan.0 (/ 1 (* k k)) (- (fma +nan.0 (/ 1 k) (* (- +nan.0) (/ 1 (* (* k k) k))))))) (- (fma +nan.0 (/ 1 (* k k)) (- (fma +nan.0 (/ 1 k) (- +nan.0))))) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (- (fma +nan.0 (* (sqrt 2) (* (* n PI) k)) (- (fma +nan.0 (* (* (sqrt 2) n) PI) (- (fma +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* (* n PI) k))) (- (fma +nan.0 (* (* (sqrt 2) n) (* PI (* (log n) k))) (* (- +nan.0) (* (* (sqrt 2) (* n n)) (* PI PI))))))))))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (* (* k k) k)) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) k) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (* k k)))))))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* k k)) (* +nan.0 (- (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) (- (fma 1/4 (* (* (log (* 2 PI)) (exp (* 1/2 (log (* (* n 2) PI))))) (* (log n) (* k k))) (fma 1/8 (* (exp (* 1/2 (log (* (* n 2) PI)))) (* (* (log n) (log n)) (* k k))) (+ (exp (* 1/2 (log (* (* n 2) PI)))) (* (* 1/8 (* (log (* 2 PI)) (log (* 2 PI)))) (* (exp (* 1/2 (log (* (* n 2) PI)))) (* k k)))))) (* 1/2 (+ (* (exp (* 1/2 (log (* (* n 2) PI)))) (* (log n) k)) (* (* (log (* 2 PI)) (exp (* 1/2 (log (* (* n 2) PI))))) k)))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 40.666 * * * [progress]: adding candidates to table 65.909 * * [progress]: iteration 4 / 4 65.909 * * * [progress]: picking best candidate 65.955 * * * * [pick]: Picked # 65.956 * * * [progress]: localizing error 66.011 * * * [progress]: generating rewritten candidates 66.011 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 1) 66.025 * * * * [progress]: [ 2 / 4 ] rewriting at (2) 66.065 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2) 66.099 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2) 66.237 * * * [progress]: generating series expansions 66.237 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 1) 66.237 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI)) 66.237 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 66.237 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 66.237 * [taylor]: Taking taylor expansion of 2 in n 66.237 * [backup-simplify]: Simplify 2 into 2 66.237 * [taylor]: Taking taylor expansion of (* n PI) in n 66.237 * [taylor]: Taking taylor expansion of n in n 66.237 * [backup-simplify]: Simplify 0 into 0 66.237 * [backup-simplify]: Simplify 1 into 1 66.237 * [taylor]: Taking taylor expansion of PI in n 66.237 * [backup-simplify]: Simplify PI into PI 66.238 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 66.238 * [taylor]: Taking taylor expansion of 2 in n 66.238 * [backup-simplify]: Simplify 2 into 2 66.238 * [taylor]: Taking taylor expansion of (* n PI) in n 66.238 * [taylor]: Taking taylor expansion of n in n 66.238 * [backup-simplify]: Simplify 0 into 0 66.238 * [backup-simplify]: Simplify 1 into 1 66.238 * [taylor]: Taking taylor expansion of PI in n 66.238 * [backup-simplify]: Simplify PI into PI 66.239 * [backup-simplify]: Simplify (* 0 PI) into 0 66.239 * [backup-simplify]: Simplify (* 2 0) into 0 66.239 * [backup-simplify]: Simplify 0 into 0 66.241 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 66.243 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 66.243 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 66.245 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 66.246 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 66.246 * [backup-simplify]: Simplify 0 into 0 66.247 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 66.248 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 66.249 * [backup-simplify]: Simplify 0 into 0 66.250 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 66.252 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 66.252 * [backup-simplify]: Simplify 0 into 0 66.253 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 66.255 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 66.255 * [backup-simplify]: Simplify 0 into 0 66.257 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 66.259 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 66.259 * [backup-simplify]: Simplify 0 into 0 66.261 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 66.282 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 66.282 * [backup-simplify]: Simplify 0 into 0 66.283 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 66.283 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n)) 66.283 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 66.283 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 66.283 * [taylor]: Taking taylor expansion of 2 in n 66.283 * [backup-simplify]: Simplify 2 into 2 66.283 * [taylor]: Taking taylor expansion of (/ PI n) in n 66.283 * [taylor]: Taking taylor expansion of PI in n 66.283 * [backup-simplify]: Simplify PI into PI 66.283 * [taylor]: Taking taylor expansion of n in n 66.283 * [backup-simplify]: Simplify 0 into 0 66.284 * [backup-simplify]: Simplify 1 into 1 66.284 * [backup-simplify]: Simplify (/ PI 1) into PI 66.284 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 66.284 * [taylor]: Taking taylor expansion of 2 in n 66.284 * [backup-simplify]: Simplify 2 into 2 66.284 * [taylor]: Taking taylor expansion of (/ PI n) in n 66.284 * [taylor]: Taking taylor expansion of PI in n 66.284 * [backup-simplify]: Simplify PI into PI 66.284 * [taylor]: Taking taylor expansion of n in n 66.284 * [backup-simplify]: Simplify 0 into 0 66.284 * [backup-simplify]: Simplify 1 into 1 66.285 * [backup-simplify]: Simplify (/ PI 1) into PI 66.285 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 66.286 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 66.287 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 66.288 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 66.288 * [backup-simplify]: Simplify 0 into 0 66.289 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 66.290 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 66.290 * [backup-simplify]: Simplify 0 into 0 66.291 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 66.293 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 66.293 * [backup-simplify]: Simplify 0 into 0 66.294 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 66.295 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 66.295 * [backup-simplify]: Simplify 0 into 0 66.297 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 66.299 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 66.299 * [backup-simplify]: Simplify 0 into 0 66.300 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 66.302 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 66.302 * [backup-simplify]: Simplify 0 into 0 66.302 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 66.302 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n)) 66.302 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 66.302 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 66.303 * [taylor]: Taking taylor expansion of -2 in n 66.303 * [backup-simplify]: Simplify -2 into -2 66.303 * [taylor]: Taking taylor expansion of (/ PI n) in n 66.303 * [taylor]: Taking taylor expansion of PI in n 66.303 * [backup-simplify]: Simplify PI into PI 66.303 * [taylor]: Taking taylor expansion of n in n 66.303 * [backup-simplify]: Simplify 0 into 0 66.303 * [backup-simplify]: Simplify 1 into 1 66.303 * [backup-simplify]: Simplify (/ PI 1) into PI 66.303 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 66.303 * [taylor]: Taking taylor expansion of -2 in n 66.303 * [backup-simplify]: Simplify -2 into -2 66.303 * [taylor]: Taking taylor expansion of (/ PI n) in n 66.303 * [taylor]: Taking taylor expansion of PI in n 66.303 * [backup-simplify]: Simplify PI into PI 66.303 * [taylor]: Taking taylor expansion of n in n 66.303 * [backup-simplify]: Simplify 0 into 0 66.303 * [backup-simplify]: Simplify 1 into 1 66.304 * [backup-simplify]: Simplify (/ PI 1) into PI 66.305 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 66.305 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 66.306 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 66.307 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 66.307 * [backup-simplify]: Simplify 0 into 0 66.308 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 66.309 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 66.309 * [backup-simplify]: Simplify 0 into 0 66.311 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 66.312 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 66.312 * [backup-simplify]: Simplify 0 into 0 66.313 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 66.314 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 66.314 * [backup-simplify]: Simplify 0 into 0 66.316 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 66.317 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 66.317 * [backup-simplify]: Simplify 0 into 0 66.318 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 66.320 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 66.320 * [backup-simplify]: Simplify 0 into 0 66.321 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 66.321 * * * * [progress]: [ 2 / 4 ] generating series at (2) 66.322 * [backup-simplify]: Simplify (/ (pow k (- 1/2)) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) into (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) 66.322 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in (k n) around 0 66.322 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 66.322 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 66.322 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 66.322 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 66.322 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 66.322 * [taylor]: Taking taylor expansion of 1/2 in n 66.322 * [backup-simplify]: Simplify 1/2 into 1/2 66.322 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 66.322 * [taylor]: Taking taylor expansion of 1/2 in n 66.322 * [backup-simplify]: Simplify 1/2 into 1/2 66.322 * [taylor]: Taking taylor expansion of k in n 66.322 * [backup-simplify]: Simplify k into k 66.322 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 66.322 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 66.322 * [taylor]: Taking taylor expansion of 2 in n 66.322 * [backup-simplify]: Simplify 2 into 2 66.322 * [taylor]: Taking taylor expansion of (* n PI) in n 66.322 * [taylor]: Taking taylor expansion of n in n 66.322 * [backup-simplify]: Simplify 0 into 0 66.322 * [backup-simplify]: Simplify 1 into 1 66.322 * [taylor]: Taking taylor expansion of PI in n 66.322 * [backup-simplify]: Simplify PI into PI 66.323 * [backup-simplify]: Simplify (* 0 PI) into 0 66.323 * [backup-simplify]: Simplify (* 2 0) into 0 66.325 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 66.327 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 66.328 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 66.328 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 66.328 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 66.328 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 66.329 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 66.330 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 66.332 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 66.332 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 66.332 * [taylor]: Taking taylor expansion of (/ 1 k) in n 66.332 * [taylor]: Taking taylor expansion of k in n 66.332 * [backup-simplify]: Simplify k into k 66.332 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 66.332 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 66.332 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 66.332 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 66.332 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 66.332 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 66.332 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 66.332 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 66.332 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 66.332 * [taylor]: Taking taylor expansion of 1/2 in k 66.332 * [backup-simplify]: Simplify 1/2 into 1/2 66.332 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 66.332 * [taylor]: Taking taylor expansion of 1/2 in k 66.332 * [backup-simplify]: Simplify 1/2 into 1/2 66.332 * [taylor]: Taking taylor expansion of k in k 66.332 * [backup-simplify]: Simplify 0 into 0 66.332 * [backup-simplify]: Simplify 1 into 1 66.332 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 66.333 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 66.333 * [taylor]: Taking taylor expansion of 2 in k 66.333 * [backup-simplify]: Simplify 2 into 2 66.333 * [taylor]: Taking taylor expansion of (* n PI) in k 66.333 * [taylor]: Taking taylor expansion of n in k 66.333 * [backup-simplify]: Simplify n into n 66.333 * [taylor]: Taking taylor expansion of PI in k 66.333 * [backup-simplify]: Simplify PI into PI 66.333 * [backup-simplify]: Simplify (* n PI) into (* n PI) 66.333 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 66.333 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 66.333 * [backup-simplify]: Simplify (* 1/2 0) into 0 66.334 * [backup-simplify]: Simplify (- 0) into 0 66.334 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 66.334 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 66.334 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 66.334 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 66.334 * [taylor]: Taking taylor expansion of (/ 1 k) in k 66.334 * [taylor]: Taking taylor expansion of k in k 66.334 * [backup-simplify]: Simplify 0 into 0 66.335 * [backup-simplify]: Simplify 1 into 1 66.335 * [backup-simplify]: Simplify (/ 1 1) into 1 66.335 * [backup-simplify]: Simplify (sqrt 0) into 0 66.337 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 66.337 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 66.337 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 66.337 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 66.337 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 66.337 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 66.337 * [taylor]: Taking taylor expansion of 1/2 in k 66.337 * [backup-simplify]: Simplify 1/2 into 1/2 66.337 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 66.337 * [taylor]: Taking taylor expansion of 1/2 in k 66.337 * [backup-simplify]: Simplify 1/2 into 1/2 66.337 * [taylor]: Taking taylor expansion of k in k 66.337 * [backup-simplify]: Simplify 0 into 0 66.337 * [backup-simplify]: Simplify 1 into 1 66.337 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 66.337 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 66.337 * [taylor]: Taking taylor expansion of 2 in k 66.337 * [backup-simplify]: Simplify 2 into 2 66.337 * [taylor]: Taking taylor expansion of (* n PI) in k 66.337 * [taylor]: Taking taylor expansion of n in k 66.337 * [backup-simplify]: Simplify n into n 66.337 * [taylor]: Taking taylor expansion of PI in k 66.337 * [backup-simplify]: Simplify PI into PI 66.337 * [backup-simplify]: Simplify (* n PI) into (* n PI) 66.337 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 66.337 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 66.338 * [backup-simplify]: Simplify (* 1/2 0) into 0 66.338 * [backup-simplify]: Simplify (- 0) into 0 66.339 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 66.339 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 66.339 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 66.339 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 66.339 * [taylor]: Taking taylor expansion of (/ 1 k) in k 66.339 * [taylor]: Taking taylor expansion of k in k 66.339 * [backup-simplify]: Simplify 0 into 0 66.339 * [backup-simplify]: Simplify 1 into 1 66.340 * [backup-simplify]: Simplify (/ 1 1) into 1 66.340 * [backup-simplify]: Simplify (sqrt 0) into 0 66.341 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 66.341 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0 66.341 * [taylor]: Taking taylor expansion of 0 in n 66.341 * [backup-simplify]: Simplify 0 into 0 66.342 * [backup-simplify]: Simplify 0 into 0 66.342 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 66.343 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 66.344 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 66.344 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 66.345 * [backup-simplify]: Simplify (- 1/2) into -1/2 66.345 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 66.346 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 66.346 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 66.347 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 66.347 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 66.347 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 66.347 * [taylor]: Taking taylor expansion of +nan.0 in n 66.347 * [backup-simplify]: Simplify +nan.0 into +nan.0 66.347 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 66.347 * [taylor]: Taking taylor expansion of (sqrt 2) in n 66.347 * [taylor]: Taking taylor expansion of 2 in n 66.347 * [backup-simplify]: Simplify 2 into 2 66.347 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 66.348 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 66.348 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 66.348 * [taylor]: Taking taylor expansion of (* n PI) in n 66.348 * [taylor]: Taking taylor expansion of n in n 66.348 * [backup-simplify]: Simplify 0 into 0 66.348 * [backup-simplify]: Simplify 1 into 1 66.348 * [taylor]: Taking taylor expansion of PI in n 66.348 * [backup-simplify]: Simplify PI into PI 66.349 * [backup-simplify]: Simplify (* 0 PI) into 0 66.350 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 66.350 * [backup-simplify]: Simplify (sqrt 0) into 0 66.352 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 66.353 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 66.353 * [backup-simplify]: Simplify (* +nan.0 0) into 0 66.353 * [backup-simplify]: Simplify (- 0) into 0 66.353 * [backup-simplify]: Simplify 0 into 0 66.353 * [backup-simplify]: Simplify 0 into 0 66.354 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 66.357 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 66.358 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 66.359 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 66.361 * [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 66.362 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 66.362 * [backup-simplify]: Simplify (- 0) into 0 66.363 * [backup-simplify]: Simplify (+ 0 0) into 0 66.364 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 66.365 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 66.366 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 66.366 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 66.366 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 66.366 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 66.366 * [taylor]: Taking taylor expansion of +nan.0 in n 66.366 * [backup-simplify]: Simplify +nan.0 into +nan.0 66.366 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 66.366 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 66.366 * [taylor]: Taking taylor expansion of (sqrt 2) in n 66.366 * [taylor]: Taking taylor expansion of 2 in n 66.366 * [backup-simplify]: Simplify 2 into 2 66.366 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 66.367 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 66.367 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 66.367 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 66.367 * [taylor]: Taking taylor expansion of 2 in n 66.367 * [backup-simplify]: Simplify 2 into 2 66.367 * [taylor]: Taking taylor expansion of (* n PI) in n 66.367 * [taylor]: Taking taylor expansion of n in n 66.367 * [backup-simplify]: Simplify 0 into 0 66.367 * [backup-simplify]: Simplify 1 into 1 66.367 * [taylor]: Taking taylor expansion of PI in n 66.367 * [backup-simplify]: Simplify PI into PI 66.368 * [backup-simplify]: Simplify (* 0 PI) into 0 66.368 * [backup-simplify]: Simplify (* 2 0) into 0 66.370 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 66.371 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 66.372 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 66.373 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 66.373 * [taylor]: Taking taylor expansion of (* n PI) in n 66.373 * [taylor]: Taking taylor expansion of n in n 66.373 * [backup-simplify]: Simplify 0 into 0 66.373 * [backup-simplify]: Simplify 1 into 1 66.373 * [taylor]: Taking taylor expansion of PI in n 66.373 * [backup-simplify]: Simplify PI into PI 66.373 * [backup-simplify]: Simplify (* 0 PI) into 0 66.375 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 66.375 * [backup-simplify]: Simplify (sqrt 0) into 0 66.376 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 66.376 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 66.376 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 66.376 * [taylor]: Taking taylor expansion of +nan.0 in n 66.377 * [backup-simplify]: Simplify +nan.0 into +nan.0 66.377 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 66.377 * [taylor]: Taking taylor expansion of (sqrt 2) in n 66.377 * [taylor]: Taking taylor expansion of 2 in n 66.377 * [backup-simplify]: Simplify 2 into 2 66.377 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 66.378 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 66.378 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 66.378 * [taylor]: Taking taylor expansion of (* n PI) in n 66.378 * [taylor]: Taking taylor expansion of n in n 66.378 * [backup-simplify]: Simplify 0 into 0 66.378 * [backup-simplify]: Simplify 1 into 1 66.378 * [taylor]: Taking taylor expansion of PI in n 66.378 * [backup-simplify]: Simplify PI into PI 66.378 * [backup-simplify]: Simplify (* 0 PI) into 0 66.380 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 66.380 * [backup-simplify]: Simplify (sqrt 0) into 0 66.382 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 66.383 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 66.385 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 66.387 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 66.387 * [backup-simplify]: Simplify (* +nan.0 0) into 0 66.388 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 66.388 * [backup-simplify]: Simplify (* +nan.0 0) into 0 66.389 * [backup-simplify]: Simplify (- 0) into 0 66.389 * [backup-simplify]: Simplify (+ 0 0) into 0 66.390 * [backup-simplify]: Simplify (- 0) into 0 66.390 * [backup-simplify]: Simplify 0 into 0 66.393 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 66.400 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 66.403 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 66.407 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 66.407 * [backup-simplify]: Simplify 0 into 0 66.408 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 66.413 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 66.414 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 66.415 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 66.418 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0 66.419 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 66.420 * [backup-simplify]: Simplify (- 0) into 0 66.420 * [backup-simplify]: Simplify (+ 0 0) into 0 66.421 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 66.423 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 66.425 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) 66.425 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n 66.425 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n 66.425 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 66.425 * [taylor]: Taking taylor expansion of +nan.0 in n 66.425 * [backup-simplify]: Simplify +nan.0 into +nan.0 66.425 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 66.425 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 66.425 * [taylor]: Taking taylor expansion of (sqrt 2) in n 66.425 * [taylor]: Taking taylor expansion of 2 in n 66.425 * [backup-simplify]: Simplify 2 into 2 66.426 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 66.426 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 66.426 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 66.426 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 66.426 * [taylor]: Taking taylor expansion of 2 in n 66.426 * [backup-simplify]: Simplify 2 into 2 66.426 * [taylor]: Taking taylor expansion of (* n PI) in n 66.426 * [taylor]: Taking taylor expansion of n in n 66.426 * [backup-simplify]: Simplify 0 into 0 66.426 * [backup-simplify]: Simplify 1 into 1 66.426 * [taylor]: Taking taylor expansion of PI in n 66.426 * [backup-simplify]: Simplify PI into PI 66.427 * [backup-simplify]: Simplify (* 0 PI) into 0 66.427 * [backup-simplify]: Simplify (* 2 0) into 0 66.429 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 66.437 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 66.438 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 66.438 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 66.438 * [taylor]: Taking taylor expansion of (* n PI) in n 66.438 * [taylor]: Taking taylor expansion of n in n 66.438 * [backup-simplify]: Simplify 0 into 0 66.438 * [backup-simplify]: Simplify 1 into 1 66.438 * [taylor]: Taking taylor expansion of PI in n 66.438 * [backup-simplify]: Simplify PI into PI 66.439 * [backup-simplify]: Simplify (* 0 PI) into 0 66.440 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 66.441 * [backup-simplify]: Simplify (sqrt 0) into 0 66.443 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 66.443 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n 66.443 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n 66.443 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 66.443 * [taylor]: Taking taylor expansion of +nan.0 in n 66.443 * [backup-simplify]: Simplify +nan.0 into +nan.0 66.443 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 66.443 * [taylor]: Taking taylor expansion of (sqrt 2) in n 66.443 * [taylor]: Taking taylor expansion of 2 in n 66.443 * [backup-simplify]: Simplify 2 into 2 66.443 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 66.444 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 66.444 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 66.444 * [taylor]: Taking taylor expansion of (* n PI) in n 66.444 * [taylor]: Taking taylor expansion of n in n 66.444 * [backup-simplify]: Simplify 0 into 0 66.444 * [backup-simplify]: Simplify 1 into 1 66.444 * [taylor]: Taking taylor expansion of PI in n 66.444 * [backup-simplify]: Simplify PI into PI 66.445 * [backup-simplify]: Simplify (* 0 PI) into 0 66.446 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 66.447 * [backup-simplify]: Simplify (sqrt 0) into 0 66.448 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 66.448 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n 66.448 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 66.448 * [taylor]: Taking taylor expansion of +nan.0 in n 66.448 * [backup-simplify]: Simplify +nan.0 into +nan.0 66.448 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 66.448 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 66.448 * [taylor]: Taking taylor expansion of (sqrt 2) in n 66.448 * [taylor]: Taking taylor expansion of 2 in n 66.448 * [backup-simplify]: Simplify 2 into 2 66.449 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 66.450 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 66.450 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 66.450 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 66.450 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 66.450 * [taylor]: Taking taylor expansion of 2 in n 66.450 * [backup-simplify]: Simplify 2 into 2 66.450 * [taylor]: Taking taylor expansion of (* n PI) in n 66.450 * [taylor]: Taking taylor expansion of n in n 66.450 * [backup-simplify]: Simplify 0 into 0 66.450 * [backup-simplify]: Simplify 1 into 1 66.450 * [taylor]: Taking taylor expansion of PI in n 66.450 * [backup-simplify]: Simplify PI into PI 66.450 * [backup-simplify]: Simplify (* 0 PI) into 0 66.451 * [backup-simplify]: Simplify (* 2 0) into 0 66.452 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 66.454 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 66.455 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 66.457 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 66.457 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 66.457 * [taylor]: Taking taylor expansion of (* n PI) in n 66.457 * [taylor]: Taking taylor expansion of n in n 66.457 * [backup-simplify]: Simplify 0 into 0 66.457 * [backup-simplify]: Simplify 1 into 1 66.457 * [taylor]: Taking taylor expansion of PI in n 66.457 * [backup-simplify]: Simplify PI into PI 66.457 * [backup-simplify]: Simplify (* 0 PI) into 0 66.459 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 66.459 * [backup-simplify]: Simplify (sqrt 0) into 0 66.461 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 66.462 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 66.464 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 66.466 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 66.466 * [backup-simplify]: Simplify (* +nan.0 0) into 0 66.467 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 66.467 * [backup-simplify]: Simplify (* +nan.0 0) into 0 66.469 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 66.470 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 66.472 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 66.473 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 66.474 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 66.474 * [backup-simplify]: Simplify (* +nan.0 0) into 0 66.474 * [backup-simplify]: Simplify (- 0) into 0 66.475 * [backup-simplify]: Simplify (+ 0 0) into 0 66.475 * [backup-simplify]: Simplify (- 0) into 0 66.475 * [backup-simplify]: Simplify (+ 0 0) into 0 66.475 * [backup-simplify]: Simplify (- 0) into 0 66.475 * [backup-simplify]: Simplify 0 into 0 66.476 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 66.477 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 66.478 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 66.479 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 66.480 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 66.481 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 66.486 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 66.488 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 66.491 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 66.493 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 66.499 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) 66.507 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 66.515 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 66.516 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 66.520 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 66.521 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 66.527 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 66.536 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 66.541 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 66.545 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 66.566 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 66.568 * [backup-simplify]: Simplify (/ (pow (/ 1 k) (- 1/2)) (/ 1 (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))))) into (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 66.568 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (k n) around 0 66.568 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 66.568 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 66.568 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 66.568 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 66.568 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 66.568 * [taylor]: Taking taylor expansion of 1/2 in n 66.568 * [backup-simplify]: Simplify 1/2 into 1/2 66.568 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 66.568 * [taylor]: Taking taylor expansion of 1/2 in n 66.568 * [backup-simplify]: Simplify 1/2 into 1/2 66.568 * [taylor]: Taking taylor expansion of (/ 1 k) in n 66.568 * [taylor]: Taking taylor expansion of k in n 66.568 * [backup-simplify]: Simplify k into k 66.568 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 66.568 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 66.568 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 66.568 * [taylor]: Taking taylor expansion of 2 in n 66.568 * [backup-simplify]: Simplify 2 into 2 66.568 * [taylor]: Taking taylor expansion of (/ PI n) in n 66.568 * [taylor]: Taking taylor expansion of PI in n 66.568 * [backup-simplify]: Simplify PI into PI 66.568 * [taylor]: Taking taylor expansion of n in n 66.568 * [backup-simplify]: Simplify 0 into 0 66.568 * [backup-simplify]: Simplify 1 into 1 66.569 * [backup-simplify]: Simplify (/ PI 1) into PI 66.569 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 66.570 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 66.570 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 66.570 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 66.571 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 66.572 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 66.573 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 66.574 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 66.574 * [taylor]: Taking taylor expansion of (sqrt k) in n 66.574 * [taylor]: Taking taylor expansion of k in n 66.574 * [backup-simplify]: Simplify k into k 66.574 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 66.575 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 66.575 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 66.575 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 66.575 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 66.575 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 66.575 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 66.575 * [taylor]: Taking taylor expansion of 1/2 in k 66.575 * [backup-simplify]: Simplify 1/2 into 1/2 66.575 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 66.575 * [taylor]: Taking taylor expansion of 1/2 in k 66.575 * [backup-simplify]: Simplify 1/2 into 1/2 66.575 * [taylor]: Taking taylor expansion of (/ 1 k) in k 66.575 * [taylor]: Taking taylor expansion of k in k 66.575 * [backup-simplify]: Simplify 0 into 0 66.575 * [backup-simplify]: Simplify 1 into 1 66.575 * [backup-simplify]: Simplify (/ 1 1) into 1 66.575 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 66.575 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 66.575 * [taylor]: Taking taylor expansion of 2 in k 66.575 * [backup-simplify]: Simplify 2 into 2 66.575 * [taylor]: Taking taylor expansion of (/ PI n) in k 66.575 * [taylor]: Taking taylor expansion of PI in k 66.575 * [backup-simplify]: Simplify PI into PI 66.575 * [taylor]: Taking taylor expansion of n in k 66.575 * [backup-simplify]: Simplify n into n 66.576 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 66.576 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 66.576 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 66.576 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 66.577 * [backup-simplify]: Simplify (- 1/2) into -1/2 66.577 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 66.577 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 66.577 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 66.577 * [taylor]: Taking taylor expansion of (sqrt k) in k 66.577 * [taylor]: Taking taylor expansion of k in k 66.577 * [backup-simplify]: Simplify 0 into 0 66.577 * [backup-simplify]: Simplify 1 into 1 66.578 * [backup-simplify]: Simplify (sqrt 0) into 0 66.579 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 66.579 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 66.579 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 66.579 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 66.579 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 66.579 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 66.580 * [taylor]: Taking taylor expansion of 1/2 in k 66.580 * [backup-simplify]: Simplify 1/2 into 1/2 66.580 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 66.580 * [taylor]: Taking taylor expansion of 1/2 in k 66.580 * [backup-simplify]: Simplify 1/2 into 1/2 66.580 * [taylor]: Taking taylor expansion of (/ 1 k) in k 66.580 * [taylor]: Taking taylor expansion of k in k 66.580 * [backup-simplify]: Simplify 0 into 0 66.580 * [backup-simplify]: Simplify 1 into 1 66.580 * [backup-simplify]: Simplify (/ 1 1) into 1 66.580 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 66.580 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 66.580 * [taylor]: Taking taylor expansion of 2 in k 66.580 * [backup-simplify]: Simplify 2 into 2 66.580 * [taylor]: Taking taylor expansion of (/ PI n) in k 66.580 * [taylor]: Taking taylor expansion of PI in k 66.580 * [backup-simplify]: Simplify PI into PI 66.580 * [taylor]: Taking taylor expansion of n in k 66.580 * [backup-simplify]: Simplify n into n 66.580 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 66.580 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 66.581 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 66.581 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 66.581 * [backup-simplify]: Simplify (- 1/2) into -1/2 66.582 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 66.582 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 66.582 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 66.582 * [taylor]: Taking taylor expansion of (sqrt k) in k 66.582 * [taylor]: Taking taylor expansion of k in k 66.582 * [backup-simplify]: Simplify 0 into 0 66.582 * [backup-simplify]: Simplify 1 into 1 66.583 * [backup-simplify]: Simplify (sqrt 0) into 0 66.584 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 66.584 * [backup-simplify]: Simplify (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 0) into 0 66.584 * [taylor]: Taking taylor expansion of 0 in n 66.584 * [backup-simplify]: Simplify 0 into 0 66.584 * [backup-simplify]: Simplify 0 into 0 66.585 * [backup-simplify]: Simplify (+ (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 66.585 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 66.585 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 66.585 * [taylor]: Taking taylor expansion of +nan.0 in n 66.585 * [backup-simplify]: Simplify +nan.0 into +nan.0 66.585 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 66.585 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 66.585 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 66.585 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 66.585 * [taylor]: Taking taylor expansion of 1/2 in n 66.585 * [backup-simplify]: Simplify 1/2 into 1/2 66.585 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 66.585 * [taylor]: Taking taylor expansion of 1/2 in n 66.585 * [backup-simplify]: Simplify 1/2 into 1/2 66.585 * [taylor]: Taking taylor expansion of (/ 1 k) in n 66.585 * [taylor]: Taking taylor expansion of k in n 66.585 * [backup-simplify]: Simplify k into k 66.586 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 66.586 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 66.586 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 66.586 * [taylor]: Taking taylor expansion of 2 in n 66.586 * [backup-simplify]: Simplify 2 into 2 66.586 * [taylor]: Taking taylor expansion of (/ PI n) in n 66.586 * [taylor]: Taking taylor expansion of PI in n 66.586 * [backup-simplify]: Simplify PI into PI 66.586 * [taylor]: Taking taylor expansion of n in n 66.586 * [backup-simplify]: Simplify 0 into 0 66.586 * [backup-simplify]: Simplify 1 into 1 66.586 * [backup-simplify]: Simplify (/ PI 1) into PI 66.587 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 66.588 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 66.588 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 66.588 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 66.588 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 66.590 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 66.591 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 66.592 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 66.594 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 66.596 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 66.597 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 66.597 * [backup-simplify]: Simplify 0 into 0 66.601 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 66.602 * [backup-simplify]: Simplify (+ (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 66.602 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 66.602 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 66.602 * [taylor]: Taking taylor expansion of +nan.0 in n 66.602 * [backup-simplify]: Simplify +nan.0 into +nan.0 66.602 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 66.602 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 66.602 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 66.602 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 66.602 * [taylor]: Taking taylor expansion of 1/2 in n 66.602 * [backup-simplify]: Simplify 1/2 into 1/2 66.602 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 66.602 * [taylor]: Taking taylor expansion of 1/2 in n 66.602 * [backup-simplify]: Simplify 1/2 into 1/2 66.602 * [taylor]: Taking taylor expansion of (/ 1 k) in n 66.602 * [taylor]: Taking taylor expansion of k in n 66.602 * [backup-simplify]: Simplify k into k 66.602 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 66.602 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 66.602 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 66.602 * [taylor]: Taking taylor expansion of 2 in n 66.602 * [backup-simplify]: Simplify 2 into 2 66.602 * [taylor]: Taking taylor expansion of (/ PI n) in n 66.602 * [taylor]: Taking taylor expansion of PI in n 66.602 * [backup-simplify]: Simplify PI into PI 66.602 * [taylor]: Taking taylor expansion of n in n 66.602 * [backup-simplify]: Simplify 0 into 0 66.602 * [backup-simplify]: Simplify 1 into 1 66.603 * [backup-simplify]: Simplify (/ PI 1) into PI 66.604 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 66.605 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 66.605 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 66.605 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 66.605 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 66.606 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 66.608 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 66.609 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 66.610 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 66.612 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 66.613 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 66.614 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 66.615 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 66.618 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 66.618 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 66.619 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 66.619 * [backup-simplify]: Simplify (- 0) into 0 66.619 * [backup-simplify]: Simplify (+ 0 0) into 0 66.621 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 66.622 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 66.624 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 66.626 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 66.627 * [backup-simplify]: Simplify (- 0) into 0 66.627 * [backup-simplify]: Simplify 0 into 0 66.627 * [backup-simplify]: Simplify 0 into 0 66.631 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 66.632 * [backup-simplify]: Simplify (+ (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 66.632 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 66.632 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 66.632 * [taylor]: Taking taylor expansion of +nan.0 in n 66.632 * [backup-simplify]: Simplify +nan.0 into +nan.0 66.632 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 66.632 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 66.632 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 66.632 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 66.632 * [taylor]: Taking taylor expansion of 1/2 in n 66.632 * [backup-simplify]: Simplify 1/2 into 1/2 66.632 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 66.632 * [taylor]: Taking taylor expansion of 1/2 in n 66.632 * [backup-simplify]: Simplify 1/2 into 1/2 66.632 * [taylor]: Taking taylor expansion of (/ 1 k) in n 66.632 * [taylor]: Taking taylor expansion of k in n 66.632 * [backup-simplify]: Simplify k into k 66.632 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 66.632 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 66.632 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 66.632 * [taylor]: Taking taylor expansion of 2 in n 66.633 * [backup-simplify]: Simplify 2 into 2 66.633 * [taylor]: Taking taylor expansion of (/ PI n) in n 66.633 * [taylor]: Taking taylor expansion of PI in n 66.633 * [backup-simplify]: Simplify PI into PI 66.633 * [taylor]: Taking taylor expansion of n in n 66.633 * [backup-simplify]: Simplify 0 into 0 66.633 * [backup-simplify]: Simplify 1 into 1 66.633 * [backup-simplify]: Simplify (/ PI 1) into PI 66.634 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 66.635 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 66.635 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 66.635 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 66.635 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 66.636 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 66.638 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 66.639 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 66.640 * [backup-simplify]: Simplify (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 66.640 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 66.641 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 66.644 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 66.644 * [backup-simplify]: Simplify (/ (pow (/ 1 (- k)) (- 1/2)) (/ 1 (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))))) into (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 66.644 * [approximate]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 66.644 * [taylor]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 66.644 * [taylor]: Taking taylor expansion of (sqrt (/ k -1)) in n 66.644 * [taylor]: Taking taylor expansion of (/ k -1) in n 66.644 * [taylor]: Taking taylor expansion of k in n 66.644 * [backup-simplify]: Simplify k into k 66.644 * [taylor]: Taking taylor expansion of -1 in n 66.644 * [backup-simplify]: Simplify -1 into -1 66.644 * [backup-simplify]: Simplify (/ k -1) into (* -1 k) 66.645 * [backup-simplify]: Simplify (sqrt (* -1 k)) into (sqrt (* -1 k)) 66.645 * [backup-simplify]: Simplify (- (/ 0 -1) (+ (* (* -1 k) (/ 0 -1)))) into 0 66.645 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (* -1 k)))) into 0 66.645 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 66.645 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 66.645 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 66.645 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 66.645 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 66.645 * [taylor]: Taking taylor expansion of 1/2 in n 66.645 * [backup-simplify]: Simplify 1/2 into 1/2 66.645 * [taylor]: Taking taylor expansion of (/ 1 k) in n 66.645 * [taylor]: Taking taylor expansion of k in n 66.645 * [backup-simplify]: Simplify k into k 66.645 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 66.645 * [taylor]: Taking taylor expansion of 1/2 in n 66.645 * [backup-simplify]: Simplify 1/2 into 1/2 66.645 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 66.645 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 66.645 * [taylor]: Taking taylor expansion of -2 in n 66.645 * [backup-simplify]: Simplify -2 into -2 66.645 * [taylor]: Taking taylor expansion of (/ PI n) in n 66.645 * [taylor]: Taking taylor expansion of PI in n 66.645 * [backup-simplify]: Simplify PI into PI 66.645 * [taylor]: Taking taylor expansion of n in n 66.646 * [backup-simplify]: Simplify 0 into 0 66.646 * [backup-simplify]: Simplify 1 into 1 66.646 * [backup-simplify]: Simplify (/ PI 1) into PI 66.646 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 66.647 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 66.647 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 66.647 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 66.648 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 66.649 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 66.649 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 66.649 * [taylor]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 66.649 * [taylor]: Taking taylor expansion of (sqrt (/ k -1)) in k 66.649 * [taylor]: Taking taylor expansion of (/ k -1) in k 66.649 * [taylor]: Taking taylor expansion of k in k 66.649 * [backup-simplify]: Simplify 0 into 0 66.649 * [backup-simplify]: Simplify 1 into 1 66.650 * [taylor]: Taking taylor expansion of -1 in k 66.650 * [backup-simplify]: Simplify -1 into -1 66.650 * [backup-simplify]: Simplify (/ 1 -1) into -1 66.650 * [backup-simplify]: Simplify (sqrt 0) into 0 66.651 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 66.651 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 66.651 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 66.651 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 66.651 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 66.651 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 66.651 * [taylor]: Taking taylor expansion of 1/2 in k 66.651 * [backup-simplify]: Simplify 1/2 into 1/2 66.651 * [taylor]: Taking taylor expansion of (/ 1 k) in k 66.651 * [taylor]: Taking taylor expansion of k in k 66.651 * [backup-simplify]: Simplify 0 into 0 66.651 * [backup-simplify]: Simplify 1 into 1 66.651 * [backup-simplify]: Simplify (/ 1 1) into 1 66.651 * [taylor]: Taking taylor expansion of 1/2 in k 66.651 * [backup-simplify]: Simplify 1/2 into 1/2 66.651 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 66.652 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 66.652 * [taylor]: Taking taylor expansion of -2 in k 66.652 * [backup-simplify]: Simplify -2 into -2 66.652 * [taylor]: Taking taylor expansion of (/ PI n) in k 66.652 * [taylor]: Taking taylor expansion of PI in k 66.652 * [backup-simplify]: Simplify PI into PI 66.652 * [taylor]: Taking taylor expansion of n in k 66.652 * [backup-simplify]: Simplify n into n 66.652 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 66.652 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 66.652 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 66.652 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 66.652 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 66.652 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 66.653 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 66.653 * [taylor]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 66.653 * [taylor]: Taking taylor expansion of (sqrt (/ k -1)) in k 66.653 * [taylor]: Taking taylor expansion of (/ k -1) in k 66.653 * [taylor]: Taking taylor expansion of k in k 66.653 * [backup-simplify]: Simplify 0 into 0 66.653 * [backup-simplify]: Simplify 1 into 1 66.653 * [taylor]: Taking taylor expansion of -1 in k 66.653 * [backup-simplify]: Simplify -1 into -1 66.653 * [backup-simplify]: Simplify (/ 1 -1) into -1 66.653 * [backup-simplify]: Simplify (sqrt 0) into 0 66.654 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 66.654 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 66.654 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 66.654 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 66.654 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 66.654 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 66.654 * [taylor]: Taking taylor expansion of 1/2 in k 66.654 * [backup-simplify]: Simplify 1/2 into 1/2 66.654 * [taylor]: Taking taylor expansion of (/ 1 k) in k 66.654 * [taylor]: Taking taylor expansion of k in k 66.654 * [backup-simplify]: Simplify 0 into 0 66.654 * [backup-simplify]: Simplify 1 into 1 66.655 * [backup-simplify]: Simplify (/ 1 1) into 1 66.655 * [taylor]: Taking taylor expansion of 1/2 in k 66.655 * [backup-simplify]: Simplify 1/2 into 1/2 66.655 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 66.655 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 66.655 * [taylor]: Taking taylor expansion of -2 in k 66.655 * [backup-simplify]: Simplify -2 into -2 66.655 * [taylor]: Taking taylor expansion of (/ PI n) in k 66.655 * [taylor]: Taking taylor expansion of PI in k 66.655 * [backup-simplify]: Simplify PI into PI 66.655 * [taylor]: Taking taylor expansion of n in k 66.655 * [backup-simplify]: Simplify n into n 66.655 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 66.655 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 66.655 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 66.655 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 66.656 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 66.656 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 66.656 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 66.656 * [backup-simplify]: Simplify (* 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 66.656 * [taylor]: Taking taylor expansion of 0 in n 66.656 * [backup-simplify]: Simplify 0 into 0 66.656 * [backup-simplify]: Simplify 0 into 0 66.656 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 66.656 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 66.656 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 66.656 * [taylor]: Taking taylor expansion of +nan.0 in n 66.656 * [backup-simplify]: Simplify +nan.0 into +nan.0 66.656 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 66.656 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 66.657 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 66.657 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 66.657 * [taylor]: Taking taylor expansion of -2 in n 66.657 * [backup-simplify]: Simplify -2 into -2 66.657 * [taylor]: Taking taylor expansion of (/ PI n) in n 66.657 * [taylor]: Taking taylor expansion of PI in n 66.657 * [backup-simplify]: Simplify PI into PI 66.657 * [taylor]: Taking taylor expansion of n in n 66.657 * [backup-simplify]: Simplify 0 into 0 66.657 * [backup-simplify]: Simplify 1 into 1 66.657 * [backup-simplify]: Simplify (/ PI 1) into PI 66.657 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 66.658 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 66.658 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 66.658 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 66.658 * [taylor]: Taking taylor expansion of 1/2 in n 66.658 * [backup-simplify]: Simplify 1/2 into 1/2 66.658 * [taylor]: Taking taylor expansion of (/ 1 k) in n 66.658 * [taylor]: Taking taylor expansion of k in n 66.658 * [backup-simplify]: Simplify k into k 66.658 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 66.658 * [taylor]: Taking taylor expansion of 1/2 in n 66.658 * [backup-simplify]: Simplify 1/2 into 1/2 66.660 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 66.660 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 66.660 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 66.661 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 66.662 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 66.663 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 66.665 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 66.666 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 66.666 * [backup-simplify]: Simplify 0 into 0 66.667 * [backup-simplify]: Simplify (- (/ 0 -1) (+ (* -1 (/ 0 -1)))) into 0 66.670 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 66.671 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 66.671 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 66.671 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 66.671 * [taylor]: Taking taylor expansion of +nan.0 in n 66.671 * [backup-simplify]: Simplify +nan.0 into +nan.0 66.671 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 66.671 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 66.671 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 66.671 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 66.671 * [taylor]: Taking taylor expansion of -2 in n 66.671 * [backup-simplify]: Simplify -2 into -2 66.671 * [taylor]: Taking taylor expansion of (/ PI n) in n 66.671 * [taylor]: Taking taylor expansion of PI in n 66.672 * [backup-simplify]: Simplify PI into PI 66.672 * [taylor]: Taking taylor expansion of n in n 66.672 * [backup-simplify]: Simplify 0 into 0 66.672 * [backup-simplify]: Simplify 1 into 1 66.672 * [backup-simplify]: Simplify (/ PI 1) into PI 66.673 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 66.674 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 66.674 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 66.674 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 66.674 * [taylor]: Taking taylor expansion of 1/2 in n 66.674 * [backup-simplify]: Simplify 1/2 into 1/2 66.674 * [taylor]: Taking taylor expansion of (/ 1 k) in n 66.674 * [taylor]: Taking taylor expansion of k in n 66.674 * [backup-simplify]: Simplify k into k 66.674 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 66.674 * [taylor]: Taking taylor expansion of 1/2 in n 66.674 * [backup-simplify]: Simplify 1/2 into 1/2 66.675 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 66.675 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 66.676 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 66.677 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 66.678 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 66.679 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 66.680 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 66.682 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 66.683 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 66.683 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 66.684 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 66.684 * [backup-simplify]: Simplify (+ 0 0) into 0 66.685 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 66.686 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 66.688 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 66.689 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 66.691 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 66.693 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 66.693 * [backup-simplify]: Simplify (- 0) into 0 66.693 * [backup-simplify]: Simplify 0 into 0 66.693 * [backup-simplify]: Simplify 0 into 0 66.694 * [backup-simplify]: Simplify (- (/ 0 -1) (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 66.698 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 66.700 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 66.700 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 66.700 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 66.700 * [taylor]: Taking taylor expansion of +nan.0 in n 66.700 * [backup-simplify]: Simplify +nan.0 into +nan.0 66.700 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 66.700 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 66.700 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 66.700 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 66.700 * [taylor]: Taking taylor expansion of -2 in n 66.700 * [backup-simplify]: Simplify -2 into -2 66.700 * [taylor]: Taking taylor expansion of (/ PI n) in n 66.700 * [taylor]: Taking taylor expansion of PI in n 66.700 * [backup-simplify]: Simplify PI into PI 66.700 * [taylor]: Taking taylor expansion of n in n 66.700 * [backup-simplify]: Simplify 0 into 0 66.700 * [backup-simplify]: Simplify 1 into 1 66.701 * [backup-simplify]: Simplify (/ PI 1) into PI 66.701 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 66.707 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 66.707 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 66.707 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 66.707 * [taylor]: Taking taylor expansion of 1/2 in n 66.707 * [backup-simplify]: Simplify 1/2 into 1/2 66.707 * [taylor]: Taking taylor expansion of (/ 1 k) in n 66.707 * [taylor]: Taking taylor expansion of k in n 66.707 * [backup-simplify]: Simplify k into k 66.707 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 66.707 * [taylor]: Taking taylor expansion of 1/2 in n 66.707 * [backup-simplify]: Simplify 1/2 into 1/2 66.708 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 66.708 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 66.708 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 66.709 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 66.710 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 66.710 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 66.711 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 66.712 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 66.715 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 3)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 2)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* 1 (/ 1 (- k)))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 3))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))))))) 66.715 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2) 66.715 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 66.715 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 66.715 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 66.715 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 66.715 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 66.715 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 66.715 * [taylor]: Taking taylor expansion of 1/2 in k 66.715 * [backup-simplify]: Simplify 1/2 into 1/2 66.715 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 66.715 * [taylor]: Taking taylor expansion of 1/2 in k 66.715 * [backup-simplify]: Simplify 1/2 into 1/2 66.715 * [taylor]: Taking taylor expansion of k in k 66.715 * [backup-simplify]: Simplify 0 into 0 66.715 * [backup-simplify]: Simplify 1 into 1 66.715 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 66.715 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 66.715 * [taylor]: Taking taylor expansion of 2 in k 66.715 * [backup-simplify]: Simplify 2 into 2 66.715 * [taylor]: Taking taylor expansion of (* n PI) in k 66.715 * [taylor]: Taking taylor expansion of n in k 66.715 * [backup-simplify]: Simplify n into n 66.715 * [taylor]: Taking taylor expansion of PI in k 66.715 * [backup-simplify]: Simplify PI into PI 66.715 * [backup-simplify]: Simplify (* n PI) into (* n PI) 66.715 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 66.716 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 66.716 * [backup-simplify]: Simplify (* 1/2 0) into 0 66.716 * [backup-simplify]: Simplify (- 0) into 0 66.716 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 66.716 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 66.716 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 66.716 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 66.717 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 66.717 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 66.717 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 66.717 * [taylor]: Taking taylor expansion of 1/2 in n 66.717 * [backup-simplify]: Simplify 1/2 into 1/2 66.717 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 66.717 * [taylor]: Taking taylor expansion of 1/2 in n 66.717 * [backup-simplify]: Simplify 1/2 into 1/2 66.717 * [taylor]: Taking taylor expansion of k in n 66.717 * [backup-simplify]: Simplify k into k 66.717 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 66.717 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 66.717 * [taylor]: Taking taylor expansion of 2 in n 66.717 * [backup-simplify]: Simplify 2 into 2 66.717 * [taylor]: Taking taylor expansion of (* n PI) in n 66.717 * [taylor]: Taking taylor expansion of n in n 66.717 * [backup-simplify]: Simplify 0 into 0 66.717 * [backup-simplify]: Simplify 1 into 1 66.717 * [taylor]: Taking taylor expansion of PI in n 66.717 * [backup-simplify]: Simplify PI into PI 66.717 * [backup-simplify]: Simplify (* 0 PI) into 0 66.717 * [backup-simplify]: Simplify (* 2 0) into 0 66.718 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 66.719 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 66.720 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 66.720 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 66.720 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 66.720 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 66.721 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 66.722 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 66.723 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 66.723 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 66.723 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 66.723 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 66.723 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 66.723 * [taylor]: Taking taylor expansion of 1/2 in n 66.723 * [backup-simplify]: Simplify 1/2 into 1/2 66.723 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 66.723 * [taylor]: Taking taylor expansion of 1/2 in n 66.723 * [backup-simplify]: Simplify 1/2 into 1/2 66.723 * [taylor]: Taking taylor expansion of k in n 66.723 * [backup-simplify]: Simplify k into k 66.723 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 66.723 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 66.723 * [taylor]: Taking taylor expansion of 2 in n 66.723 * [backup-simplify]: Simplify 2 into 2 66.723 * [taylor]: Taking taylor expansion of (* n PI) in n 66.723 * [taylor]: Taking taylor expansion of n in n 66.723 * [backup-simplify]: Simplify 0 into 0 66.723 * [backup-simplify]: Simplify 1 into 1 66.723 * [taylor]: Taking taylor expansion of PI in n 66.723 * [backup-simplify]: Simplify PI into PI 66.723 * [backup-simplify]: Simplify (* 0 PI) into 0 66.723 * [backup-simplify]: Simplify (* 2 0) into 0 66.724 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 66.725 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 66.726 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 66.726 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 66.726 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 66.726 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 66.727 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 66.728 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 66.729 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 66.729 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 66.729 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 66.729 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 66.729 * [taylor]: Taking taylor expansion of 1/2 in k 66.729 * [backup-simplify]: Simplify 1/2 into 1/2 66.729 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 66.729 * [taylor]: Taking taylor expansion of 1/2 in k 66.729 * [backup-simplify]: Simplify 1/2 into 1/2 66.729 * [taylor]: Taking taylor expansion of k in k 66.729 * [backup-simplify]: Simplify 0 into 0 66.729 * [backup-simplify]: Simplify 1 into 1 66.729 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 66.729 * [taylor]: Taking taylor expansion of (log n) in k 66.729 * [taylor]: Taking taylor expansion of n in k 66.729 * [backup-simplify]: Simplify n into n 66.729 * [backup-simplify]: Simplify (log n) into (log n) 66.729 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 66.729 * [taylor]: Taking taylor expansion of (* 2 PI) in k 66.729 * [taylor]: Taking taylor expansion of 2 in k 66.729 * [backup-simplify]: Simplify 2 into 2 66.729 * [taylor]: Taking taylor expansion of PI in k 66.729 * [backup-simplify]: Simplify PI into PI 66.730 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 66.730 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 66.731 * [backup-simplify]: Simplify (* 1/2 0) into 0 66.731 * [backup-simplify]: Simplify (- 0) into 0 66.731 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 66.732 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 66.733 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 66.733 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 66.734 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 66.735 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 66.736 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 66.738 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 66.738 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 66.739 * [backup-simplify]: Simplify (- 0) into 0 66.739 * [backup-simplify]: Simplify (+ 0 0) into 0 66.741 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 66.742 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 66.744 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 66.744 * [taylor]: Taking taylor expansion of 0 in k 66.744 * [backup-simplify]: Simplify 0 into 0 66.744 * [backup-simplify]: Simplify 0 into 0 66.745 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 66.746 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 66.748 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 66.748 * [backup-simplify]: Simplify (+ 0 0) into 0 66.749 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 66.749 * [backup-simplify]: Simplify (- 1/2) into -1/2 66.750 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 66.751 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 66.755 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 66.758 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 66.759 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 66.760 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 66.764 * [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 66.765 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 66.766 * [backup-simplify]: Simplify (- 0) into 0 66.766 * [backup-simplify]: Simplify (+ 0 0) into 0 66.767 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 66.769 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 66.771 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 66.772 * [taylor]: Taking taylor expansion of 0 in k 66.772 * [backup-simplify]: Simplify 0 into 0 66.772 * [backup-simplify]: Simplify 0 into 0 66.772 * [backup-simplify]: Simplify 0 into 0 66.774 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 66.775 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 66.778 * [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 66.779 * [backup-simplify]: Simplify (+ 0 0) into 0 66.780 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 66.780 * [backup-simplify]: Simplify (- 0) into 0 66.781 * [backup-simplify]: Simplify (+ 0 0) into 0 66.783 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 66.787 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 66.792 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 66.802 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 66.802 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 66.802 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 66.803 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 66.803 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 66.803 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 66.803 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 66.803 * [taylor]: Taking taylor expansion of 1/2 in k 66.803 * [backup-simplify]: Simplify 1/2 into 1/2 66.803 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 66.803 * [taylor]: Taking taylor expansion of 1/2 in k 66.803 * [backup-simplify]: Simplify 1/2 into 1/2 66.803 * [taylor]: Taking taylor expansion of (/ 1 k) in k 66.803 * [taylor]: Taking taylor expansion of k in k 66.803 * [backup-simplify]: Simplify 0 into 0 66.803 * [backup-simplify]: Simplify 1 into 1 66.803 * [backup-simplify]: Simplify (/ 1 1) into 1 66.803 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 66.803 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 66.803 * [taylor]: Taking taylor expansion of 2 in k 66.803 * [backup-simplify]: Simplify 2 into 2 66.803 * [taylor]: Taking taylor expansion of (/ PI n) in k 66.803 * [taylor]: Taking taylor expansion of PI in k 66.803 * [backup-simplify]: Simplify PI into PI 66.803 * [taylor]: Taking taylor expansion of n in k 66.803 * [backup-simplify]: Simplify n into n 66.803 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 66.804 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 66.804 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 66.804 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 66.804 * [backup-simplify]: Simplify (- 1/2) into -1/2 66.805 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 66.805 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 66.805 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 66.805 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 66.805 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 66.805 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 66.805 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 66.805 * [taylor]: Taking taylor expansion of 1/2 in n 66.805 * [backup-simplify]: Simplify 1/2 into 1/2 66.805 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 66.805 * [taylor]: Taking taylor expansion of 1/2 in n 66.805 * [backup-simplify]: Simplify 1/2 into 1/2 66.805 * [taylor]: Taking taylor expansion of (/ 1 k) in n 66.805 * [taylor]: Taking taylor expansion of k in n 66.805 * [backup-simplify]: Simplify k into k 66.806 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 66.806 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 66.806 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 66.806 * [taylor]: Taking taylor expansion of 2 in n 66.806 * [backup-simplify]: Simplify 2 into 2 66.806 * [taylor]: Taking taylor expansion of (/ PI n) in n 66.806 * [taylor]: Taking taylor expansion of PI in n 66.806 * [backup-simplify]: Simplify PI into PI 66.806 * [taylor]: Taking taylor expansion of n in n 66.806 * [backup-simplify]: Simplify 0 into 0 66.806 * [backup-simplify]: Simplify 1 into 1 66.806 * [backup-simplify]: Simplify (/ PI 1) into PI 66.807 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 66.808 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 66.808 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 66.808 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 66.808 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 66.810 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 66.811 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 66.812 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 66.812 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 66.812 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 66.812 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 66.812 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 66.812 * [taylor]: Taking taylor expansion of 1/2 in n 66.812 * [backup-simplify]: Simplify 1/2 into 1/2 66.812 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 66.812 * [taylor]: Taking taylor expansion of 1/2 in n 66.812 * [backup-simplify]: Simplify 1/2 into 1/2 66.812 * [taylor]: Taking taylor expansion of (/ 1 k) in n 66.812 * [taylor]: Taking taylor expansion of k in n 66.812 * [backup-simplify]: Simplify k into k 66.812 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 66.813 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 66.813 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 66.813 * [taylor]: Taking taylor expansion of 2 in n 66.813 * [backup-simplify]: Simplify 2 into 2 66.813 * [taylor]: Taking taylor expansion of (/ PI n) in n 66.813 * [taylor]: Taking taylor expansion of PI in n 66.813 * [backup-simplify]: Simplify PI into PI 66.813 * [taylor]: Taking taylor expansion of n in n 66.813 * [backup-simplify]: Simplify 0 into 0 66.813 * [backup-simplify]: Simplify 1 into 1 66.813 * [backup-simplify]: Simplify (/ PI 1) into PI 66.814 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 66.815 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 66.815 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 66.815 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 66.816 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 66.817 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 66.818 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 66.820 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 66.820 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 66.820 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 66.820 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 66.820 * [taylor]: Taking taylor expansion of 1/2 in k 66.820 * [backup-simplify]: Simplify 1/2 into 1/2 66.820 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 66.820 * [taylor]: Taking taylor expansion of 1/2 in k 66.820 * [backup-simplify]: Simplify 1/2 into 1/2 66.820 * [taylor]: Taking taylor expansion of (/ 1 k) in k 66.820 * [taylor]: Taking taylor expansion of k in k 66.820 * [backup-simplify]: Simplify 0 into 0 66.820 * [backup-simplify]: Simplify 1 into 1 66.820 * [backup-simplify]: Simplify (/ 1 1) into 1 66.820 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 66.820 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 66.820 * [taylor]: Taking taylor expansion of (* 2 PI) in k 66.820 * [taylor]: Taking taylor expansion of 2 in k 66.820 * [backup-simplify]: Simplify 2 into 2 66.820 * [taylor]: Taking taylor expansion of PI in k 66.820 * [backup-simplify]: Simplify PI into PI 66.821 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 66.822 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 66.822 * [taylor]: Taking taylor expansion of (log n) in k 66.822 * [taylor]: Taking taylor expansion of n in k 66.822 * [backup-simplify]: Simplify n into n 66.822 * [backup-simplify]: Simplify (log n) into (log n) 66.823 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 66.823 * [backup-simplify]: Simplify (- 1/2) into -1/2 66.824 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 66.824 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 66.825 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 66.826 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 66.827 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 66.829 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 66.830 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 66.831 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 66.833 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 66.833 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 66.833 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 66.834 * [backup-simplify]: Simplify (- 0) into 0 66.834 * [backup-simplify]: Simplify (+ 0 0) into 0 66.835 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 66.843 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 66.845 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 66.845 * [taylor]: Taking taylor expansion of 0 in k 66.845 * [backup-simplify]: Simplify 0 into 0 66.845 * [backup-simplify]: Simplify 0 into 0 66.846 * [backup-simplify]: Simplify 0 into 0 66.847 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 66.847 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 66.849 * [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 66.850 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 66.850 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 66.852 * [backup-simplify]: Simplify (- 0) into 0 66.852 * [backup-simplify]: Simplify (+ 0 0) into 0 66.853 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 66.855 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 66.856 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 66.856 * [taylor]: Taking taylor expansion of 0 in k 66.856 * [backup-simplify]: Simplify 0 into 0 66.856 * [backup-simplify]: Simplify 0 into 0 66.856 * [backup-simplify]: Simplify 0 into 0 66.856 * [backup-simplify]: Simplify 0 into 0 66.857 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 66.858 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 66.861 * [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 66.862 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 66.862 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 66.863 * [backup-simplify]: Simplify (- 0) into 0 66.863 * [backup-simplify]: Simplify (+ 0 0) into 0 66.864 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 66.865 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 66.867 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 66.867 * [taylor]: Taking taylor expansion of 0 in k 66.867 * [backup-simplify]: Simplify 0 into 0 66.867 * [backup-simplify]: Simplify 0 into 0 66.868 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 66.868 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 66.868 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 66.868 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 66.868 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 66.868 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 66.868 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 66.868 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 66.868 * [taylor]: Taking taylor expansion of 1/2 in k 66.868 * [backup-simplify]: Simplify 1/2 into 1/2 66.868 * [taylor]: Taking taylor expansion of (/ 1 k) in k 66.868 * [taylor]: Taking taylor expansion of k in k 66.868 * [backup-simplify]: Simplify 0 into 0 66.868 * [backup-simplify]: Simplify 1 into 1 66.868 * [backup-simplify]: Simplify (/ 1 1) into 1 66.868 * [taylor]: Taking taylor expansion of 1/2 in k 66.868 * [backup-simplify]: Simplify 1/2 into 1/2 66.868 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 66.868 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 66.868 * [taylor]: Taking taylor expansion of -2 in k 66.868 * [backup-simplify]: Simplify -2 into -2 66.868 * [taylor]: Taking taylor expansion of (/ PI n) in k 66.868 * [taylor]: Taking taylor expansion of PI in k 66.868 * [backup-simplify]: Simplify PI into PI 66.868 * [taylor]: Taking taylor expansion of n in k 66.868 * [backup-simplify]: Simplify n into n 66.869 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 66.869 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 66.869 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 66.869 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 66.869 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 66.869 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 66.869 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 66.869 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 66.869 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 66.869 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 66.869 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 66.869 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 66.869 * [taylor]: Taking taylor expansion of 1/2 in n 66.869 * [backup-simplify]: Simplify 1/2 into 1/2 66.869 * [taylor]: Taking taylor expansion of (/ 1 k) in n 66.870 * [taylor]: Taking taylor expansion of k in n 66.870 * [backup-simplify]: Simplify k into k 66.870 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 66.870 * [taylor]: Taking taylor expansion of 1/2 in n 66.870 * [backup-simplify]: Simplify 1/2 into 1/2 66.870 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 66.870 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 66.870 * [taylor]: Taking taylor expansion of -2 in n 66.870 * [backup-simplify]: Simplify -2 into -2 66.870 * [taylor]: Taking taylor expansion of (/ PI n) in n 66.870 * [taylor]: Taking taylor expansion of PI in n 66.870 * [backup-simplify]: Simplify PI into PI 66.870 * [taylor]: Taking taylor expansion of n in n 66.870 * [backup-simplify]: Simplify 0 into 0 66.870 * [backup-simplify]: Simplify 1 into 1 66.870 * [backup-simplify]: Simplify (/ PI 1) into PI 66.870 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 66.871 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 66.871 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 66.871 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 66.872 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 66.873 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 66.874 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 66.874 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 66.874 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 66.874 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 66.874 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 66.874 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 66.874 * [taylor]: Taking taylor expansion of 1/2 in n 66.874 * [backup-simplify]: Simplify 1/2 into 1/2 66.874 * [taylor]: Taking taylor expansion of (/ 1 k) in n 66.874 * [taylor]: Taking taylor expansion of k in n 66.874 * [backup-simplify]: Simplify k into k 66.874 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 66.874 * [taylor]: Taking taylor expansion of 1/2 in n 66.874 * [backup-simplify]: Simplify 1/2 into 1/2 66.874 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 66.874 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 66.874 * [taylor]: Taking taylor expansion of -2 in n 66.874 * [backup-simplify]: Simplify -2 into -2 66.874 * [taylor]: Taking taylor expansion of (/ PI n) in n 66.874 * [taylor]: Taking taylor expansion of PI in n 66.874 * [backup-simplify]: Simplify PI into PI 66.874 * [taylor]: Taking taylor expansion of n in n 66.874 * [backup-simplify]: Simplify 0 into 0 66.874 * [backup-simplify]: Simplify 1 into 1 66.874 * [backup-simplify]: Simplify (/ PI 1) into PI 66.875 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 66.876 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 66.876 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 66.876 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 66.877 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 66.879 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 66.880 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 66.880 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 66.880 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 66.880 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 66.880 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 66.880 * [taylor]: Taking taylor expansion of 1/2 in k 66.880 * [backup-simplify]: Simplify 1/2 into 1/2 66.880 * [taylor]: Taking taylor expansion of (/ 1 k) in k 66.880 * [taylor]: Taking taylor expansion of k in k 66.880 * [backup-simplify]: Simplify 0 into 0 66.880 * [backup-simplify]: Simplify 1 into 1 66.881 * [backup-simplify]: Simplify (/ 1 1) into 1 66.881 * [taylor]: Taking taylor expansion of 1/2 in k 66.881 * [backup-simplify]: Simplify 1/2 into 1/2 66.881 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 66.881 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 66.881 * [taylor]: Taking taylor expansion of (* -2 PI) in k 66.881 * [taylor]: Taking taylor expansion of -2 in k 66.881 * [backup-simplify]: Simplify -2 into -2 66.881 * [taylor]: Taking taylor expansion of PI in k 66.881 * [backup-simplify]: Simplify PI into PI 66.881 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 66.883 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 66.883 * [taylor]: Taking taylor expansion of (log n) in k 66.883 * [taylor]: Taking taylor expansion of n in k 66.883 * [backup-simplify]: Simplify n into n 66.883 * [backup-simplify]: Simplify (log n) into (log n) 66.883 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 66.884 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 66.884 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 66.885 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 66.886 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 66.888 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 66.889 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 66.890 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 66.891 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 66.893 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 66.893 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 66.893 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 66.894 * [backup-simplify]: Simplify (+ 0 0) into 0 66.895 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 66.897 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 66.898 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 66.898 * [taylor]: Taking taylor expansion of 0 in k 66.899 * [backup-simplify]: Simplify 0 into 0 66.899 * [backup-simplify]: Simplify 0 into 0 66.899 * [backup-simplify]: Simplify 0 into 0 66.900 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 66.901 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 66.904 * [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 66.904 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 66.905 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 66.905 * [backup-simplify]: Simplify (+ 0 0) into 0 66.906 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 66.907 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 66.908 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 66.908 * [taylor]: Taking taylor expansion of 0 in k 66.908 * [backup-simplify]: Simplify 0 into 0 66.908 * [backup-simplify]: Simplify 0 into 0 66.908 * [backup-simplify]: Simplify 0 into 0 66.908 * [backup-simplify]: Simplify 0 into 0 66.909 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 66.910 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 66.913 * [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 66.913 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 66.914 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 66.914 * [backup-simplify]: Simplify (+ 0 0) into 0 66.916 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 66.917 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 66.918 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 66.918 * [taylor]: Taking taylor expansion of 0 in k 66.918 * [backup-simplify]: Simplify 0 into 0 66.918 * [backup-simplify]: Simplify 0 into 0 66.919 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 66.919 * * * * [progress]: [ 4 / 4 ] generating series at (2 2) 66.919 * [backup-simplify]: Simplify (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) into (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 66.919 * [approximate]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 66.920 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 66.920 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 66.920 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 66.920 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 66.920 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 66.920 * [taylor]: Taking taylor expansion of 1/2 in k 66.920 * [backup-simplify]: Simplify 1/2 into 1/2 66.920 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 66.920 * [taylor]: Taking taylor expansion of 1/2 in k 66.920 * [backup-simplify]: Simplify 1/2 into 1/2 66.920 * [taylor]: Taking taylor expansion of k in k 66.920 * [backup-simplify]: Simplify 0 into 0 66.920 * [backup-simplify]: Simplify 1 into 1 66.920 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 66.920 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 66.920 * [taylor]: Taking taylor expansion of 2 in k 66.920 * [backup-simplify]: Simplify 2 into 2 66.920 * [taylor]: Taking taylor expansion of (* n PI) in k 66.920 * [taylor]: Taking taylor expansion of n in k 66.920 * [backup-simplify]: Simplify n into n 66.920 * [taylor]: Taking taylor expansion of PI in k 66.920 * [backup-simplify]: Simplify PI into PI 66.920 * [backup-simplify]: Simplify (* n PI) into (* n PI) 66.920 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 66.920 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 66.920 * [backup-simplify]: Simplify (* 1/2 0) into 0 66.920 * [backup-simplify]: Simplify (- 0) into 0 66.921 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 66.921 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 66.921 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 66.921 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 66.921 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 66.921 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 66.921 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 66.921 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 66.921 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 66.921 * [taylor]: Taking taylor expansion of 1/2 in n 66.921 * [backup-simplify]: Simplify 1/2 into 1/2 66.921 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 66.921 * [taylor]: Taking taylor expansion of 1/2 in n 66.921 * [backup-simplify]: Simplify 1/2 into 1/2 66.921 * [taylor]: Taking taylor expansion of k in n 66.921 * [backup-simplify]: Simplify k into k 66.921 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 66.921 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 66.921 * [taylor]: Taking taylor expansion of 2 in n 66.921 * [backup-simplify]: Simplify 2 into 2 66.921 * [taylor]: Taking taylor expansion of (* n PI) in n 66.921 * [taylor]: Taking taylor expansion of n in n 66.921 * [backup-simplify]: Simplify 0 into 0 66.921 * [backup-simplify]: Simplify 1 into 1 66.921 * [taylor]: Taking taylor expansion of PI in n 66.921 * [backup-simplify]: Simplify PI into PI 66.922 * [backup-simplify]: Simplify (* 0 PI) into 0 66.922 * [backup-simplify]: Simplify (* 2 0) into 0 66.923 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 66.924 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 66.925 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 66.925 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 66.925 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 66.925 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 66.926 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 66.926 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 66.927 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 66.928 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 66.928 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 66.928 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 66.928 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 66.928 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 66.928 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 66.928 * [taylor]: Taking taylor expansion of 1/2 in n 66.928 * [backup-simplify]: Simplify 1/2 into 1/2 66.928 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 66.928 * [taylor]: Taking taylor expansion of 1/2 in n 66.928 * [backup-simplify]: Simplify 1/2 into 1/2 66.928 * [taylor]: Taking taylor expansion of k in n 66.928 * [backup-simplify]: Simplify k into k 66.928 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 66.928 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 66.928 * [taylor]: Taking taylor expansion of 2 in n 66.928 * [backup-simplify]: Simplify 2 into 2 66.928 * [taylor]: Taking taylor expansion of (* n PI) in n 66.928 * [taylor]: Taking taylor expansion of n in n 66.928 * [backup-simplify]: Simplify 0 into 0 66.928 * [backup-simplify]: Simplify 1 into 1 66.928 * [taylor]: Taking taylor expansion of PI in n 66.928 * [backup-simplify]: Simplify PI into PI 66.928 * [backup-simplify]: Simplify (* 0 PI) into 0 66.929 * [backup-simplify]: Simplify (* 2 0) into 0 66.930 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 66.931 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 66.931 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 66.931 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 66.932 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 66.932 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 66.932 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 66.933 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 66.934 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 66.935 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 66.935 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k 66.935 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 66.935 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 66.935 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 66.935 * [taylor]: Taking taylor expansion of 1/2 in k 66.935 * [backup-simplify]: Simplify 1/2 into 1/2 66.935 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 66.935 * [taylor]: Taking taylor expansion of 1/2 in k 66.935 * [backup-simplify]: Simplify 1/2 into 1/2 66.935 * [taylor]: Taking taylor expansion of k in k 66.935 * [backup-simplify]: Simplify 0 into 0 66.935 * [backup-simplify]: Simplify 1 into 1 66.935 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 66.935 * [taylor]: Taking taylor expansion of (log n) in k 66.935 * [taylor]: Taking taylor expansion of n in k 66.935 * [backup-simplify]: Simplify n into n 66.935 * [backup-simplify]: Simplify (log n) into (log n) 66.935 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 66.935 * [taylor]: Taking taylor expansion of (* 2 PI) in k 66.935 * [taylor]: Taking taylor expansion of 2 in k 66.935 * [backup-simplify]: Simplify 2 into 2 66.935 * [taylor]: Taking taylor expansion of PI in k 66.935 * [backup-simplify]: Simplify PI into PI 66.936 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 66.937 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 66.937 * [backup-simplify]: Simplify (* 1/2 0) into 0 66.938 * [backup-simplify]: Simplify (- 0) into 0 66.938 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 66.939 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 66.940 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 66.942 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 66.943 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) 66.944 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) 66.945 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 66.946 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 66.948 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 66.948 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 66.948 * [backup-simplify]: Simplify (- 0) into 0 66.948 * [backup-simplify]: Simplify (+ 0 0) into 0 66.949 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 66.950 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 66.956 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 66.957 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (/ 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 66.957 * [taylor]: Taking taylor expansion of 0 in k 66.958 * [backup-simplify]: Simplify 0 into 0 66.958 * [backup-simplify]: Simplify 0 into 0 66.958 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 66.959 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 66.960 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 66.960 * [backup-simplify]: Simplify (+ 0 0) into 0 66.960 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 66.961 * [backup-simplify]: Simplify (- 1/2) into -1/2 66.961 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 66.962 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 66.964 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 66.967 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (/ (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) 66.970 * [backup-simplify]: Simplify (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) into (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) 66.970 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 66.971 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 66.973 * [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 66.974 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 66.974 * [backup-simplify]: Simplify (- 0) into 0 66.974 * [backup-simplify]: Simplify (+ 0 0) into 0 66.975 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 66.976 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 66.977 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 66.980 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (/ 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 66.980 * [taylor]: Taking taylor expansion of 0 in k 66.980 * [backup-simplify]: Simplify 0 into 0 66.980 * [backup-simplify]: Simplify 0 into 0 66.980 * [backup-simplify]: Simplify 0 into 0 66.981 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 66.981 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 66.984 * [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 66.984 * [backup-simplify]: Simplify (+ 0 0) into 0 66.985 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 66.986 * [backup-simplify]: Simplify (- 0) into 0 66.986 * [backup-simplify]: Simplify (+ 0 0) into 0 66.988 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 66.993 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 67.009 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (/ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (/ (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) 67.016 * [backup-simplify]: Simplify (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) 67.028 * [backup-simplify]: Simplify (+ (* (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) (pow (* k 1) 2)) (+ (* (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (* k 1)) (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) into (+ (* 1/8 (/ (* (pow (log (* 2 PI)) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* k (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* (log n) k) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/4 (/ (* (log (* 2 PI)) (* (log n) (pow k 2))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (* 1/8 (/ (* (pow (log n) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))) 67.029 * [backup-simplify]: Simplify (/ 1 (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2)))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 67.029 * [approximate]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 67.029 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 67.029 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 67.029 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 67.029 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 67.029 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 67.029 * [taylor]: Taking taylor expansion of 1/2 in k 67.029 * [backup-simplify]: Simplify 1/2 into 1/2 67.029 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 67.029 * [taylor]: Taking taylor expansion of 1/2 in k 67.029 * [backup-simplify]: Simplify 1/2 into 1/2 67.029 * [taylor]: Taking taylor expansion of (/ 1 k) in k 67.029 * [taylor]: Taking taylor expansion of k in k 67.029 * [backup-simplify]: Simplify 0 into 0 67.029 * [backup-simplify]: Simplify 1 into 1 67.029 * [backup-simplify]: Simplify (/ 1 1) into 1 67.030 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 67.030 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 67.030 * [taylor]: Taking taylor expansion of 2 in k 67.030 * [backup-simplify]: Simplify 2 into 2 67.030 * [taylor]: Taking taylor expansion of (/ PI n) in k 67.030 * [taylor]: Taking taylor expansion of PI in k 67.030 * [backup-simplify]: Simplify PI into PI 67.030 * [taylor]: Taking taylor expansion of n in k 67.030 * [backup-simplify]: Simplify n into n 67.030 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 67.030 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 67.030 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 67.030 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 67.031 * [backup-simplify]: Simplify (- 1/2) into -1/2 67.031 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 67.031 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 67.032 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 67.032 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 67.032 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 67.032 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 67.032 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 67.032 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 67.032 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 67.032 * [taylor]: Taking taylor expansion of 1/2 in n 67.032 * [backup-simplify]: Simplify 1/2 into 1/2 67.032 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 67.032 * [taylor]: Taking taylor expansion of 1/2 in n 67.032 * [backup-simplify]: Simplify 1/2 into 1/2 67.032 * [taylor]: Taking taylor expansion of (/ 1 k) in n 67.032 * [taylor]: Taking taylor expansion of k in n 67.032 * [backup-simplify]: Simplify k into k 67.032 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 67.032 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 67.032 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 67.032 * [taylor]: Taking taylor expansion of 2 in n 67.032 * [backup-simplify]: Simplify 2 into 2 67.032 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.032 * [taylor]: Taking taylor expansion of PI in n 67.032 * [backup-simplify]: Simplify PI into PI 67.032 * [taylor]: Taking taylor expansion of n in n 67.032 * [backup-simplify]: Simplify 0 into 0 67.032 * [backup-simplify]: Simplify 1 into 1 67.033 * [backup-simplify]: Simplify (/ PI 1) into PI 67.034 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.035 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 67.035 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 67.035 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 67.035 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 67.037 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 67.038 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 67.039 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 67.040 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 67.040 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 67.040 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 67.040 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 67.040 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 67.040 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 67.041 * [taylor]: Taking taylor expansion of 1/2 in n 67.041 * [backup-simplify]: Simplify 1/2 into 1/2 67.041 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 67.041 * [taylor]: Taking taylor expansion of 1/2 in n 67.041 * [backup-simplify]: Simplify 1/2 into 1/2 67.041 * [taylor]: Taking taylor expansion of (/ 1 k) in n 67.041 * [taylor]: Taking taylor expansion of k in n 67.041 * [backup-simplify]: Simplify k into k 67.041 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 67.041 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 67.041 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 67.041 * [taylor]: Taking taylor expansion of 2 in n 67.041 * [backup-simplify]: Simplify 2 into 2 67.041 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.041 * [taylor]: Taking taylor expansion of PI in n 67.041 * [backup-simplify]: Simplify PI into PI 67.041 * [taylor]: Taking taylor expansion of n in n 67.041 * [backup-simplify]: Simplify 0 into 0 67.041 * [backup-simplify]: Simplify 1 into 1 67.042 * [backup-simplify]: Simplify (/ PI 1) into PI 67.042 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.043 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 67.043 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 67.043 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 67.043 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 67.045 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 67.046 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 67.047 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 67.049 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 67.049 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k 67.049 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 67.049 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 67.049 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 67.049 * [taylor]: Taking taylor expansion of 1/2 in k 67.049 * [backup-simplify]: Simplify 1/2 into 1/2 67.049 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 67.049 * [taylor]: Taking taylor expansion of 1/2 in k 67.049 * [backup-simplify]: Simplify 1/2 into 1/2 67.049 * [taylor]: Taking taylor expansion of (/ 1 k) in k 67.049 * [taylor]: Taking taylor expansion of k in k 67.049 * [backup-simplify]: Simplify 0 into 0 67.049 * [backup-simplify]: Simplify 1 into 1 67.050 * [backup-simplify]: Simplify (/ 1 1) into 1 67.050 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 67.050 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 67.050 * [taylor]: Taking taylor expansion of (* 2 PI) in k 67.050 * [taylor]: Taking taylor expansion of 2 in k 67.050 * [backup-simplify]: Simplify 2 into 2 67.050 * [taylor]: Taking taylor expansion of PI in k 67.050 * [backup-simplify]: Simplify PI into PI 67.050 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.051 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 67.051 * [taylor]: Taking taylor expansion of (log n) in k 67.051 * [taylor]: Taking taylor expansion of n in k 67.051 * [backup-simplify]: Simplify n into n 67.051 * [backup-simplify]: Simplify (log n) into (log n) 67.052 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 67.052 * [backup-simplify]: Simplify (- 1/2) into -1/2 67.053 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 67.053 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 67.054 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 67.055 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 67.057 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 67.059 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 67.060 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 67.061 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 67.062 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 67.064 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 67.064 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 67.064 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 67.065 * [backup-simplify]: Simplify (- 0) into 0 67.065 * [backup-simplify]: Simplify (+ 0 0) into 0 67.067 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 67.068 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 67.070 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 67.072 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 67.073 * [taylor]: Taking taylor expansion of 0 in k 67.073 * [backup-simplify]: Simplify 0 into 0 67.073 * [backup-simplify]: Simplify 0 into 0 67.075 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 67.075 * [backup-simplify]: Simplify 0 into 0 67.076 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.077 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 67.080 * [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 67.080 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 67.087 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 67.088 * [backup-simplify]: Simplify (- 0) into 0 67.088 * [backup-simplify]: Simplify (+ 0 0) into 0 67.090 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 67.091 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 67.093 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 67.096 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 67.097 * [taylor]: Taking taylor expansion of 0 in k 67.097 * [backup-simplify]: Simplify 0 into 0 67.097 * [backup-simplify]: Simplify 0 into 0 67.097 * [backup-simplify]: Simplify 0 into 0 67.100 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 67.100 * [backup-simplify]: Simplify 0 into 0 67.100 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.101 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 67.104 * [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 67.104 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 67.105 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 67.106 * [backup-simplify]: Simplify (- 0) into 0 67.106 * [backup-simplify]: Simplify (+ 0 0) into 0 67.107 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 67.108 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 67.110 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 67.113 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 67.113 * [taylor]: Taking taylor expansion of 0 in k 67.113 * [backup-simplify]: Simplify 0 into 0 67.113 * [backup-simplify]: Simplify 0 into 0 67.114 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 67.114 * [backup-simplify]: Simplify (/ 1 (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 67.114 * [approximate]: Taking taylor expansion of (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0 67.114 * [taylor]: Taking taylor expansion of (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 67.114 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 67.114 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 67.114 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 67.114 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 67.114 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 67.114 * [taylor]: Taking taylor expansion of 1/2 in k 67.114 * [backup-simplify]: Simplify 1/2 into 1/2 67.114 * [taylor]: Taking taylor expansion of (/ 1 k) in k 67.114 * [taylor]: Taking taylor expansion of k in k 67.114 * [backup-simplify]: Simplify 0 into 0 67.114 * [backup-simplify]: Simplify 1 into 1 67.114 * [backup-simplify]: Simplify (/ 1 1) into 1 67.114 * [taylor]: Taking taylor expansion of 1/2 in k 67.114 * [backup-simplify]: Simplify 1/2 into 1/2 67.114 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 67.114 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 67.114 * [taylor]: Taking taylor expansion of -2 in k 67.115 * [backup-simplify]: Simplify -2 into -2 67.115 * [taylor]: Taking taylor expansion of (/ PI n) in k 67.115 * [taylor]: Taking taylor expansion of PI in k 67.115 * [backup-simplify]: Simplify PI into PI 67.115 * [taylor]: Taking taylor expansion of n in k 67.115 * [backup-simplify]: Simplify n into n 67.115 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 67.115 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 67.115 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 67.115 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 67.115 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 67.115 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 67.115 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 67.116 * [backup-simplify]: Simplify (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 67.116 * [taylor]: Taking taylor expansion of (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 67.116 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 67.116 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 67.116 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 67.116 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 67.116 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 67.116 * [taylor]: Taking taylor expansion of 1/2 in n 67.116 * [backup-simplify]: Simplify 1/2 into 1/2 67.116 * [taylor]: Taking taylor expansion of (/ 1 k) in n 67.116 * [taylor]: Taking taylor expansion of k in n 67.116 * [backup-simplify]: Simplify k into k 67.116 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 67.116 * [taylor]: Taking taylor expansion of 1/2 in n 67.116 * [backup-simplify]: Simplify 1/2 into 1/2 67.116 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 67.116 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 67.116 * [taylor]: Taking taylor expansion of -2 in n 67.116 * [backup-simplify]: Simplify -2 into -2 67.116 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.116 * [taylor]: Taking taylor expansion of PI in n 67.116 * [backup-simplify]: Simplify PI into PI 67.116 * [taylor]: Taking taylor expansion of n in n 67.116 * [backup-simplify]: Simplify 0 into 0 67.116 * [backup-simplify]: Simplify 1 into 1 67.116 * [backup-simplify]: Simplify (/ PI 1) into PI 67.117 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 67.118 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 67.118 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 67.118 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 67.119 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 67.119 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 67.120 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 67.121 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 67.121 * [taylor]: Taking taylor expansion of (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 67.121 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 67.121 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 67.121 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 67.121 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 67.121 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 67.121 * [taylor]: Taking taylor expansion of 1/2 in n 67.121 * [backup-simplify]: Simplify 1/2 into 1/2 67.121 * [taylor]: Taking taylor expansion of (/ 1 k) in n 67.121 * [taylor]: Taking taylor expansion of k in n 67.121 * [backup-simplify]: Simplify k into k 67.121 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 67.121 * [taylor]: Taking taylor expansion of 1/2 in n 67.121 * [backup-simplify]: Simplify 1/2 into 1/2 67.121 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 67.121 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 67.121 * [taylor]: Taking taylor expansion of -2 in n 67.121 * [backup-simplify]: Simplify -2 into -2 67.121 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.121 * [taylor]: Taking taylor expansion of PI in n 67.122 * [backup-simplify]: Simplify PI into PI 67.122 * [taylor]: Taking taylor expansion of n in n 67.122 * [backup-simplify]: Simplify 0 into 0 67.122 * [backup-simplify]: Simplify 1 into 1 67.122 * [backup-simplify]: Simplify (/ PI 1) into PI 67.122 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 67.123 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 67.123 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 67.123 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 67.124 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 67.125 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 67.125 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 67.126 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 67.126 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k 67.126 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 67.126 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 67.126 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 67.126 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 67.126 * [taylor]: Taking taylor expansion of 1/2 in k 67.126 * [backup-simplify]: Simplify 1/2 into 1/2 67.126 * [taylor]: Taking taylor expansion of (/ 1 k) in k 67.126 * [taylor]: Taking taylor expansion of k in k 67.126 * [backup-simplify]: Simplify 0 into 0 67.126 * [backup-simplify]: Simplify 1 into 1 67.127 * [backup-simplify]: Simplify (/ 1 1) into 1 67.127 * [taylor]: Taking taylor expansion of 1/2 in k 67.127 * [backup-simplify]: Simplify 1/2 into 1/2 67.127 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 67.127 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 67.127 * [taylor]: Taking taylor expansion of (* -2 PI) in k 67.127 * [taylor]: Taking taylor expansion of -2 in k 67.127 * [backup-simplify]: Simplify -2 into -2 67.127 * [taylor]: Taking taylor expansion of PI in k 67.127 * [backup-simplify]: Simplify PI into PI 67.127 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 67.128 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 67.128 * [taylor]: Taking taylor expansion of (log n) in k 67.128 * [taylor]: Taking taylor expansion of n in k 67.128 * [backup-simplify]: Simplify n into n 67.128 * [backup-simplify]: Simplify (log n) into (log n) 67.128 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 67.129 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 67.129 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 67.129 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 67.130 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 67.131 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 67.132 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 67.132 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 67.133 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 67.133 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 67.135 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 67.135 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 67.135 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 67.135 * [backup-simplify]: Simplify (+ 0 0) into 0 67.136 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 67.137 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 67.138 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 67.140 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 67.140 * [taylor]: Taking taylor expansion of 0 in k 67.140 * [backup-simplify]: Simplify 0 into 0 67.140 * [backup-simplify]: Simplify 0 into 0 67.141 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 67.141 * [backup-simplify]: Simplify 0 into 0 67.142 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.143 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 67.145 * [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 67.145 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 67.145 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 67.146 * [backup-simplify]: Simplify (+ 0 0) into 0 67.147 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 67.148 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 67.149 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 67.151 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 67.151 * [taylor]: Taking taylor expansion of 0 in k 67.151 * [backup-simplify]: Simplify 0 into 0 67.151 * [backup-simplify]: Simplify 0 into 0 67.151 * [backup-simplify]: Simplify 0 into 0 67.154 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 67.154 * [backup-simplify]: Simplify 0 into 0 67.154 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.155 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 67.159 * [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 67.159 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 67.160 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 67.160 * [backup-simplify]: Simplify (+ 0 0) into 0 67.161 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 67.162 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 67.164 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 67.167 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 67.167 * [taylor]: Taking taylor expansion of 0 in k 67.167 * [backup-simplify]: Simplify 0 into 0 67.167 * [backup-simplify]: Simplify 0 into 0 67.168 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 67.168 * * * [progress]: simplifying candidates 67.168 * * * * [progress]: [ 1 / 1536 ] simplifiying candidate # 67.168 * * * * [progress]: [ 2 / 1536 ] simplifiying candidate # 67.168 * * * * [progress]: [ 3 / 1536 ] simplifiying candidate # 67.168 * * * * [progress]: [ 4 / 1536 ] simplifiying candidate # 67.168 * * * * [progress]: [ 5 / 1536 ] simplifiying candidate # 67.168 * * * * [progress]: [ 6 / 1536 ] simplifiying candidate # 67.168 * * * * [progress]: [ 7 / 1536 ] simplifiying candidate # 67.168 * * * * [progress]: [ 8 / 1536 ] simplifiying candidate # 67.169 * * * * [progress]: [ 9 / 1536 ] simplifiying candidate # 67.169 * * * * [progress]: [ 10 / 1536 ] simplifiying candidate # 67.169 * * * * [progress]: [ 11 / 1536 ] simplifiying candidate # 67.169 * * * * [progress]: [ 12 / 1536 ] simplifiying candidate # 67.169 * * * * [progress]: [ 13 / 1536 ] simplifiying candidate # 67.169 * * * * [progress]: [ 14 / 1536 ] simplifiying candidate # 67.169 * * * * [progress]: [ 15 / 1536 ] simplifiying candidate # 67.169 * * * * [progress]: [ 16 / 1536 ] simplifiying candidate # 67.169 * * * * [progress]: [ 17 / 1536 ] simplifiying candidate # 67.169 * * * * [progress]: [ 18 / 1536 ] simplifiying candidate # 67.169 * * * * [progress]: [ 19 / 1536 ] simplifiying candidate # 67.169 * * * * [progress]: [ 20 / 1536 ] simplifiying candidate #real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))))))> 67.169 * * * * [progress]: [ 21 / 1536 ] simplifiying candidate # 67.169 * * * * [progress]: [ 22 / 1536 ] simplifiying 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[progress]: [ 1530 / 1536 ] simplifiying candidate # 67.273 * * * * [progress]: [ 1531 / 1536 ] simplifiying candidate # 67.273 * * * * [progress]: [ 1532 / 1536 ] simplifiying candidate # 67.273 * * * * [progress]: [ 1533 / 1536 ] simplifiying candidate # 67.273 * * * * [progress]: [ 1534 / 1536 ] simplifiying candidate # 67.273 * * * * [progress]: [ 1535 / 1536 ] simplifiying candidate # 67.273 * * * * [progress]: [ 1536 / 1536 ] simplifiying candidate # 67.343 * [simplify]: Simplifying: (expm1 (* (* n 2) PI)) (log1p (* (* n 2) PI)) (* (* n 2) PI) (* (* n 2) PI) (+ (+ (log n) (log 2)) (log PI)) (+ (log (* n 2)) (log PI)) (log (* (* n 2) PI)) (exp (* (* n 2) PI)) (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI)) (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI)) (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI)) (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI)) (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI)) (* (* n 2) (* (cbrt PI) (cbrt PI))) (* (* n 2) (sqrt 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(sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) (/ 1 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) 1))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k 2)) 1 (* (/ k 2) 1)))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ 1 2) k))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ 1 2)) k (* (/ 1 2) k)))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (sqrt (/ k 2)) (sqrt (/ k 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (sqrt k) 2) (/ (sqrt k) 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ k 2) (/ 1 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ k 2) 1))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k 2)) 1 (* (/ k 2) 1)))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ 1 2) k))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ 1 2)) k (* (/ 1 2) k)))) (/ 1 (pow (* (* n 2) PI) 1/2)) (/ 1 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k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (sqrt k) 2) (/ (sqrt k) 1)))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ k 2) (/ 1 1)))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ k 2) 1))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ 1 2) k))))) (/ 1 (pow (* (* n 2) PI) 1/2)) (/ 1 (pow (* (* n 2) PI) 1/2)) (/ 1 (pow (* n 2) (- 1/2 (/ k 2)))) (/ 1 (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))) (/ 1 (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (/ 1 1) (/ 1 (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt 1)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (/ 1 (pow (* (* n 2) PI) 1/2)) (real->posit16 (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 3))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))))))) (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (+ (* 1/8 (/ (* (pow (log (* 2 PI)) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* k (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* (log n) k) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/4 (/ (* (log (* 2 PI)) (* (log n) (pow k 2))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (* 1/8 (/ (* (pow (log n) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))) (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 67.481 * * [simplify]: iteration 0: 2099 enodes 68.838 * * [simplify]: iteration complete: 5001 enodes 68.853 * * [simplify]: Extracting #0: cost 1417 inf + 0 68.864 * * [simplify]: Extracting #1: cost 2754 inf + 1 68.884 * * [simplify]: Extracting #2: cost 2848 inf + 4437 68.912 * * [simplify]: Extracting #3: cost 2643 inf + 73232 68.964 * * [simplify]: Extracting #4: cost 1692 inf + 516210 69.066 * * [simplify]: Extracting #5: cost 1283 inf + 777227 69.206 * * [simplify]: Extracting #6: cost 873 inf + 1099507 69.439 * * [simplify]: Extracting #7: cost 308 inf + 1635232 69.721 * * [simplify]: Extracting #8: cost 38 inf + 1911495 70.042 * * [simplify]: Extracting #9: cost 26 inf + 1926660 70.355 * * [simplify]: Extracting #10: cost 22 inf + 1931891 70.644 * * [simplify]: Extracting #11: cost 15 inf + 1931843 70.909 * * [simplify]: Extracting #12: cost 9 inf + 1934604 71.186 * * [simplify]: Extracting #13: cost 6 inf + 1936714 71.475 * * [simplify]: Extracting #14: cost 3 inf + 1939754 71.741 * * [simplify]: Extracting #15: cost 0 inf + 1943064 72.074 * * [simplify]: Extracting #16: cost 0 inf + 1942944 72.377 * [simplify]: Simplified to: (expm1 (* (* n 2) PI)) (log1p (* (* n 2) PI)) (* (* n 2) PI) (* (* n 2) PI) (log (* (* n 2) PI)) (log (* (* n 2) PI)) (log (* (* n 2) PI)) (exp (* (* n 2) PI)) (* (* (* n n) n) (* (* 2 (* 2 2)) (* (* PI PI) PI))) (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI)) (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI)) (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI)) (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI)) (* (* n 2) (* (cbrt PI) (cbrt PI))) (* (* n 2) (sqrt PI)) (* n 2) (* 2 PI) (real->posit16 (* (* n 2) PI)) (expm1 (* (/ (pow k (- 1/2)) 1) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (log1p (* (/ (pow k (- 1/2)) 1) (pow (* (* n 2) PI) (- 1/2 (/ k 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(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt 1)) (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (/ 1 (sqrt (* (* n 2) PI))) (real->posit16 (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (* 2 n) PI) (* (* 2 n) PI) (* (* 2 n) PI) (- (fma +nan.0 (* (sqrt 2) (* (* n PI) k)) (- (+ (* (* +nan.0 (sqrt 2)) (* n PI)) (- (fma +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* (* n PI) k))) (- (+ (* (* +nan.0 (sqrt 2)) (* (* n PI) (* (log n) k))) (- (* (* +nan.0 (sqrt 2)) (* (* n n) (* PI PI)))))))))))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (* k (* k k))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) k) (* (- +nan.0) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (* k k))))))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* k (* k k))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* k k)))))))) (- (fma 1/4 (* (* (log (* 2 PI)) (exp (* 1/2 (log (* (* n 2) PI))))) (* (log n) (* k k))) (fma 1/8 (* (* (exp (* 1/2 (log (* (* n 2) PI)))) (* (log n) (log n))) (* k k)) (+ (exp (* 1/2 (log (* (* n 2) PI)))) (* 1/8 (* (* (log (* 2 PI)) (log (* 2 PI))) (* (exp (* 1/2 (log (* (* n 2) PI)))) (* k k))))))) (* 1/2 (+ (* (exp (* 1/2 (log (* (* n 2) PI)))) (* (log n) k)) (* (log (* 2 PI)) (* (exp (* 1/2 (log (* (* n 2) PI)))) k))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (fma 1/8 (/ (* (* (log (* 2 PI)) (log (* 2 PI))) (* k k)) (exp (* 1/2 (log (* (* n 2) PI))))) (fma 1/2 (/ (* k (log (* 2 PI))) (exp (* 1/2 (log (* (* n 2) PI))))) (fma 1/2 (/ (* (log n) k) (exp (* 1/2 (log (* (* n 2) PI))))) (fma 1/4 (/ (log (* 2 PI)) (/ (exp (* 1/2 (log (* (* n 2) PI)))) (* (log n) (* k k)))) (+ (exp (- (* 1/2 (log (* (* n 2) PI))))) (* 1/8 (/ (* (log n) (log n)) (/ (exp (* 1/2 (log (* (* n 2) PI)))) (* k k))))))))) (exp (- (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n)))))) (exp (- (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 72.944 * * * [progress]: adding candidates to table 85.327 * [progress]: [Phase 3 of 3] Extracting. 85.327 * * [regime]: Finding splitpoints for: (# # # # #) 85.329 * * * [regime-changes]: Trying 2 branch expressions: (n k) 85.329 * * * * [regimes]: Trying to branch on n from (# # # # #) 85.381 * * * * [regimes]: Trying to branch on k from (# # # # #) 85.423 * * * [regime]: Found split indices: #