0.001 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.232 * * * [progress]: [2/2] Setting up program. 0.263 * [progress]: [Phase 2 of 3] Improving. 0.263 * * * * [progress]: [ 1 / 1 ] simplifiying candidate # 0.263 * [simplify]: Simplifying: (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 0.264 * * [simplify]: iteration 1: (13 enodes) 0.272 * * [simplify]: iteration 2: (57 enodes) 0.296 * * [simplify]: iteration 3: (102 enodes) 0.329 * * [simplify]: iteration 4: (189 enodes) 0.384 * * [simplify]: iteration 5: (376 enodes) 0.534 * * [simplify]: iteration 6: (949 enodes) 1.567 * * [simplify]: Extracting #0: cost 1 inf + 0 1.567 * * [simplify]: Extracting #1: cost 59 inf + 0 1.568 * * [simplify]: Extracting #2: cost 220 inf + 1 1.569 * * [simplify]: Extracting #3: cost 281 inf + 210 1.571 * * [simplify]: Extracting #4: cost 293 inf + 1056 1.575 * * [simplify]: Extracting #5: cost 217 inf + 10983 1.588 * * [simplify]: Extracting #6: cost 139 inf + 50407 1.620 * * [simplify]: Extracting #7: cost 26 inf + 145304 1.682 * * [simplify]: Extracting #8: cost 0 inf + 167058 1.730 * * [simplify]: Extracting #9: cost 0 inf + 165504 1.806 * * [simplify]: Extracting #10: cost 0 inf + 164849 1.874 * [simplify]: Simplified to: (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) 1.881 * * [progress]: iteration 1 / 4 1.881 * * * [progress]: picking best candidate 1.886 * * * * [pick]: Picked # 1.886 * * * [progress]: localizing error 1.919 * * * [progress]: generating rewritten candidates 1.919 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1) 1.950 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1) 1.976 * * * * [progress]: [ 3 / 3 ] rewriting at (2) 2.013 * * * [progress]: generating series expansions 2.013 * * * * [progress]: [ 1 / 3 ] generating series at (2 1) 2.014 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 2.014 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 2.014 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 2.014 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 2.014 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 2.014 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.014 * [taylor]: Taking taylor expansion of 1/2 in k 2.014 * [backup-simplify]: Simplify 1/2 into 1/2 2.014 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.014 * [taylor]: Taking taylor expansion of 1/2 in k 2.014 * [backup-simplify]: Simplify 1/2 into 1/2 2.014 * [taylor]: Taking taylor expansion of k in k 2.014 * [backup-simplify]: Simplify 0 into 0 2.014 * [backup-simplify]: Simplify 1 into 1 2.014 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 2.014 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 2.014 * [taylor]: Taking taylor expansion of 2 in k 2.014 * [backup-simplify]: Simplify 2 into 2 2.014 * [taylor]: Taking taylor expansion of (* n PI) in k 2.014 * [taylor]: Taking taylor expansion of n in k 2.014 * [backup-simplify]: Simplify n into n 2.014 * [taylor]: Taking taylor expansion of PI in k 2.014 * [backup-simplify]: Simplify PI into PI 2.014 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.014 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 2.014 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 2.014 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.015 * [backup-simplify]: Simplify (- 0) into 0 2.015 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.015 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 2.015 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 2.015 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.015 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.015 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.015 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.015 * [taylor]: Taking taylor expansion of 1/2 in n 2.015 * [backup-simplify]: Simplify 1/2 into 1/2 2.015 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.015 * [taylor]: Taking taylor expansion of 1/2 in n 2.015 * [backup-simplify]: Simplify 1/2 into 1/2 2.015 * [taylor]: Taking taylor expansion of k in n 2.015 * [backup-simplify]: Simplify k into k 2.015 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.015 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.015 * [taylor]: Taking taylor expansion of 2 in n 2.015 * [backup-simplify]: Simplify 2 into 2 2.015 * [taylor]: Taking taylor expansion of (* n PI) in n 2.015 * [taylor]: Taking taylor expansion of n in n 2.015 * [backup-simplify]: Simplify 0 into 0 2.015 * [backup-simplify]: Simplify 1 into 1 2.015 * [taylor]: Taking taylor expansion of PI in n 2.015 * [backup-simplify]: Simplify PI into PI 2.016 * [backup-simplify]: Simplify (* 0 PI) into 0 2.016 * [backup-simplify]: Simplify (* 2 0) into 0 2.017 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.018 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.018 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.018 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.018 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.019 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.020 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.020 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.021 * [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))))) 2.021 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.021 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.021 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.021 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.021 * [taylor]: Taking taylor expansion of 1/2 in n 2.021 * [backup-simplify]: Simplify 1/2 into 1/2 2.021 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.021 * [taylor]: Taking taylor expansion of 1/2 in n 2.021 * [backup-simplify]: Simplify 1/2 into 1/2 2.021 * [taylor]: Taking taylor expansion of k in n 2.021 * [backup-simplify]: Simplify k into k 2.021 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.021 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.021 * [taylor]: Taking taylor expansion of 2 in n 2.021 * [backup-simplify]: Simplify 2 into 2 2.021 * [taylor]: Taking taylor expansion of (* n PI) in n 2.021 * [taylor]: Taking taylor expansion of n in n 2.021 * [backup-simplify]: Simplify 0 into 0 2.021 * [backup-simplify]: Simplify 1 into 1 2.021 * [taylor]: Taking taylor expansion of PI in n 2.021 * [backup-simplify]: Simplify PI into PI 2.022 * [backup-simplify]: Simplify (* 0 PI) into 0 2.022 * [backup-simplify]: Simplify (* 2 0) into 0 2.023 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.024 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.024 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.024 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.024 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.024 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.025 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.026 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.027 * [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))))) 2.027 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 2.027 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 2.027 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.027 * [taylor]: Taking taylor expansion of 1/2 in k 2.027 * [backup-simplify]: Simplify 1/2 into 1/2 2.027 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.027 * [taylor]: Taking taylor expansion of 1/2 in k 2.027 * [backup-simplify]: Simplify 1/2 into 1/2 2.027 * [taylor]: Taking taylor expansion of k in k 2.027 * [backup-simplify]: Simplify 0 into 0 2.027 * [backup-simplify]: Simplify 1 into 1 2.027 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 2.027 * [taylor]: Taking taylor expansion of (log n) in k 2.027 * [taylor]: Taking taylor expansion of n in k 2.027 * [backup-simplify]: Simplify n into n 2.027 * [backup-simplify]: Simplify (log n) into (log n) 2.027 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.027 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.027 * [taylor]: Taking taylor expansion of 2 in k 2.027 * [backup-simplify]: Simplify 2 into 2 2.027 * [taylor]: Taking taylor expansion of PI in k 2.027 * [backup-simplify]: Simplify PI into PI 2.027 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.028 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.028 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.028 * [backup-simplify]: Simplify (- 0) into 0 2.029 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.029 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.030 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 2.031 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 2.031 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 2.032 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.033 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.034 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.034 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 2.034 * [backup-simplify]: Simplify (- 0) into 0 2.034 * [backup-simplify]: Simplify (+ 0 0) into 0 2.035 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.036 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 2.037 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.037 * [taylor]: Taking taylor expansion of 0 in k 2.037 * [backup-simplify]: Simplify 0 into 0 2.037 * [backup-simplify]: Simplify 0 into 0 2.037 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.038 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.039 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.039 * [backup-simplify]: Simplify (+ 0 0) into 0 2.039 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 2.040 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.040 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.041 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2.043 * [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))))))) 2.045 * [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))))))) 2.047 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.049 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.052 * [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 2.054 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 2.054 * [backup-simplify]: Simplify (- 0) into 0 2.054 * [backup-simplify]: Simplify (+ 0 0) into 0 2.056 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.057 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.059 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.059 * [taylor]: Taking taylor expansion of 0 in k 2.060 * [backup-simplify]: Simplify 0 into 0 2.060 * [backup-simplify]: Simplify 0 into 0 2.060 * [backup-simplify]: Simplify 0 into 0 2.070 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.071 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.074 * [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 2.075 * [backup-simplify]: Simplify (+ 0 0) into 0 2.076 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 2.076 * [backup-simplify]: Simplify (- 0) into 0 2.077 * [backup-simplify]: Simplify (+ 0 0) into 0 2.078 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.082 * [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))))) 2.087 * [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))))) 2.097 * [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))))) 2.098 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 2.098 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 2.098 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 2.098 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 2.098 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 2.098 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.098 * [taylor]: Taking taylor expansion of 1/2 in k 2.098 * [backup-simplify]: Simplify 1/2 into 1/2 2.098 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.098 * [taylor]: Taking taylor expansion of 1/2 in k 2.098 * [backup-simplify]: Simplify 1/2 into 1/2 2.098 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.098 * [taylor]: Taking taylor expansion of k in k 2.098 * [backup-simplify]: Simplify 0 into 0 2.098 * [backup-simplify]: Simplify 1 into 1 2.098 * [backup-simplify]: Simplify (/ 1 1) into 1 2.098 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 2.099 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 2.099 * [taylor]: Taking taylor expansion of 2 in k 2.099 * [backup-simplify]: Simplify 2 into 2 2.099 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.099 * [taylor]: Taking taylor expansion of PI in k 2.099 * [backup-simplify]: Simplify PI into PI 2.099 * [taylor]: Taking taylor expansion of n in k 2.099 * [backup-simplify]: Simplify n into n 2.099 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.099 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 2.099 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 2.099 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.100 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.100 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.100 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 2.101 * [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)))) 2.101 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.101 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.101 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.101 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.101 * [taylor]: Taking taylor expansion of 1/2 in n 2.101 * [backup-simplify]: Simplify 1/2 into 1/2 2.101 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.101 * [taylor]: Taking taylor expansion of 1/2 in n 2.101 * [backup-simplify]: Simplify 1/2 into 1/2 2.101 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.101 * [taylor]: Taking taylor expansion of k in n 2.101 * [backup-simplify]: Simplify k into k 2.101 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.101 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.101 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.101 * [taylor]: Taking taylor expansion of 2 in n 2.101 * [backup-simplify]: Simplify 2 into 2 2.101 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.101 * [taylor]: Taking taylor expansion of PI in n 2.101 * [backup-simplify]: Simplify PI into PI 2.101 * [taylor]: Taking taylor expansion of n in n 2.101 * [backup-simplify]: Simplify 0 into 0 2.101 * [backup-simplify]: Simplify 1 into 1 2.102 * [backup-simplify]: Simplify (/ PI 1) into PI 2.102 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.103 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.103 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.103 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.104 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.105 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.106 * [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))) 2.107 * [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)))) 2.107 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.107 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.107 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.107 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.107 * [taylor]: Taking taylor expansion of 1/2 in n 2.107 * [backup-simplify]: Simplify 1/2 into 1/2 2.107 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.107 * [taylor]: Taking taylor expansion of 1/2 in n 2.107 * [backup-simplify]: Simplify 1/2 into 1/2 2.107 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.107 * [taylor]: Taking taylor expansion of k in n 2.108 * [backup-simplify]: Simplify k into k 2.108 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.108 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.108 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.108 * [taylor]: Taking taylor expansion of 2 in n 2.108 * [backup-simplify]: Simplify 2 into 2 2.108 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.108 * [taylor]: Taking taylor expansion of PI in n 2.108 * [backup-simplify]: Simplify PI into PI 2.108 * [taylor]: Taking taylor expansion of n in n 2.108 * [backup-simplify]: Simplify 0 into 0 2.108 * [backup-simplify]: Simplify 1 into 1 2.108 * [backup-simplify]: Simplify (/ PI 1) into PI 2.109 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.110 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.110 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.110 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.110 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.111 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.113 * [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))) 2.114 * [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)))) 2.115 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 2.115 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 2.115 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.115 * [taylor]: Taking taylor expansion of 1/2 in k 2.115 * [backup-simplify]: Simplify 1/2 into 1/2 2.115 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.115 * [taylor]: Taking taylor expansion of 1/2 in k 2.115 * [backup-simplify]: Simplify 1/2 into 1/2 2.115 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.115 * [taylor]: Taking taylor expansion of k in k 2.115 * [backup-simplify]: Simplify 0 into 0 2.115 * [backup-simplify]: Simplify 1 into 1 2.115 * [backup-simplify]: Simplify (/ 1 1) into 1 2.115 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 2.115 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.115 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.115 * [taylor]: Taking taylor expansion of 2 in k 2.115 * [backup-simplify]: Simplify 2 into 2 2.115 * [taylor]: Taking taylor expansion of PI in k 2.115 * [backup-simplify]: Simplify PI into PI 2.116 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.117 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.117 * [taylor]: Taking taylor expansion of (log n) in k 2.117 * [taylor]: Taking taylor expansion of n in k 2.117 * [backup-simplify]: Simplify n into n 2.117 * [backup-simplify]: Simplify (log n) into (log n) 2.117 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.118 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.118 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.118 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.119 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 2.120 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 2.121 * [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)))) 2.123 * [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)))) 2.124 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.124 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.126 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.126 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.127 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.127 * [backup-simplify]: Simplify (- 0) into 0 2.127 * [backup-simplify]: Simplify (+ 0 0) into 0 2.129 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.130 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 2.132 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.132 * [taylor]: Taking taylor expansion of 0 in k 2.132 * [backup-simplify]: Simplify 0 into 0 2.132 * [backup-simplify]: Simplify 0 into 0 2.132 * [backup-simplify]: Simplify 0 into 0 2.133 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.135 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.138 * [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 2.138 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.139 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.140 * [backup-simplify]: Simplify (- 0) into 0 2.140 * [backup-simplify]: Simplify (+ 0 0) into 0 2.142 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.143 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 2.146 * [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 2.146 * [taylor]: Taking taylor expansion of 0 in k 2.146 * [backup-simplify]: Simplify 0 into 0 2.146 * [backup-simplify]: Simplify 0 into 0 2.146 * [backup-simplify]: Simplify 0 into 0 2.146 * [backup-simplify]: Simplify 0 into 0 2.147 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.148 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.154 * [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 2.155 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.155 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.156 * [backup-simplify]: Simplify (- 0) into 0 2.156 * [backup-simplify]: Simplify (+ 0 0) into 0 2.157 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.158 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 2.159 * [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 2.160 * [taylor]: Taking taylor expansion of 0 in k 2.160 * [backup-simplify]: Simplify 0 into 0 2.160 * [backup-simplify]: Simplify 0 into 0 2.160 * [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))))) 2.161 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 2.161 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 2.161 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 2.161 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 2.161 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 2.161 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.161 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.161 * [taylor]: Taking taylor expansion of 1/2 in k 2.161 * [backup-simplify]: Simplify 1/2 into 1/2 2.161 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.161 * [taylor]: Taking taylor expansion of k in k 2.161 * [backup-simplify]: Simplify 0 into 0 2.161 * [backup-simplify]: Simplify 1 into 1 2.161 * [backup-simplify]: Simplify (/ 1 1) into 1 2.161 * [taylor]: Taking taylor expansion of 1/2 in k 2.161 * [backup-simplify]: Simplify 1/2 into 1/2 2.161 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 2.161 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 2.161 * [taylor]: Taking taylor expansion of -2 in k 2.161 * [backup-simplify]: Simplify -2 into -2 2.161 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.161 * [taylor]: Taking taylor expansion of PI in k 2.161 * [backup-simplify]: Simplify PI into PI 2.162 * [taylor]: Taking taylor expansion of n in k 2.162 * [backup-simplify]: Simplify n into n 2.162 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.162 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 2.162 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 2.162 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.162 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.162 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 2.162 * [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))) 2.163 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.163 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.163 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.163 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.163 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.163 * [taylor]: Taking taylor expansion of 1/2 in n 2.163 * [backup-simplify]: Simplify 1/2 into 1/2 2.163 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.163 * [taylor]: Taking taylor expansion of k in n 2.163 * [backup-simplify]: Simplify k into k 2.163 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.163 * [taylor]: Taking taylor expansion of 1/2 in n 2.163 * [backup-simplify]: Simplify 1/2 into 1/2 2.163 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.163 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.163 * [taylor]: Taking taylor expansion of -2 in n 2.163 * [backup-simplify]: Simplify -2 into -2 2.163 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.163 * [taylor]: Taking taylor expansion of PI in n 2.163 * [backup-simplify]: Simplify PI into PI 2.163 * [taylor]: Taking taylor expansion of n in n 2.163 * [backup-simplify]: Simplify 0 into 0 2.163 * [backup-simplify]: Simplify 1 into 1 2.163 * [backup-simplify]: Simplify (/ PI 1) into PI 2.163 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.164 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.164 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.164 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.165 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.166 * [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))) 2.166 * [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)))) 2.166 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.166 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.166 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.166 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.166 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.166 * [taylor]: Taking taylor expansion of 1/2 in n 2.166 * [backup-simplify]: Simplify 1/2 into 1/2 2.167 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.167 * [taylor]: Taking taylor expansion of k in n 2.167 * [backup-simplify]: Simplify k into k 2.167 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.167 * [taylor]: Taking taylor expansion of 1/2 in n 2.167 * [backup-simplify]: Simplify 1/2 into 1/2 2.167 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.167 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.167 * [taylor]: Taking taylor expansion of -2 in n 2.167 * [backup-simplify]: Simplify -2 into -2 2.167 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.167 * [taylor]: Taking taylor expansion of PI in n 2.167 * [backup-simplify]: Simplify PI into PI 2.167 * [taylor]: Taking taylor expansion of n in n 2.167 * [backup-simplify]: Simplify 0 into 0 2.167 * [backup-simplify]: Simplify 1 into 1 2.167 * [backup-simplify]: Simplify (/ PI 1) into PI 2.167 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.168 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.168 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.168 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.169 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.170 * [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))) 2.170 * [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)))) 2.170 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.170 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.170 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.170 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.170 * [taylor]: Taking taylor expansion of 1/2 in k 2.170 * [backup-simplify]: Simplify 1/2 into 1/2 2.170 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.170 * [taylor]: Taking taylor expansion of k in k 2.170 * [backup-simplify]: Simplify 0 into 0 2.170 * [backup-simplify]: Simplify 1 into 1 2.171 * [backup-simplify]: Simplify (/ 1 1) into 1 2.171 * [taylor]: Taking taylor expansion of 1/2 in k 2.171 * [backup-simplify]: Simplify 1/2 into 1/2 2.171 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.171 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.171 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.171 * [taylor]: Taking taylor expansion of -2 in k 2.171 * [backup-simplify]: Simplify -2 into -2 2.171 * [taylor]: Taking taylor expansion of PI in k 2.171 * [backup-simplify]: Simplify PI into PI 2.171 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.172 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.172 * [taylor]: Taking taylor expansion of (log n) in k 2.172 * [taylor]: Taking taylor expansion of n in k 2.172 * [backup-simplify]: Simplify n into n 2.172 * [backup-simplify]: Simplify (log n) into (log n) 2.172 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.172 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.172 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.173 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.174 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 2.175 * [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)))) 2.175 * [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)))) 2.176 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.176 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.177 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.177 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.178 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.178 * [backup-simplify]: Simplify (+ 0 0) into 0 2.179 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.179 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.181 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.181 * [taylor]: Taking taylor expansion of 0 in k 2.181 * [backup-simplify]: Simplify 0 into 0 2.181 * [backup-simplify]: Simplify 0 into 0 2.181 * [backup-simplify]: Simplify 0 into 0 2.181 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.182 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.185 * [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 2.185 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.187 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.187 * [backup-simplify]: Simplify (+ 0 0) into 0 2.188 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.190 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.192 * [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 2.193 * [taylor]: Taking taylor expansion of 0 in k 2.193 * [backup-simplify]: Simplify 0 into 0 2.193 * [backup-simplify]: Simplify 0 into 0 2.193 * [backup-simplify]: Simplify 0 into 0 2.193 * [backup-simplify]: Simplify 0 into 0 2.194 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.197 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.204 * [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 2.204 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.205 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.206 * [backup-simplify]: Simplify (+ 0 0) into 0 2.207 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.209 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 2.212 * [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 2.212 * [taylor]: Taking taylor expansion of 0 in k 2.212 * [backup-simplify]: Simplify 0 into 0 2.212 * [backup-simplify]: Simplify 0 into 0 2.213 * [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))))) 2.213 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1) 2.214 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 2.214 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 2.214 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.214 * [taylor]: Taking taylor expansion of 2 in n 2.214 * [backup-simplify]: Simplify 2 into 2 2.214 * [taylor]: Taking taylor expansion of (* n PI) in n 2.214 * [taylor]: Taking taylor expansion of n in n 2.214 * [backup-simplify]: Simplify 0 into 0 2.214 * [backup-simplify]: Simplify 1 into 1 2.214 * [taylor]: Taking taylor expansion of PI in n 2.214 * [backup-simplify]: Simplify PI into PI 2.214 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.214 * [taylor]: Taking taylor expansion of 2 in n 2.214 * [backup-simplify]: Simplify 2 into 2 2.214 * [taylor]: Taking taylor expansion of (* n PI) in n 2.214 * [taylor]: Taking taylor expansion of n in n 2.214 * [backup-simplify]: Simplify 0 into 0 2.214 * [backup-simplify]: Simplify 1 into 1 2.214 * [taylor]: Taking taylor expansion of PI in n 2.214 * [backup-simplify]: Simplify PI into PI 2.215 * [backup-simplify]: Simplify (* 0 PI) into 0 2.215 * [backup-simplify]: Simplify (* 2 0) into 0 2.215 * [backup-simplify]: Simplify 0 into 0 2.217 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.218 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.218 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.219 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.220 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.220 * [backup-simplify]: Simplify 0 into 0 2.221 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.223 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.223 * [backup-simplify]: Simplify 0 into 0 2.223 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.225 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.225 * [backup-simplify]: Simplify 0 into 0 2.225 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.226 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.226 * [backup-simplify]: Simplify 0 into 0 2.227 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.228 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.228 * [backup-simplify]: Simplify 0 into 0 2.229 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.231 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.231 * [backup-simplify]: Simplify 0 into 0 2.231 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 2.231 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 2.231 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 2.231 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.231 * [taylor]: Taking taylor expansion of 2 in n 2.231 * [backup-simplify]: Simplify 2 into 2 2.231 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.231 * [taylor]: Taking taylor expansion of PI in n 2.231 * [backup-simplify]: Simplify PI into PI 2.231 * [taylor]: Taking taylor expansion of n in n 2.231 * [backup-simplify]: Simplify 0 into 0 2.231 * [backup-simplify]: Simplify 1 into 1 2.232 * [backup-simplify]: Simplify (/ PI 1) into PI 2.232 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.232 * [taylor]: Taking taylor expansion of 2 in n 2.232 * [backup-simplify]: Simplify 2 into 2 2.232 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.232 * [taylor]: Taking taylor expansion of PI in n 2.232 * [backup-simplify]: Simplify PI into PI 2.232 * [taylor]: Taking taylor expansion of n in n 2.232 * [backup-simplify]: Simplify 0 into 0 2.232 * [backup-simplify]: Simplify 1 into 1 2.232 * [backup-simplify]: Simplify (/ PI 1) into PI 2.233 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.233 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.233 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.234 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.234 * [backup-simplify]: Simplify 0 into 0 2.235 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.235 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.235 * [backup-simplify]: Simplify 0 into 0 2.236 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.237 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.237 * [backup-simplify]: Simplify 0 into 0 2.237 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.238 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.238 * [backup-simplify]: Simplify 0 into 0 2.239 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.240 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.240 * [backup-simplify]: Simplify 0 into 0 2.240 * [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 2.241 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.241 * [backup-simplify]: Simplify 0 into 0 2.242 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 2.242 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 2.242 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 2.242 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.242 * [taylor]: Taking taylor expansion of -2 in n 2.242 * [backup-simplify]: Simplify -2 into -2 2.242 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.242 * [taylor]: Taking taylor expansion of PI in n 2.242 * [backup-simplify]: Simplify PI into PI 2.242 * [taylor]: Taking taylor expansion of n in n 2.242 * [backup-simplify]: Simplify 0 into 0 2.242 * [backup-simplify]: Simplify 1 into 1 2.243 * [backup-simplify]: Simplify (/ PI 1) into PI 2.243 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.243 * [taylor]: Taking taylor expansion of -2 in n 2.243 * [backup-simplify]: Simplify -2 into -2 2.243 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.243 * [taylor]: Taking taylor expansion of PI in n 2.243 * [backup-simplify]: Simplify PI into PI 2.243 * [taylor]: Taking taylor expansion of n in n 2.243 * [backup-simplify]: Simplify 0 into 0 2.243 * [backup-simplify]: Simplify 1 into 1 2.243 * [backup-simplify]: Simplify (/ PI 1) into PI 2.243 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.244 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.244 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.245 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.245 * [backup-simplify]: Simplify 0 into 0 2.245 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.246 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.246 * [backup-simplify]: Simplify 0 into 0 2.247 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.247 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.247 * [backup-simplify]: Simplify 0 into 0 2.248 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.249 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.249 * [backup-simplify]: Simplify 0 into 0 2.249 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.250 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.250 * [backup-simplify]: Simplify 0 into 0 2.251 * [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 2.253 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.253 * [backup-simplify]: Simplify 0 into 0 2.254 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 2.254 * * * * [progress]: [ 3 / 3 ] generating series at (2) 2.254 * [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)))) 2.254 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 2.254 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 2.254 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.254 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.254 * [taylor]: Taking taylor expansion of k in k 2.254 * [backup-simplify]: Simplify 0 into 0 2.255 * [backup-simplify]: Simplify 1 into 1 2.255 * [backup-simplify]: Simplify (/ 1 1) into 1 2.255 * [backup-simplify]: Simplify (sqrt 0) into 0 2.257 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.257 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 2.257 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 2.257 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 2.257 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.257 * [taylor]: Taking taylor expansion of 1/2 in k 2.257 * [backup-simplify]: Simplify 1/2 into 1/2 2.257 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.257 * [taylor]: Taking taylor expansion of 1/2 in k 2.257 * [backup-simplify]: Simplify 1/2 into 1/2 2.257 * [taylor]: Taking taylor expansion of k in k 2.257 * [backup-simplify]: Simplify 0 into 0 2.257 * [backup-simplify]: Simplify 1 into 1 2.257 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 2.257 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 2.257 * [taylor]: Taking taylor expansion of 2 in k 2.257 * [backup-simplify]: Simplify 2 into 2 2.257 * [taylor]: Taking taylor expansion of (* n PI) in k 2.257 * [taylor]: Taking taylor expansion of n in k 2.257 * [backup-simplify]: Simplify n into n 2.257 * [taylor]: Taking taylor expansion of PI in k 2.257 * [backup-simplify]: Simplify PI into PI 2.258 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.258 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 2.258 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 2.258 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.259 * [backup-simplify]: Simplify (- 0) into 0 2.259 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.259 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 2.259 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 2.259 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.259 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.259 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.259 * [taylor]: Taking taylor expansion of k in n 2.259 * [backup-simplify]: Simplify k into k 2.260 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.260 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.260 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.260 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.260 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.260 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.260 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.260 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.260 * [taylor]: Taking taylor expansion of 1/2 in n 2.260 * [backup-simplify]: Simplify 1/2 into 1/2 2.260 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.260 * [taylor]: Taking taylor expansion of 1/2 in n 2.260 * [backup-simplify]: Simplify 1/2 into 1/2 2.260 * [taylor]: Taking taylor expansion of k in n 2.260 * [backup-simplify]: Simplify k into k 2.260 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.260 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.260 * [taylor]: Taking taylor expansion of 2 in n 2.260 * [backup-simplify]: Simplify 2 into 2 2.260 * [taylor]: Taking taylor expansion of (* n PI) in n 2.260 * [taylor]: Taking taylor expansion of n in n 2.260 * [backup-simplify]: Simplify 0 into 0 2.260 * [backup-simplify]: Simplify 1 into 1 2.260 * [taylor]: Taking taylor expansion of PI in n 2.260 * [backup-simplify]: Simplify PI into PI 2.261 * [backup-simplify]: Simplify (* 0 PI) into 0 2.261 * [backup-simplify]: Simplify (* 2 0) into 0 2.263 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.264 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.265 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.266 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.266 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.266 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.267 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.268 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.269 * [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))))) 2.269 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.270 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.270 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.270 * [taylor]: Taking taylor expansion of k in n 2.270 * [backup-simplify]: Simplify k into k 2.270 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.270 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.270 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.270 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.270 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.270 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.270 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.270 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.270 * [taylor]: Taking taylor expansion of 1/2 in n 2.270 * [backup-simplify]: Simplify 1/2 into 1/2 2.270 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.270 * [taylor]: Taking taylor expansion of 1/2 in n 2.270 * [backup-simplify]: Simplify 1/2 into 1/2 2.270 * [taylor]: Taking taylor expansion of k in n 2.270 * [backup-simplify]: Simplify k into k 2.270 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.270 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.270 * [taylor]: Taking taylor expansion of 2 in n 2.270 * [backup-simplify]: Simplify 2 into 2 2.270 * [taylor]: Taking taylor expansion of (* n PI) in n 2.270 * [taylor]: Taking taylor expansion of n in n 2.271 * [backup-simplify]: Simplify 0 into 0 2.271 * [backup-simplify]: Simplify 1 into 1 2.271 * [taylor]: Taking taylor expansion of PI in n 2.271 * [backup-simplify]: Simplify PI into PI 2.271 * [backup-simplify]: Simplify (* 0 PI) into 0 2.272 * [backup-simplify]: Simplify (* 2 0) into 0 2.273 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.275 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.276 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.276 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.276 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.276 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.277 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.279 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.280 * [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))))) 2.281 * [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))) 2.281 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 2.281 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 2.281 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 2.281 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.281 * [taylor]: Taking taylor expansion of 1/2 in k 2.281 * [backup-simplify]: Simplify 1/2 into 1/2 2.281 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.281 * [taylor]: Taking taylor expansion of 1/2 in k 2.281 * [backup-simplify]: Simplify 1/2 into 1/2 2.281 * [taylor]: Taking taylor expansion of k in k 2.281 * [backup-simplify]: Simplify 0 into 0 2.281 * [backup-simplify]: Simplify 1 into 1 2.281 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 2.281 * [taylor]: Taking taylor expansion of (log n) in k 2.281 * [taylor]: Taking taylor expansion of n in k 2.281 * [backup-simplify]: Simplify n into n 2.281 * [backup-simplify]: Simplify (log n) into (log n) 2.281 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.282 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.282 * [taylor]: Taking taylor expansion of 2 in k 2.282 * [backup-simplify]: Simplify 2 into 2 2.282 * [taylor]: Taking taylor expansion of PI in k 2.282 * [backup-simplify]: Simplify PI into PI 2.282 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.283 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.284 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.284 * [backup-simplify]: Simplify (- 0) into 0 2.285 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.286 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.287 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 2.288 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 2.288 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.288 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.288 * [taylor]: Taking taylor expansion of k in k 2.288 * [backup-simplify]: Simplify 0 into 0 2.288 * [backup-simplify]: Simplify 1 into 1 2.289 * [backup-simplify]: Simplify (/ 1 1) into 1 2.289 * [backup-simplify]: Simplify (sqrt 0) into 0 2.291 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.292 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 2.292 * [backup-simplify]: Simplify 0 into 0 2.293 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.294 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.296 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.296 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 2.297 * [backup-simplify]: Simplify (- 0) into 0 2.297 * [backup-simplify]: Simplify (+ 0 0) into 0 2.299 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.300 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 2.302 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.303 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 2.303 * [taylor]: Taking taylor expansion of 0 in k 2.303 * [backup-simplify]: Simplify 0 into 0 2.304 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.305 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.306 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.307 * [backup-simplify]: Simplify (+ 0 0) into 0 2.308 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 2.308 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.308 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.310 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2.313 * [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))))))) 2.317 * [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))))))) 2.318 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.319 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.320 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.324 * [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 2.325 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 2.326 * [backup-simplify]: Simplify (- 0) into 0 2.326 * [backup-simplify]: Simplify (+ 0 0) into 0 2.330 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.331 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.334 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.334 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.335 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 2.336 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 2.337 * [taylor]: Taking taylor expansion of 0 in k 2.337 * [backup-simplify]: Simplify 0 into 0 2.337 * [backup-simplify]: Simplify 0 into 0 2.337 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.341 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.342 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.343 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.347 * [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 2.347 * [backup-simplify]: Simplify (+ 0 0) into 0 2.348 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 2.348 * [backup-simplify]: Simplify (- 0) into 0 2.349 * [backup-simplify]: Simplify (+ 0 0) into 0 2.351 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.355 * [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))))) 2.364 * [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)))))))) 2.368 * [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)))))))) 2.370 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.371 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.377 * [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 2.378 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 2.379 * [backup-simplify]: Simplify (- 0) into 0 2.379 * [backup-simplify]: Simplify (+ 0 0) into 0 2.381 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.383 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.386 * [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 2.386 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.387 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 2.389 * [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 2.389 * [taylor]: Taking taylor expansion of 0 in k 2.389 * [backup-simplify]: Simplify 0 into 0 2.389 * [backup-simplify]: Simplify 0 into 0 2.389 * [backup-simplify]: Simplify 0 into 0 2.390 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.394 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.397 * [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 2.399 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.404 * [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 2.405 * [backup-simplify]: Simplify (+ 0 0) into 0 2.406 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 2.407 * [backup-simplify]: Simplify (- 0) into 0 2.407 * [backup-simplify]: Simplify (+ 0 0) into 0 2.409 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.414 * [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))))))) 2.423 * [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)))))))))))))) 2.430 * [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)))))))))))))) 2.442 * [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)))))))))))))))))))))) 2.445 * [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))))) 2.445 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 2.445 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 2.445 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.445 * [taylor]: Taking taylor expansion of k in k 2.445 * [backup-simplify]: Simplify 0 into 0 2.445 * [backup-simplify]: Simplify 1 into 1 2.446 * [backup-simplify]: Simplify (sqrt 0) into 0 2.447 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.447 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 2.447 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 2.447 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 2.447 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.448 * [taylor]: Taking taylor expansion of 1/2 in k 2.448 * [backup-simplify]: Simplify 1/2 into 1/2 2.448 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.448 * [taylor]: Taking taylor expansion of 1/2 in k 2.448 * [backup-simplify]: Simplify 1/2 into 1/2 2.448 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.448 * [taylor]: Taking taylor expansion of k in k 2.448 * [backup-simplify]: Simplify 0 into 0 2.448 * [backup-simplify]: Simplify 1 into 1 2.448 * [backup-simplify]: Simplify (/ 1 1) into 1 2.448 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 2.448 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 2.448 * [taylor]: Taking taylor expansion of 2 in k 2.448 * [backup-simplify]: Simplify 2 into 2 2.448 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.448 * [taylor]: Taking taylor expansion of PI in k 2.448 * [backup-simplify]: Simplify PI into PI 2.448 * [taylor]: Taking taylor expansion of n in k 2.448 * [backup-simplify]: Simplify n into n 2.448 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.449 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 2.449 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 2.449 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.449 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.450 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.450 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 2.450 * [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)))) 2.450 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.450 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.450 * [taylor]: Taking taylor expansion of k in n 2.450 * [backup-simplify]: Simplify k into k 2.450 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.450 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.450 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.451 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.451 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.451 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.451 * [taylor]: Taking taylor expansion of 1/2 in n 2.451 * [backup-simplify]: Simplify 1/2 into 1/2 2.451 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.451 * [taylor]: Taking taylor expansion of 1/2 in n 2.451 * [backup-simplify]: Simplify 1/2 into 1/2 2.451 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.451 * [taylor]: Taking taylor expansion of k in n 2.451 * [backup-simplify]: Simplify k into k 2.451 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.451 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.451 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.451 * [taylor]: Taking taylor expansion of 2 in n 2.451 * [backup-simplify]: Simplify 2 into 2 2.451 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.451 * [taylor]: Taking taylor expansion of PI in n 2.451 * [backup-simplify]: Simplify PI into PI 2.451 * [taylor]: Taking taylor expansion of n in n 2.451 * [backup-simplify]: Simplify 0 into 0 2.451 * [backup-simplify]: Simplify 1 into 1 2.452 * [backup-simplify]: Simplify (/ PI 1) into PI 2.452 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.453 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.453 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.453 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.453 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.455 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.456 * [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))) 2.457 * [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)))) 2.457 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.457 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.457 * [taylor]: Taking taylor expansion of k in n 2.457 * [backup-simplify]: Simplify k into k 2.457 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.457 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.457 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.457 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.457 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.457 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.457 * [taylor]: Taking taylor expansion of 1/2 in n 2.458 * [backup-simplify]: Simplify 1/2 into 1/2 2.458 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.458 * [taylor]: Taking taylor expansion of 1/2 in n 2.458 * [backup-simplify]: Simplify 1/2 into 1/2 2.458 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.458 * [taylor]: Taking taylor expansion of k in n 2.458 * [backup-simplify]: Simplify k into k 2.458 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.458 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.458 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.458 * [taylor]: Taking taylor expansion of 2 in n 2.458 * [backup-simplify]: Simplify 2 into 2 2.458 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.458 * [taylor]: Taking taylor expansion of PI in n 2.458 * [backup-simplify]: Simplify PI into PI 2.458 * [taylor]: Taking taylor expansion of n in n 2.458 * [backup-simplify]: Simplify 0 into 0 2.458 * [backup-simplify]: Simplify 1 into 1 2.458 * [backup-simplify]: Simplify (/ PI 1) into PI 2.459 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.460 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.460 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.460 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.460 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.462 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.463 * [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))) 2.464 * [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)))) 2.466 * [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)) 2.466 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 2.466 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 2.466 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 2.466 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.466 * [taylor]: Taking taylor expansion of 1/2 in k 2.466 * [backup-simplify]: Simplify 1/2 into 1/2 2.466 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.466 * [taylor]: Taking taylor expansion of 1/2 in k 2.466 * [backup-simplify]: Simplify 1/2 into 1/2 2.466 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.466 * [taylor]: Taking taylor expansion of k in k 2.466 * [backup-simplify]: Simplify 0 into 0 2.466 * [backup-simplify]: Simplify 1 into 1 2.467 * [backup-simplify]: Simplify (/ 1 1) into 1 2.467 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 2.467 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.467 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.467 * [taylor]: Taking taylor expansion of 2 in k 2.467 * [backup-simplify]: Simplify 2 into 2 2.467 * [taylor]: Taking taylor expansion of PI in k 2.467 * [backup-simplify]: Simplify PI into PI 2.467 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.468 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.468 * [taylor]: Taking taylor expansion of (log n) in k 2.468 * [taylor]: Taking taylor expansion of n in k 2.468 * [backup-simplify]: Simplify n into n 2.468 * [backup-simplify]: Simplify (log n) into (log n) 2.469 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.469 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.470 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.470 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.471 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 2.472 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 2.473 * [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)))) 2.473 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.473 * [taylor]: Taking taylor expansion of k in k 2.473 * [backup-simplify]: Simplify 0 into 0 2.473 * [backup-simplify]: Simplify 1 into 1 2.473 * [backup-simplify]: Simplify (sqrt 0) into 0 2.475 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.476 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 2.476 * [backup-simplify]: Simplify 0 into 0 2.477 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.478 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.479 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.480 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.480 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.480 * [backup-simplify]: Simplify (- 0) into 0 2.481 * [backup-simplify]: Simplify (+ 0 0) into 0 2.482 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.483 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 2.485 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.487 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 2.487 * [taylor]: Taking taylor expansion of 0 in k 2.487 * [backup-simplify]: Simplify 0 into 0 2.487 * [backup-simplify]: Simplify 0 into 0 2.488 * [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)))))) 2.490 * [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)))))) 2.491 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.492 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.495 * [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 2.495 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.497 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.497 * [backup-simplify]: Simplify (- 0) into 0 2.498 * [backup-simplify]: Simplify (+ 0 0) into 0 2.499 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.501 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 2.504 * [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 2.504 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 2.506 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 2.506 * [taylor]: Taking taylor expansion of 0 in k 2.506 * [backup-simplify]: Simplify 0 into 0 2.506 * [backup-simplify]: Simplify 0 into 0 2.506 * [backup-simplify]: Simplify 0 into 0 2.510 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.512 * [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)))))) 2.513 * [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)))))) 2.514 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.515 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.521 * [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 2.521 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.523 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.523 * [backup-simplify]: Simplify (- 0) into 0 2.524 * [backup-simplify]: Simplify (+ 0 0) into 0 2.525 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.527 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 2.530 * [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 2.531 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 2.533 * [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 2.533 * [taylor]: Taking taylor expansion of 0 in k 2.533 * [backup-simplify]: Simplify 0 into 0 2.533 * [backup-simplify]: Simplify 0 into 0 2.533 * [backup-simplify]: Simplify 0 into 0 2.533 * [backup-simplify]: Simplify 0 into 0 2.537 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.539 * [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)))))) 2.540 * [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)))))) 2.544 * [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)))))))) 2.545 * [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))) 2.545 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 2.545 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 2.545 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 2.545 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 2.545 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 2.545 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.545 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.545 * [taylor]: Taking taylor expansion of 1/2 in k 2.545 * [backup-simplify]: Simplify 1/2 into 1/2 2.545 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.545 * [taylor]: Taking taylor expansion of k in k 2.545 * [backup-simplify]: Simplify 0 into 0 2.546 * [backup-simplify]: Simplify 1 into 1 2.546 * [backup-simplify]: Simplify (/ 1 1) into 1 2.546 * [taylor]: Taking taylor expansion of 1/2 in k 2.546 * [backup-simplify]: Simplify 1/2 into 1/2 2.546 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 2.546 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 2.546 * [taylor]: Taking taylor expansion of -2 in k 2.546 * [backup-simplify]: Simplify -2 into -2 2.546 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.546 * [taylor]: Taking taylor expansion of PI in k 2.546 * [backup-simplify]: Simplify PI into PI 2.546 * [taylor]: Taking taylor expansion of n in k 2.547 * [backup-simplify]: Simplify n into n 2.547 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.547 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 2.547 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 2.547 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.548 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.548 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 2.548 * [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))) 2.548 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.548 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.548 * [taylor]: Taking taylor expansion of -1 in k 2.548 * [backup-simplify]: Simplify -1 into -1 2.548 * [taylor]: Taking taylor expansion of k in k 2.548 * [backup-simplify]: Simplify 0 into 0 2.548 * [backup-simplify]: Simplify 1 into 1 2.549 * [backup-simplify]: Simplify (/ -1 1) into -1 2.549 * [backup-simplify]: Simplify (sqrt 0) into 0 2.551 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.551 * [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)))) 2.551 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.551 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.551 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.551 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.551 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.551 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.551 * [taylor]: Taking taylor expansion of 1/2 in n 2.551 * [backup-simplify]: Simplify 1/2 into 1/2 2.551 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.551 * [taylor]: Taking taylor expansion of k in n 2.551 * [backup-simplify]: Simplify k into k 2.551 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.551 * [taylor]: Taking taylor expansion of 1/2 in n 2.551 * [backup-simplify]: Simplify 1/2 into 1/2 2.551 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.552 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.552 * [taylor]: Taking taylor expansion of -2 in n 2.552 * [backup-simplify]: Simplify -2 into -2 2.552 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.552 * [taylor]: Taking taylor expansion of PI in n 2.552 * [backup-simplify]: Simplify PI into PI 2.552 * [taylor]: Taking taylor expansion of n in n 2.552 * [backup-simplify]: Simplify 0 into 0 2.552 * [backup-simplify]: Simplify 1 into 1 2.552 * [backup-simplify]: Simplify (/ PI 1) into PI 2.553 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.554 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.554 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.554 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.555 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.556 * [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))) 2.558 * [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)))) 2.558 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.558 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.558 * [taylor]: Taking taylor expansion of -1 in n 2.558 * [backup-simplify]: Simplify -1 into -1 2.558 * [taylor]: Taking taylor expansion of k in n 2.558 * [backup-simplify]: Simplify k into k 2.558 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.558 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.558 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.558 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.559 * [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))) 2.559 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.560 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.560 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.560 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.560 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.560 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.560 * [taylor]: Taking taylor expansion of 1/2 in n 2.560 * [backup-simplify]: Simplify 1/2 into 1/2 2.560 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.560 * [taylor]: Taking taylor expansion of k in n 2.560 * [backup-simplify]: Simplify k into k 2.560 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.560 * [taylor]: Taking taylor expansion of 1/2 in n 2.560 * [backup-simplify]: Simplify 1/2 into 1/2 2.560 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.560 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.560 * [taylor]: Taking taylor expansion of -2 in n 2.560 * [backup-simplify]: Simplify -2 into -2 2.560 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.560 * [taylor]: Taking taylor expansion of PI in n 2.560 * [backup-simplify]: Simplify PI into PI 2.560 * [taylor]: Taking taylor expansion of n in n 2.560 * [backup-simplify]: Simplify 0 into 0 2.560 * [backup-simplify]: Simplify 1 into 1 2.561 * [backup-simplify]: Simplify (/ PI 1) into PI 2.561 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.562 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.562 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.562 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.564 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.565 * [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))) 2.566 * [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)))) 2.566 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.566 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.566 * [taylor]: Taking taylor expansion of -1 in n 2.566 * [backup-simplify]: Simplify -1 into -1 2.566 * [taylor]: Taking taylor expansion of k in n 2.566 * [backup-simplify]: Simplify k into k 2.566 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.566 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.566 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.567 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.568 * [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))) 2.568 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 2.568 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.568 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.568 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.568 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.568 * [taylor]: Taking taylor expansion of 1/2 in k 2.568 * [backup-simplify]: Simplify 1/2 into 1/2 2.568 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.568 * [taylor]: Taking taylor expansion of k in k 2.568 * [backup-simplify]: Simplify 0 into 0 2.568 * [backup-simplify]: Simplify 1 into 1 2.568 * [backup-simplify]: Simplify (/ 1 1) into 1 2.568 * [taylor]: Taking taylor expansion of 1/2 in k 2.569 * [backup-simplify]: Simplify 1/2 into 1/2 2.569 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.569 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.569 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.569 * [taylor]: Taking taylor expansion of -2 in k 2.569 * [backup-simplify]: Simplify -2 into -2 2.569 * [taylor]: Taking taylor expansion of PI in k 2.569 * [backup-simplify]: Simplify PI into PI 2.569 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.570 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.570 * [taylor]: Taking taylor expansion of (log n) in k 2.570 * [taylor]: Taking taylor expansion of n in k 2.570 * [backup-simplify]: Simplify n into n 2.570 * [backup-simplify]: Simplify (log n) into (log n) 2.570 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.571 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.571 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.572 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.573 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 2.574 * [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)))) 2.575 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.575 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.575 * [taylor]: Taking taylor expansion of -1 in k 2.575 * [backup-simplify]: Simplify -1 into -1 2.575 * [taylor]: Taking taylor expansion of k in k 2.575 * [backup-simplify]: Simplify 0 into 0 2.575 * [backup-simplify]: Simplify 1 into 1 2.575 * [backup-simplify]: Simplify (/ -1 1) into -1 2.576 * [backup-simplify]: Simplify (sqrt 0) into 0 2.577 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.578 * [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))))) 2.579 * [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))))) 2.580 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.581 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.583 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.583 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.584 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.584 * [backup-simplify]: Simplify (+ 0 0) into 0 2.586 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.587 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.589 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.590 * [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 2.590 * [taylor]: Taking taylor expansion of 0 in k 2.590 * [backup-simplify]: Simplify 0 into 0 2.590 * [backup-simplify]: Simplify 0 into 0 2.594 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.598 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.600 * [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)))))) 2.601 * [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)))))) 2.603 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.604 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.607 * [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 2.608 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.609 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.609 * [backup-simplify]: Simplify (+ 0 0) into 0 2.611 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.613 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.615 * [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 2.616 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.616 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 2.618 * [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 2.618 * [taylor]: Taking taylor expansion of 0 in k 2.618 * [backup-simplify]: Simplify 0 into 0 2.618 * [backup-simplify]: Simplify 0 into 0 2.618 * [backup-simplify]: Simplify 0 into 0 2.619 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.623 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.627 * [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)))))) 2.628 * [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)))))) 2.631 * [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))))))))))) 2.631 * * * [progress]: simplifying candidates 2.632 * * * * [progress]: [ 1 / 445 ] simplifiying candidate # 2.632 * * * * [progress]: [ 2 / 445 ] simplifiying candidate # 2.632 * * * * [progress]: [ 3 / 445 ] simplifiying candidate # 2.632 * * * * [progress]: [ 4 / 445 ] simplifiying candidate # 2.632 * * * * [progress]: [ 5 / 445 ] simplifiying candidate # 2.632 * * * * [progress]: [ 6 / 445 ] simplifiying candidate # 2.632 * * * * [progress]: [ 7 / 445 ] simplifiying candidate # 2.632 * * * * [progress]: [ 8 / 445 ] simplifiying candidate # 2.632 * * * * [progress]: [ 9 / 445 ] simplifiying candidate # 2.632 * * * * [progress]: [ 10 / 445 ] simplifiying candidate # 2.632 * * * * [progress]: [ 11 / 445 ] simplifiying candidate # 2.632 * * * * [progress]: [ 12 / 445 ] simplifiying candidate # 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candidate # 2.636 * * * * [progress]: [ 60 / 445 ] simplifiying candidate # 2.636 * * * * [progress]: [ 61 / 445 ] simplifiying candidate # 2.636 * * * * [progress]: [ 62 / 445 ] simplifiying candidate # 2.636 * * * * [progress]: [ 63 / 445 ] simplifiying candidate # 2.637 * * * * [progress]: [ 64 / 445 ] simplifiying candidate # 2.637 * * * * [progress]: [ 65 / 445 ] simplifiying candidate # 2.637 * * * * [progress]: [ 66 / 445 ] simplifiying candidate # 2.637 * * * * [progress]: [ 67 / 445 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))> 2.637 * * * * [progress]: [ 68 / 445 ] simplifiying candidate # 2.637 * * * * [progress]: [ 69 / 445 ] simplifiying candidate # 2.637 * * * * [progress]: [ 70 / 445 ] simplifiying candidate # 2.637 * * * * [progress]: [ 71 / 445 ] simplifiying candidate # 2.637 * * * * [progress]: [ 72 / 445 ] simplifiying candidate # 2.637 * * * * [progress]: [ 73 / 445 ] simplifiying candidate # 2.637 * * * * 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candidate # 2.638 * * * * [progress]: [ 89 / 445 ] simplifiying candidate # 2.638 * * * * [progress]: [ 90 / 445 ] simplifiying candidate # 2.638 * * * * [progress]: [ 91 / 445 ] simplifiying candidate # 2.638 * * * * [progress]: [ 92 / 445 ] simplifiying candidate # 2.638 * * * * [progress]: [ 93 / 445 ] simplifiying candidate # 2.638 * * * * [progress]: [ 94 / 445 ] simplifiying candidate # 2.639 * * * * [progress]: [ 95 / 445 ] simplifiying candidate # 2.639 * * * * [progress]: [ 96 / 445 ] simplifiying candidate # 2.639 * * * * [progress]: [ 97 / 445 ] simplifiying candidate # 2.639 * * * * [progress]: [ 98 / 445 ] simplifiying candidate # 2.639 * * * * [progress]: [ 99 / 445 ] simplifiying candidate # 2.639 * * * * [progress]: [ 100 / 445 ] simplifiying candidate # 2.639 * * * * [progress]: [ 101 / 445 ] simplifiying candidate # 2.639 * * * * [progress]: [ 102 / 445 ] simplifiying candidate # 2.639 * * * * [progress]: [ 103 / 445 ] simplifiying candidate # 2.639 * * * * 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(sqrt k) (sqrt 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* n (* 2 PI)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (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))))))) (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)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (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))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* n (* 2 PI)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (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)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (pow (* n (* 2 PI)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n (* 2 PI)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* n (* 2 PI)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) (pow (* n (* 2 PI)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) (pow (* n (* 2 PI)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (pow (* n (* 2 PI)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (pow (* n (* 2 PI)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 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(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)))))))))))))))))))))) (- (+ (* +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))))))))))) 2.688 * * [simplify]: iteration 1: (695 enodes) 3.052 * * [simplify]: Extracting #0: cost 311 inf + 0 3.055 * * [simplify]: Extracting #1: cost 891 inf + 1 3.060 * * [simplify]: Extracting #2: cost 1121 inf + 507 3.068 * * [simplify]: Extracting #3: cost 1217 inf + 6860 3.083 * * [simplify]: Extracting #4: cost 1073 inf + 44343 3.125 * * [simplify]: Extracting #5: cost 734 inf + 182333 3.215 * * [simplify]: Extracting #6: cost 370 inf + 395273 3.341 * * [simplify]: Extracting #7: cost 112 inf + 571810 3.445 * * [simplify]: Extracting #8: cost 70 inf + 607747 3.562 * * [simplify]: Extracting #9: cost 58 inf + 620041 3.649 * * [simplify]: Extracting #10: cost 55 inf + 626674 3.802 * * [simplify]: Extracting #11: cost 47 inf + 634260 3.927 * * [simplify]: Extracting #12: cost 34 inf + 642997 4.043 * * [simplify]: Extracting #13: cost 27 inf + 650279 4.170 * * [simplify]: Extracting #14: cost 17 inf + 663059 4.315 * * [simplify]: Extracting #15: cost 3 inf + 684783 4.444 * * [simplify]: Extracting #16: cost 0 inf + 689641 4.625 * [simplify]: Simplified to: (expm1 (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (log1p (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (/ k 2)) (pow (* (* PI 2) n) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* (* PI 2) n) (sqrt (- 1/2 (/ k 2)))) (* (* PI 2) n) (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* (* PI 2) n) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (* (* PI 2) n) (pow (* (* PI 2) n) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* (* PI 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(/ k 2))))) (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* (* PI 2) n) (- 1/4 (/ (/ k 2) 2)))) (* (pow (* (* PI 2) n) (/ k 2)) (sqrt k)) (real->posit16 (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))) (- (fma 1/4 (* (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))) (* (* k k) (log n))) (fma 1/8 (* (* (* (log n) (log n)) (* k k)) (exp (* 1/2 (log (* (* PI 2) n))))) (+ (* 1/8 (* (* (log (* PI 2)) (log (* PI 2))) (* (exp (* 1/2 (log (* (* PI 2) n)))) (* k k)))) (exp (* 1/2 (log (* (* PI 2) n))))))) (* 1/2 (+ (* (* (exp (* 1/2 (log (* (* PI 2) n)))) (log n)) k) (* (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))) k)))) (exp (* (- 1/2 (* k 1/2)) (- (log (* PI 2)) (- (log n))))) (exp (* (- 1/2 (* k 1/2)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (- (- (* +nan.0 (* (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))) (* (* k k) (log n)))) (- (* (* +nan.0 (log (* PI 2))) (* (exp (* 1/2 (log (* (* PI 2) n)))) (* k k))) (- (* (* (exp (* 1/2 (log (* (* PI 2) n)))) +nan.0) (* (* (log n) (log n)) (* k k))) (- (* (* (exp (* 1/2 (log (* (* PI 2) n)))) k) +nan.0) (- (* (exp (* 1/2 (log (* (* PI 2) n)))) +nan.0) (- (* +nan.0 (* (* (log (* PI 2)) (log (* PI 2))) (* (exp (* 1/2 (log (* (* PI 2) n)))) (* k k)))) (- (* (* (exp (* 1/2 (log (* (* PI 2) n)))) +nan.0) (* (* k k) (log n))) (- (* (* (exp (* 1/2 (log (* (* PI 2) n)))) +nan.0) (* k k)) (- (* (* (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))) k) +nan.0) (* +nan.0 (* (* (exp (* 1/2 (log (* (* PI 2) n)))) (log n)) k)))))))))))) (- (- (* +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)))) (- (- (* +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))) (* (exp (* (- 1/2 (* k 1/2)) (- (log (* -2 PI)) (log (/ -1 n))))) +nan.0)))) 4.733 * * * [progress]: adding candidates to table 11.625 * * [progress]: iteration 2 / 4 11.625 * * * [progress]: picking best candidate 11.648 * * * * [pick]: Picked # 11.648 * * * [progress]: localizing error 11.698 * * * [progress]: generating rewritten candidates 11.698 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 1) 11.719 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1) 11.732 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 11.775 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1) 12.215 * * * [progress]: generating series expansions 12.215 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 1) 12.216 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 12.216 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 12.216 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 12.216 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 12.216 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 12.216 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 12.216 * [taylor]: Taking taylor expansion of 1/2 in k 12.216 * [backup-simplify]: Simplify 1/2 into 1/2 12.216 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 12.216 * [taylor]: Taking taylor expansion of 1/2 in k 12.216 * [backup-simplify]: Simplify 1/2 into 1/2 12.216 * [taylor]: Taking taylor expansion of k in k 12.216 * [backup-simplify]: Simplify 0 into 0 12.216 * [backup-simplify]: Simplify 1 into 1 12.216 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 12.216 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 12.216 * [taylor]: Taking taylor expansion of 2 in k 12.216 * [backup-simplify]: Simplify 2 into 2 12.216 * [taylor]: Taking taylor expansion of (* n PI) in k 12.216 * [taylor]: Taking taylor expansion of n in k 12.216 * [backup-simplify]: Simplify n into n 12.216 * [taylor]: Taking taylor expansion of PI in k 12.216 * [backup-simplify]: Simplify PI into PI 12.216 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.216 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 12.217 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 12.217 * [backup-simplify]: Simplify (* 1/2 0) into 0 12.217 * [backup-simplify]: Simplify (- 0) into 0 12.217 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.217 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 12.218 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 12.218 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 12.218 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 12.218 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 12.218 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 12.218 * [taylor]: Taking taylor expansion of 1/2 in n 12.218 * [backup-simplify]: Simplify 1/2 into 1/2 12.218 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 12.218 * [taylor]: Taking taylor expansion of 1/2 in n 12.218 * [backup-simplify]: Simplify 1/2 into 1/2 12.218 * [taylor]: Taking taylor expansion of k in n 12.218 * [backup-simplify]: Simplify k into k 12.218 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 12.218 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.218 * [taylor]: Taking taylor expansion of 2 in n 12.218 * [backup-simplify]: Simplify 2 into 2 12.218 * [taylor]: Taking taylor expansion of (* n PI) in n 12.218 * [taylor]: Taking taylor expansion of n in n 12.218 * [backup-simplify]: Simplify 0 into 0 12.218 * [backup-simplify]: Simplify 1 into 1 12.218 * [taylor]: Taking taylor expansion of PI in n 12.218 * [backup-simplify]: Simplify PI into PI 12.218 * [backup-simplify]: Simplify (* 0 PI) into 0 12.218 * [backup-simplify]: Simplify (* 2 0) into 0 12.220 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.220 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.221 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.221 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 12.221 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 12.221 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 12.222 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.223 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 12.224 * [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))))) 12.224 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 12.224 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 12.224 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 12.224 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 12.224 * [taylor]: Taking taylor expansion of 1/2 in n 12.224 * [backup-simplify]: Simplify 1/2 into 1/2 12.224 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 12.224 * [taylor]: Taking taylor expansion of 1/2 in n 12.224 * [backup-simplify]: Simplify 1/2 into 1/2 12.224 * [taylor]: Taking taylor expansion of k in n 12.224 * [backup-simplify]: Simplify k into k 12.224 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 12.224 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.224 * [taylor]: Taking taylor expansion of 2 in n 12.224 * [backup-simplify]: Simplify 2 into 2 12.224 * [taylor]: Taking taylor expansion of (* n PI) in n 12.225 * [taylor]: Taking taylor expansion of n in n 12.225 * [backup-simplify]: Simplify 0 into 0 12.225 * [backup-simplify]: Simplify 1 into 1 12.225 * [taylor]: Taking taylor expansion of PI in n 12.225 * [backup-simplify]: Simplify PI into PI 12.225 * [backup-simplify]: Simplify (* 0 PI) into 0 12.225 * [backup-simplify]: Simplify (* 2 0) into 0 12.227 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.229 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.230 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.230 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 12.230 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 12.230 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 12.231 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.232 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 12.233 * [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))))) 12.234 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 12.234 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 12.234 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 12.234 * [taylor]: Taking taylor expansion of 1/2 in k 12.234 * [backup-simplify]: Simplify 1/2 into 1/2 12.234 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 12.234 * [taylor]: Taking taylor expansion of 1/2 in k 12.234 * [backup-simplify]: Simplify 1/2 into 1/2 12.234 * [taylor]: Taking taylor expansion of k in k 12.234 * [backup-simplify]: Simplify 0 into 0 12.234 * [backup-simplify]: Simplify 1 into 1 12.234 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 12.234 * [taylor]: Taking taylor expansion of (log n) in k 12.234 * [taylor]: Taking taylor expansion of n in k 12.234 * [backup-simplify]: Simplify n into n 12.234 * [backup-simplify]: Simplify (log n) into (log n) 12.234 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 12.234 * [taylor]: Taking taylor expansion of (* 2 PI) in k 12.234 * [taylor]: Taking taylor expansion of 2 in k 12.234 * [backup-simplify]: Simplify 2 into 2 12.234 * [taylor]: Taking taylor expansion of PI in k 12.234 * [backup-simplify]: Simplify PI into PI 12.235 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.236 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.236 * [backup-simplify]: Simplify (* 1/2 0) into 0 12.236 * [backup-simplify]: Simplify (- 0) into 0 12.237 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.238 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.239 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 12.240 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 12.241 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 12.242 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.243 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 12.245 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.246 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 12.246 * [backup-simplify]: Simplify (- 0) into 0 12.246 * [backup-simplify]: Simplify (+ 0 0) into 0 12.247 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.249 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 12.250 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.250 * [taylor]: Taking taylor expansion of 0 in k 12.250 * [backup-simplify]: Simplify 0 into 0 12.250 * [backup-simplify]: Simplify 0 into 0 12.251 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.252 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 12.253 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.254 * [backup-simplify]: Simplify (+ 0 0) into 0 12.254 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 12.255 * [backup-simplify]: Simplify (- 1/2) into -1/2 12.255 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 12.257 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 12.259 * [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))))))) 12.262 * [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))))))) 12.263 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.264 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.267 * [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 12.268 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 12.269 * [backup-simplify]: Simplify (- 0) into 0 12.269 * [backup-simplify]: Simplify (+ 0 0) into 0 12.270 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.272 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 12.274 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.274 * [taylor]: Taking taylor expansion of 0 in k 12.274 * [backup-simplify]: Simplify 0 into 0 12.274 * [backup-simplify]: Simplify 0 into 0 12.274 * [backup-simplify]: Simplify 0 into 0 12.276 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.277 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 12.280 * [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 12.280 * [backup-simplify]: Simplify (+ 0 0) into 0 12.281 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 12.281 * [backup-simplify]: Simplify (- 0) into 0 12.282 * [backup-simplify]: Simplify (+ 0 0) into 0 12.283 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 12.287 * [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))))) 12.291 * [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))))) 12.769 * [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))))) 12.770 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 12.770 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 12.770 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 12.770 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 12.770 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 12.770 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 12.770 * [taylor]: Taking taylor expansion of 1/2 in k 12.770 * [backup-simplify]: Simplify 1/2 into 1/2 12.770 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.770 * [taylor]: Taking taylor expansion of 1/2 in k 12.770 * [backup-simplify]: Simplify 1/2 into 1/2 12.770 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.770 * [taylor]: Taking taylor expansion of k in k 12.770 * [backup-simplify]: Simplify 0 into 0 12.770 * [backup-simplify]: Simplify 1 into 1 12.770 * [backup-simplify]: Simplify (/ 1 1) into 1 12.770 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 12.770 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 12.770 * [taylor]: Taking taylor expansion of 2 in k 12.770 * [backup-simplify]: Simplify 2 into 2 12.770 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.770 * [taylor]: Taking taylor expansion of PI in k 12.770 * [backup-simplify]: Simplify PI into PI 12.770 * [taylor]: Taking taylor expansion of n in k 12.770 * [backup-simplify]: Simplify n into n 12.770 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.771 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 12.771 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 12.771 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.771 * [backup-simplify]: Simplify (- 1/2) into -1/2 12.772 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 12.772 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 12.772 * [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)))) 12.772 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 12.772 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 12.772 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 12.772 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 12.772 * [taylor]: Taking taylor expansion of 1/2 in n 12.772 * [backup-simplify]: Simplify 1/2 into 1/2 12.772 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.772 * [taylor]: Taking taylor expansion of 1/2 in n 12.772 * [backup-simplify]: Simplify 1/2 into 1/2 12.772 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.772 * [taylor]: Taking taylor expansion of k in n 12.772 * [backup-simplify]: Simplify k into k 12.772 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.772 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.772 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.772 * [taylor]: Taking taylor expansion of 2 in n 12.772 * [backup-simplify]: Simplify 2 into 2 12.772 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.772 * [taylor]: Taking taylor expansion of PI in n 12.772 * [backup-simplify]: Simplify PI into PI 12.772 * [taylor]: Taking taylor expansion of n in n 12.772 * [backup-simplify]: Simplify 0 into 0 12.772 * [backup-simplify]: Simplify 1 into 1 12.772 * [backup-simplify]: Simplify (/ PI 1) into PI 12.773 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.773 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.773 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.774 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 12.774 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 12.774 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.775 * [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))) 12.776 * [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)))) 12.776 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 12.776 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 12.776 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 12.776 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 12.776 * [taylor]: Taking taylor expansion of 1/2 in n 12.776 * [backup-simplify]: Simplify 1/2 into 1/2 12.776 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.776 * [taylor]: Taking taylor expansion of 1/2 in n 12.776 * [backup-simplify]: Simplify 1/2 into 1/2 12.776 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.776 * [taylor]: Taking taylor expansion of k in n 12.776 * [backup-simplify]: Simplify k into k 12.776 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.776 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.776 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.776 * [taylor]: Taking taylor expansion of 2 in n 12.776 * [backup-simplify]: Simplify 2 into 2 12.776 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.776 * [taylor]: Taking taylor expansion of PI in n 12.776 * [backup-simplify]: Simplify PI into PI 12.776 * [taylor]: Taking taylor expansion of n in n 12.776 * [backup-simplify]: Simplify 0 into 0 12.776 * [backup-simplify]: Simplify 1 into 1 12.777 * [backup-simplify]: Simplify (/ PI 1) into PI 12.777 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.777 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.777 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.777 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 12.778 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 12.779 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.780 * [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))) 12.780 * [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)))) 12.780 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 12.780 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 12.780 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 12.780 * [taylor]: Taking taylor expansion of 1/2 in k 12.780 * [backup-simplify]: Simplify 1/2 into 1/2 12.780 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.780 * [taylor]: Taking taylor expansion of 1/2 in k 12.780 * [backup-simplify]: Simplify 1/2 into 1/2 12.780 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.780 * [taylor]: Taking taylor expansion of k in k 12.781 * [backup-simplify]: Simplify 0 into 0 12.781 * [backup-simplify]: Simplify 1 into 1 12.781 * [backup-simplify]: Simplify (/ 1 1) into 1 12.781 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 12.781 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 12.781 * [taylor]: Taking taylor expansion of (* 2 PI) in k 12.781 * [taylor]: Taking taylor expansion of 2 in k 12.781 * [backup-simplify]: Simplify 2 into 2 12.781 * [taylor]: Taking taylor expansion of PI in k 12.781 * [backup-simplify]: Simplify PI into PI 12.781 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.782 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.782 * [taylor]: Taking taylor expansion of (log n) in k 12.782 * [taylor]: Taking taylor expansion of n in k 12.782 * [backup-simplify]: Simplify n into n 12.782 * [backup-simplify]: Simplify (log n) into (log n) 12.782 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.782 * [backup-simplify]: Simplify (- 1/2) into -1/2 12.783 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 12.783 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.783 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 12.784 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 12.785 * [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)))) 12.785 * [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)))) 12.786 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.786 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 12.788 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.788 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.789 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 12.789 * [backup-simplify]: Simplify (- 0) into 0 12.790 * [backup-simplify]: Simplify (+ 0 0) into 0 12.791 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.792 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 12.794 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.794 * [taylor]: Taking taylor expansion of 0 in k 12.794 * [backup-simplify]: Simplify 0 into 0 12.794 * [backup-simplify]: Simplify 0 into 0 12.794 * [backup-simplify]: Simplify 0 into 0 12.795 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.796 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 12.800 * [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 12.800 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.801 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 12.801 * [backup-simplify]: Simplify (- 0) into 0 12.802 * [backup-simplify]: Simplify (+ 0 0) into 0 12.803 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.805 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 12.808 * [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 12.808 * [taylor]: Taking taylor expansion of 0 in k 12.808 * [backup-simplify]: Simplify 0 into 0 12.808 * [backup-simplify]: Simplify 0 into 0 12.808 * [backup-simplify]: Simplify 0 into 0 12.808 * [backup-simplify]: Simplify 0 into 0 12.809 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.810 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.816 * [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 12.816 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.817 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 12.818 * [backup-simplify]: Simplify (- 0) into 0 12.818 * [backup-simplify]: Simplify (+ 0 0) into 0 12.820 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.822 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 12.824 * [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 12.824 * [taylor]: Taking taylor expansion of 0 in k 12.824 * [backup-simplify]: Simplify 0 into 0 12.824 * [backup-simplify]: Simplify 0 into 0 12.826 * [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))))) 12.827 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 12.827 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 12.827 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 12.827 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 12.827 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 12.827 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 12.827 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.827 * [taylor]: Taking taylor expansion of 1/2 in k 12.827 * [backup-simplify]: Simplify 1/2 into 1/2 12.827 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.827 * [taylor]: Taking taylor expansion of k in k 12.827 * [backup-simplify]: Simplify 0 into 0 12.827 * [backup-simplify]: Simplify 1 into 1 12.827 * [backup-simplify]: Simplify (/ 1 1) into 1 12.827 * [taylor]: Taking taylor expansion of 1/2 in k 12.827 * [backup-simplify]: Simplify 1/2 into 1/2 12.827 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 12.827 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 12.827 * [taylor]: Taking taylor expansion of -2 in k 12.827 * [backup-simplify]: Simplify -2 into -2 12.828 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.828 * [taylor]: Taking taylor expansion of PI in k 12.828 * [backup-simplify]: Simplify PI into PI 12.828 * [taylor]: Taking taylor expansion of n in k 12.828 * [backup-simplify]: Simplify n into n 12.828 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.828 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 12.828 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 12.828 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.829 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.829 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 12.829 * [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))) 12.829 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.829 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 12.829 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 12.829 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.829 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.829 * [taylor]: Taking taylor expansion of 1/2 in n 12.829 * [backup-simplify]: Simplify 1/2 into 1/2 12.829 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.829 * [taylor]: Taking taylor expansion of k in n 12.829 * [backup-simplify]: Simplify k into k 12.830 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.830 * [taylor]: Taking taylor expansion of 1/2 in n 12.830 * [backup-simplify]: Simplify 1/2 into 1/2 12.830 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.830 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.830 * [taylor]: Taking taylor expansion of -2 in n 12.830 * [backup-simplify]: Simplify -2 into -2 12.830 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.830 * [taylor]: Taking taylor expansion of PI in n 12.830 * [backup-simplify]: Simplify PI into PI 12.830 * [taylor]: Taking taylor expansion of n in n 12.830 * [backup-simplify]: Simplify 0 into 0 12.830 * [backup-simplify]: Simplify 1 into 1 12.830 * [backup-simplify]: Simplify (/ PI 1) into PI 12.831 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.832 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.832 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.832 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.833 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.834 * [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))) 12.836 * [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)))) 12.836 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.836 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 12.836 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 12.836 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.836 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.836 * [taylor]: Taking taylor expansion of 1/2 in n 12.836 * [backup-simplify]: Simplify 1/2 into 1/2 12.836 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.836 * [taylor]: Taking taylor expansion of k in n 12.836 * [backup-simplify]: Simplify k into k 12.836 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.836 * [taylor]: Taking taylor expansion of 1/2 in n 12.836 * [backup-simplify]: Simplify 1/2 into 1/2 12.836 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.836 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.836 * [taylor]: Taking taylor expansion of -2 in n 12.836 * [backup-simplify]: Simplify -2 into -2 12.836 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.836 * [taylor]: Taking taylor expansion of PI in n 12.836 * [backup-simplify]: Simplify PI into PI 12.836 * [taylor]: Taking taylor expansion of n in n 12.836 * [backup-simplify]: Simplify 0 into 0 12.836 * [backup-simplify]: Simplify 1 into 1 12.837 * [backup-simplify]: Simplify (/ PI 1) into PI 12.837 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.838 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.838 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.839 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.840 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.841 * [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))) 12.842 * [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)))) 12.842 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 12.842 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 12.842 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 12.842 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.842 * [taylor]: Taking taylor expansion of 1/2 in k 12.843 * [backup-simplify]: Simplify 1/2 into 1/2 12.843 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.843 * [taylor]: Taking taylor expansion of k in k 12.843 * [backup-simplify]: Simplify 0 into 0 12.843 * [backup-simplify]: Simplify 1 into 1 12.843 * [backup-simplify]: Simplify (/ 1 1) into 1 12.843 * [taylor]: Taking taylor expansion of 1/2 in k 12.843 * [backup-simplify]: Simplify 1/2 into 1/2 12.843 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 12.843 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 12.843 * [taylor]: Taking taylor expansion of (* -2 PI) in k 12.843 * [taylor]: Taking taylor expansion of -2 in k 12.843 * [backup-simplify]: Simplify -2 into -2 12.843 * [taylor]: Taking taylor expansion of PI in k 12.843 * [backup-simplify]: Simplify PI into PI 12.844 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.845 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.845 * [taylor]: Taking taylor expansion of (log n) in k 12.845 * [taylor]: Taking taylor expansion of n in k 12.845 * [backup-simplify]: Simplify n into n 12.845 * [backup-simplify]: Simplify (log n) into (log n) 12.845 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.846 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.846 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.847 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 12.848 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 12.849 * [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)))) 12.850 * [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)))) 12.851 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.852 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 12.853 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 12.853 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.853 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 12.853 * [backup-simplify]: Simplify (+ 0 0) into 0 12.854 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.855 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 12.856 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.856 * [taylor]: Taking taylor expansion of 0 in k 12.856 * [backup-simplify]: Simplify 0 into 0 12.856 * [backup-simplify]: Simplify 0 into 0 12.856 * [backup-simplify]: Simplify 0 into 0 12.857 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.858 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 12.860 * [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 12.860 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.860 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 12.860 * [backup-simplify]: Simplify (+ 0 0) into 0 12.861 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.862 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 12.864 * [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 12.864 * [taylor]: Taking taylor expansion of 0 in k 12.864 * [backup-simplify]: Simplify 0 into 0 12.864 * [backup-simplify]: Simplify 0 into 0 12.864 * [backup-simplify]: Simplify 0 into 0 12.864 * [backup-simplify]: Simplify 0 into 0 12.864 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.865 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.868 * [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 12.869 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.869 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 12.870 * [backup-simplify]: Simplify (+ 0 0) into 0 12.871 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.872 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 12.873 * [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 12.873 * [taylor]: Taking taylor expansion of 0 in k 12.873 * [backup-simplify]: Simplify 0 into 0 12.873 * [backup-simplify]: Simplify 0 into 0 12.874 * [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))))) 12.874 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1) 12.875 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 12.875 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 12.875 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.875 * [taylor]: Taking taylor expansion of 2 in n 12.875 * [backup-simplify]: Simplify 2 into 2 12.875 * [taylor]: Taking taylor expansion of (* n PI) in n 12.875 * [taylor]: Taking taylor expansion of n in n 12.875 * [backup-simplify]: Simplify 0 into 0 12.875 * [backup-simplify]: Simplify 1 into 1 12.875 * [taylor]: Taking taylor expansion of PI in n 12.875 * [backup-simplify]: Simplify PI into PI 12.875 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.875 * [taylor]: Taking taylor expansion of 2 in n 12.875 * [backup-simplify]: Simplify 2 into 2 12.875 * [taylor]: Taking taylor expansion of (* n PI) in n 12.875 * [taylor]: Taking taylor expansion of n in n 12.875 * [backup-simplify]: Simplify 0 into 0 12.875 * [backup-simplify]: Simplify 1 into 1 12.875 * [taylor]: Taking taylor expansion of PI in n 12.875 * [backup-simplify]: Simplify PI into PI 12.875 * [backup-simplify]: Simplify (* 0 PI) into 0 12.875 * [backup-simplify]: Simplify (* 2 0) into 0 12.875 * [backup-simplify]: Simplify 0 into 0 12.876 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.877 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.878 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.878 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.879 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 12.879 * [backup-simplify]: Simplify 0 into 0 12.880 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.882 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.882 * [backup-simplify]: Simplify 0 into 0 12.886 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.888 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 12.888 * [backup-simplify]: Simplify 0 into 0 12.890 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.891 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 12.891 * [backup-simplify]: Simplify 0 into 0 12.893 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.894 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 12.895 * [backup-simplify]: Simplify 0 into 0 12.896 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 12.897 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 12.897 * [backup-simplify]: Simplify 0 into 0 12.897 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 12.897 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 12.897 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 12.897 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.897 * [taylor]: Taking taylor expansion of 2 in n 12.897 * [backup-simplify]: Simplify 2 into 2 12.897 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.897 * [taylor]: Taking taylor expansion of PI in n 12.897 * [backup-simplify]: Simplify PI into PI 12.897 * [taylor]: Taking taylor expansion of n in n 12.897 * [backup-simplify]: Simplify 0 into 0 12.897 * [backup-simplify]: Simplify 1 into 1 12.898 * [backup-simplify]: Simplify (/ PI 1) into PI 12.898 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.898 * [taylor]: Taking taylor expansion of 2 in n 12.898 * [backup-simplify]: Simplify 2 into 2 12.898 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.898 * [taylor]: Taking taylor expansion of PI in n 12.898 * [backup-simplify]: Simplify PI into PI 12.898 * [taylor]: Taking taylor expansion of n in n 12.898 * [backup-simplify]: Simplify 0 into 0 12.898 * [backup-simplify]: Simplify 1 into 1 12.898 * [backup-simplify]: Simplify (/ PI 1) into PI 12.899 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.899 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.899 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.900 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 12.900 * [backup-simplify]: Simplify 0 into 0 12.900 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.901 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 12.901 * [backup-simplify]: Simplify 0 into 0 12.902 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.902 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.902 * [backup-simplify]: Simplify 0 into 0 12.903 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.904 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.904 * [backup-simplify]: Simplify 0 into 0 12.904 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.905 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.905 * [backup-simplify]: Simplify 0 into 0 12.906 * [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 12.907 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.907 * [backup-simplify]: Simplify 0 into 0 12.907 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 12.907 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 12.907 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 12.907 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.907 * [taylor]: Taking taylor expansion of -2 in n 12.908 * [backup-simplify]: Simplify -2 into -2 12.908 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.908 * [taylor]: Taking taylor expansion of PI in n 12.908 * [backup-simplify]: Simplify PI into PI 12.908 * [taylor]: Taking taylor expansion of n in n 12.908 * [backup-simplify]: Simplify 0 into 0 12.908 * [backup-simplify]: Simplify 1 into 1 12.908 * [backup-simplify]: Simplify (/ PI 1) into PI 12.908 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.908 * [taylor]: Taking taylor expansion of -2 in n 12.908 * [backup-simplify]: Simplify -2 into -2 12.908 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.908 * [taylor]: Taking taylor expansion of PI in n 12.908 * [backup-simplify]: Simplify PI into PI 12.908 * [taylor]: Taking taylor expansion of n in n 12.908 * [backup-simplify]: Simplify 0 into 0 12.908 * [backup-simplify]: Simplify 1 into 1 12.908 * [backup-simplify]: Simplify (/ PI 1) into PI 12.909 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.909 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.909 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.910 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 12.910 * [backup-simplify]: Simplify 0 into 0 12.910 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.911 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 12.911 * [backup-simplify]: Simplify 0 into 0 12.912 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.912 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.912 * [backup-simplify]: Simplify 0 into 0 12.913 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.914 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.914 * [backup-simplify]: Simplify 0 into 0 12.915 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.915 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.916 * [backup-simplify]: Simplify 0 into 0 12.916 * [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 12.917 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.917 * [backup-simplify]: Simplify 0 into 0 12.917 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 12.918 * * * * [progress]: [ 3 / 4 ] generating series at (2) 12.918 * [backup-simplify]: Simplify (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))) into (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) 12.918 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in (n k) around 0 12.918 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 12.918 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 12.918 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 12.918 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 12.918 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 12.918 * [taylor]: Taking taylor expansion of 1/2 in k 12.918 * [backup-simplify]: Simplify 1/2 into 1/2 12.918 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 12.918 * [taylor]: Taking taylor expansion of 1/2 in k 12.918 * [backup-simplify]: Simplify 1/2 into 1/2 12.918 * [taylor]: Taking taylor expansion of k in k 12.918 * [backup-simplify]: Simplify 0 into 0 12.918 * [backup-simplify]: Simplify 1 into 1 12.918 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 12.918 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 12.918 * [taylor]: Taking taylor expansion of 2 in k 12.918 * [backup-simplify]: Simplify 2 into 2 12.918 * [taylor]: Taking taylor expansion of (* n PI) in k 12.918 * [taylor]: Taking taylor expansion of n in k 12.918 * [backup-simplify]: Simplify n into n 12.918 * [taylor]: Taking taylor expansion of PI in k 12.919 * [backup-simplify]: Simplify PI into PI 12.919 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.919 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 12.919 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 12.919 * [backup-simplify]: Simplify (* 1/2 0) into 0 12.919 * [backup-simplify]: Simplify (- 0) into 0 12.919 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.920 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 12.920 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 12.920 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.920 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.920 * [taylor]: Taking taylor expansion of k in k 12.920 * [backup-simplify]: Simplify 0 into 0 12.920 * [backup-simplify]: Simplify 1 into 1 12.920 * [backup-simplify]: Simplify (/ 1 1) into 1 12.920 * [backup-simplify]: Simplify (sqrt 0) into 0 12.921 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.921 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 12.921 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 12.921 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 12.921 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 12.921 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 12.921 * [taylor]: Taking taylor expansion of 1/2 in n 12.921 * [backup-simplify]: Simplify 1/2 into 1/2 12.921 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 12.921 * [taylor]: Taking taylor expansion of 1/2 in n 12.921 * [backup-simplify]: Simplify 1/2 into 1/2 12.921 * [taylor]: Taking taylor expansion of k in n 12.921 * [backup-simplify]: Simplify k into k 12.921 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 12.921 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.921 * [taylor]: Taking taylor expansion of 2 in n 12.921 * [backup-simplify]: Simplify 2 into 2 12.921 * [taylor]: Taking taylor expansion of (* n PI) in n 12.921 * [taylor]: Taking taylor expansion of n in n 12.921 * [backup-simplify]: Simplify 0 into 0 12.921 * [backup-simplify]: Simplify 1 into 1 12.921 * [taylor]: Taking taylor expansion of PI in n 12.921 * [backup-simplify]: Simplify PI into PI 12.922 * [backup-simplify]: Simplify (* 0 PI) into 0 12.922 * [backup-simplify]: Simplify (* 2 0) into 0 12.923 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.924 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.924 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.924 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 12.924 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 12.925 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 12.925 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.926 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 12.927 * [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))))) 12.927 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 12.927 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.927 * [taylor]: Taking taylor expansion of k in n 12.927 * [backup-simplify]: Simplify k into k 12.927 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.927 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 12.927 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.927 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 12.927 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 12.927 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 12.927 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 12.927 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 12.927 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 12.927 * [taylor]: Taking taylor expansion of 1/2 in n 12.927 * [backup-simplify]: Simplify 1/2 into 1/2 12.927 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 12.927 * [taylor]: Taking taylor expansion of 1/2 in n 12.927 * [backup-simplify]: Simplify 1/2 into 1/2 12.927 * [taylor]: Taking taylor expansion of k in n 12.927 * [backup-simplify]: Simplify k into k 12.927 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 12.927 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.927 * [taylor]: Taking taylor expansion of 2 in n 12.927 * [backup-simplify]: Simplify 2 into 2 12.927 * [taylor]: Taking taylor expansion of (* n PI) in n 12.927 * [taylor]: Taking taylor expansion of n in n 12.927 * [backup-simplify]: Simplify 0 into 0 12.927 * [backup-simplify]: Simplify 1 into 1 12.927 * [taylor]: Taking taylor expansion of PI in n 12.927 * [backup-simplify]: Simplify PI into PI 12.928 * [backup-simplify]: Simplify (* 0 PI) into 0 12.928 * [backup-simplify]: Simplify (* 2 0) into 0 12.929 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.930 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.930 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.930 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 12.930 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 12.931 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 12.932 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.932 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 12.933 * [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))))) 12.933 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 12.933 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.933 * [taylor]: Taking taylor expansion of k in n 12.933 * [backup-simplify]: Simplify k into k 12.933 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.933 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 12.933 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.933 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 12.934 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) into (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 12.934 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k 12.934 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.934 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.934 * [taylor]: Taking taylor expansion of k in k 12.934 * [backup-simplify]: Simplify 0 into 0 12.934 * [backup-simplify]: Simplify 1 into 1 12.934 * [backup-simplify]: Simplify (/ 1 1) into 1 12.934 * [backup-simplify]: Simplify (sqrt 0) into 0 12.935 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.935 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 12.936 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 12.936 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 12.936 * [taylor]: Taking taylor expansion of 1/2 in k 12.936 * [backup-simplify]: Simplify 1/2 into 1/2 12.936 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 12.936 * [taylor]: Taking taylor expansion of 1/2 in k 12.936 * [backup-simplify]: Simplify 1/2 into 1/2 12.936 * [taylor]: Taking taylor expansion of k in k 12.936 * [backup-simplify]: Simplify 0 into 0 12.936 * [backup-simplify]: Simplify 1 into 1 12.936 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 12.936 * [taylor]: Taking taylor expansion of (log n) in k 12.936 * [taylor]: Taking taylor expansion of n in k 12.936 * [backup-simplify]: Simplify n into n 12.936 * [backup-simplify]: Simplify (log n) into (log n) 12.936 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 12.936 * [taylor]: Taking taylor expansion of (* 2 PI) in k 12.936 * [taylor]: Taking taylor expansion of 2 in k 12.936 * [backup-simplify]: Simplify 2 into 2 12.936 * [taylor]: Taking taylor expansion of PI in k 12.936 * [backup-simplify]: Simplify PI into PI 12.936 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.937 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.937 * [backup-simplify]: Simplify (* 1/2 0) into 0 12.937 * [backup-simplify]: Simplify (- 0) into 0 12.938 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.938 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.939 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 12.940 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 12.940 * [backup-simplify]: Simplify (* 0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) into 0 12.940 * [backup-simplify]: Simplify 0 into 0 12.941 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.941 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 12.942 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.943 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 12.943 * [backup-simplify]: Simplify (- 0) into 0 12.943 * [backup-simplify]: Simplify (+ 0 0) into 0 12.944 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.945 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 12.946 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.947 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 0) (* 0 (sqrt (/ 1 k)))) into 0 12.947 * [taylor]: Taking taylor expansion of 0 in k 12.947 * [backup-simplify]: Simplify 0 into 0 12.947 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.947 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 12.948 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.949 * [backup-simplify]: Simplify (+ 0 0) into 0 12.949 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 12.949 * [backup-simplify]: Simplify (- 1/2) into -1/2 12.950 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 12.951 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 12.952 * [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))))))) 12.955 * [backup-simplify]: Simplify (+ (* 0 (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 12.956 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 12.956 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.957 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 12.958 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.959 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.962 * [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 12.963 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 12.964 * [backup-simplify]: Simplify (- 0) into 0 12.964 * [backup-simplify]: Simplify (+ 0 0) into 0 12.965 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.967 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 12.969 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.971 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 12.971 * [taylor]: Taking taylor expansion of 0 in k 12.971 * [backup-simplify]: Simplify 0 into 0 12.971 * [backup-simplify]: Simplify 0 into 0 12.973 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.974 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 12.977 * [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 12.978 * [backup-simplify]: Simplify (+ 0 0) into 0 12.979 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 12.979 * [backup-simplify]: Simplify (- 0) into 0 12.979 * [backup-simplify]: Simplify (+ 0 0) into 0 12.981 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 12.985 * [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))))) 12.986 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 12.990 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.995 * [backup-simplify]: Simplify (+ (* 0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))) (+ (* +nan.0 (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))) 12.998 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 12.998 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.999 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 13.000 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.001 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 13.004 * [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 13.005 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 13.005 * [backup-simplify]: Simplify (- 0) into 0 13.005 * [backup-simplify]: Simplify (+ 0 0) into 0 13.006 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.007 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 13.009 * [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 13.010 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 13.010 * [taylor]: Taking taylor expansion of 0 in k 13.010 * [backup-simplify]: Simplify 0 into 0 13.010 * [backup-simplify]: Simplify 0 into 0 13.010 * [backup-simplify]: Simplify 0 into 0 13.012 * [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 13.012 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.016 * [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 13.017 * [backup-simplify]: Simplify (+ 0 0) into 0 13.018 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 13.019 * [backup-simplify]: Simplify (- 0) into 0 13.019 * [backup-simplify]: Simplify (+ 0 0) into 0 13.021 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 13.027 * [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))))))) 13.028 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.033 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.049 * [backup-simplify]: Simplify (+ (* 0 (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))) (+ (* +nan.0 (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))))))))))))) 13.061 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 13.077 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) 13.078 * [backup-simplify]: Simplify (/ (/ (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) into (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 13.078 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (n k) around 0 13.078 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 13.078 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 13.078 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 13.078 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 13.078 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 13.078 * [taylor]: Taking taylor expansion of 1/2 in k 13.078 * [backup-simplify]: Simplify 1/2 into 1/2 13.078 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.078 * [taylor]: Taking taylor expansion of 1/2 in k 13.078 * [backup-simplify]: Simplify 1/2 into 1/2 13.078 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.078 * [taylor]: Taking taylor expansion of k in k 13.078 * [backup-simplify]: Simplify 0 into 0 13.078 * [backup-simplify]: Simplify 1 into 1 13.078 * [backup-simplify]: Simplify (/ 1 1) into 1 13.078 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 13.078 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 13.078 * [taylor]: Taking taylor expansion of 2 in k 13.078 * [backup-simplify]: Simplify 2 into 2 13.078 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.078 * [taylor]: Taking taylor expansion of PI in k 13.078 * [backup-simplify]: Simplify PI into PI 13.078 * [taylor]: Taking taylor expansion of n in k 13.078 * [backup-simplify]: Simplify n into n 13.078 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.078 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 13.078 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 13.079 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.079 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.079 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.079 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 13.079 * [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)))) 13.079 * [taylor]: Taking taylor expansion of (sqrt k) in k 13.079 * [taylor]: Taking taylor expansion of k in k 13.080 * [backup-simplify]: Simplify 0 into 0 13.080 * [backup-simplify]: Simplify 1 into 1 13.080 * [backup-simplify]: Simplify (sqrt 0) into 0 13.081 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.081 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 13.081 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 13.081 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 13.081 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 13.081 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 13.081 * [taylor]: Taking taylor expansion of 1/2 in n 13.081 * [backup-simplify]: Simplify 1/2 into 1/2 13.081 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.081 * [taylor]: Taking taylor expansion of 1/2 in n 13.081 * [backup-simplify]: Simplify 1/2 into 1/2 13.081 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.081 * [taylor]: Taking taylor expansion of k in n 13.081 * [backup-simplify]: Simplify k into k 13.081 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.081 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 13.081 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.081 * [taylor]: Taking taylor expansion of 2 in n 13.081 * [backup-simplify]: Simplify 2 into 2 13.081 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.081 * [taylor]: Taking taylor expansion of PI in n 13.081 * [backup-simplify]: Simplify PI into PI 13.081 * [taylor]: Taking taylor expansion of n in n 13.081 * [backup-simplify]: Simplify 0 into 0 13.081 * [backup-simplify]: Simplify 1 into 1 13.081 * [backup-simplify]: Simplify (/ PI 1) into PI 13.082 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.082 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.082 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.082 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 13.083 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 13.084 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.084 * [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))) 13.085 * [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)))) 13.085 * [taylor]: Taking taylor expansion of (sqrt k) in n 13.085 * [taylor]: Taking taylor expansion of k in n 13.085 * [backup-simplify]: Simplify k into k 13.085 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 13.085 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 13.085 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 13.085 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 13.085 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 13.085 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 13.085 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 13.085 * [taylor]: Taking taylor expansion of 1/2 in n 13.085 * [backup-simplify]: Simplify 1/2 into 1/2 13.085 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.085 * [taylor]: Taking taylor expansion of 1/2 in n 13.085 * [backup-simplify]: Simplify 1/2 into 1/2 13.085 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.085 * [taylor]: Taking taylor expansion of k in n 13.085 * [backup-simplify]: Simplify k into k 13.085 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.085 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 13.085 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.085 * [taylor]: Taking taylor expansion of 2 in n 13.085 * [backup-simplify]: Simplify 2 into 2 13.085 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.085 * [taylor]: Taking taylor expansion of PI in n 13.085 * [backup-simplify]: Simplify PI into PI 13.085 * [taylor]: Taking taylor expansion of n in n 13.085 * [backup-simplify]: Simplify 0 into 0 13.085 * [backup-simplify]: Simplify 1 into 1 13.086 * [backup-simplify]: Simplify (/ PI 1) into PI 13.086 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.087 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.087 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.087 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 13.087 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 13.088 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.088 * [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))) 13.089 * [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)))) 13.089 * [taylor]: Taking taylor expansion of (sqrt k) in n 13.089 * [taylor]: Taking taylor expansion of k in n 13.089 * [backup-simplify]: Simplify k into k 13.089 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 13.089 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 13.090 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) 13.090 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 13.090 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 13.090 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 13.090 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 13.090 * [taylor]: Taking taylor expansion of 1/2 in k 13.090 * [backup-simplify]: Simplify 1/2 into 1/2 13.090 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.090 * [taylor]: Taking taylor expansion of 1/2 in k 13.090 * [backup-simplify]: Simplify 1/2 into 1/2 13.090 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.090 * [taylor]: Taking taylor expansion of k in k 13.090 * [backup-simplify]: Simplify 0 into 0 13.090 * [backup-simplify]: Simplify 1 into 1 13.090 * [backup-simplify]: Simplify (/ 1 1) into 1 13.090 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 13.090 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 13.091 * [taylor]: Taking taylor expansion of (* 2 PI) in k 13.091 * [taylor]: Taking taylor expansion of 2 in k 13.091 * [backup-simplify]: Simplify 2 into 2 13.091 * [taylor]: Taking taylor expansion of PI in k 13.091 * [backup-simplify]: Simplify PI into PI 13.091 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.091 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.091 * [taylor]: Taking taylor expansion of (log n) in k 13.091 * [taylor]: Taking taylor expansion of n in k 13.092 * [backup-simplify]: Simplify n into n 13.092 * [backup-simplify]: Simplify (log n) into (log n) 13.092 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.092 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.092 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.092 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.093 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 13.095 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 13.096 * [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)))) 13.096 * [taylor]: Taking taylor expansion of (sqrt k) in k 13.096 * [taylor]: Taking taylor expansion of k in k 13.096 * [backup-simplify]: Simplify 0 into 0 13.096 * [backup-simplify]: Simplify 1 into 1 13.097 * [backup-simplify]: Simplify (sqrt 0) into 0 13.097 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.098 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 13.098 * [backup-simplify]: Simplify 0 into 0 13.099 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.099 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 13.100 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 13.100 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.100 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 13.101 * [backup-simplify]: Simplify (- 0) into 0 13.101 * [backup-simplify]: Simplify (+ 0 0) into 0 13.102 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.102 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 13.103 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.104 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (* 0 (sqrt k))) into 0 13.104 * [taylor]: Taking taylor expansion of 0 in k 13.104 * [backup-simplify]: Simplify 0 into 0 13.104 * [backup-simplify]: Simplify 0 into 0 13.105 * [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)))))) 13.106 * [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)))))) 13.107 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 13.107 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.108 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 13.109 * [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 13.110 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.110 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 13.110 * [backup-simplify]: Simplify (- 0) into 0 13.111 * [backup-simplify]: Simplify (+ 0 0) into 0 13.111 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.112 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 13.114 * [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 13.115 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 13.115 * [taylor]: Taking taylor expansion of 0 in k 13.115 * [backup-simplify]: Simplify 0 into 0 13.115 * [backup-simplify]: Simplify 0 into 0 13.115 * [backup-simplify]: Simplify 0 into 0 13.118 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.120 * [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)))))) 13.121 * [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)))))) 13.122 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 13.123 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.124 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.130 * [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 13.130 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.132 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 13.132 * [backup-simplify]: Simplify (- 0) into 0 13.132 * [backup-simplify]: Simplify (+ 0 0) into 0 13.134 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.136 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 13.138 * [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 13.140 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 13.140 * [taylor]: Taking taylor expansion of 0 in k 13.140 * [backup-simplify]: Simplify 0 into 0 13.140 * [backup-simplify]: Simplify 0 into 0 13.140 * [backup-simplify]: Simplify 0 into 0 13.140 * [backup-simplify]: Simplify 0 into 0 13.144 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.146 * [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)))))) 13.148 * [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)))))) 13.152 * [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)))))))) 13.153 * [backup-simplify]: Simplify (/ (/ (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 13.153 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 13.153 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 13.153 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 13.153 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 13.153 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 13.153 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 13.153 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.153 * [taylor]: Taking taylor expansion of 1/2 in k 13.153 * [backup-simplify]: Simplify 1/2 into 1/2 13.153 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.153 * [taylor]: Taking taylor expansion of k in k 13.153 * [backup-simplify]: Simplify 0 into 0 13.153 * [backup-simplify]: Simplify 1 into 1 13.154 * [backup-simplify]: Simplify (/ 1 1) into 1 13.154 * [taylor]: Taking taylor expansion of 1/2 in k 13.154 * [backup-simplify]: Simplify 1/2 into 1/2 13.154 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 13.154 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 13.154 * [taylor]: Taking taylor expansion of -2 in k 13.154 * [backup-simplify]: Simplify -2 into -2 13.154 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.154 * [taylor]: Taking taylor expansion of PI in k 13.154 * [backup-simplify]: Simplify PI into PI 13.154 * [taylor]: Taking taylor expansion of n in k 13.154 * [backup-simplify]: Simplify n into n 13.154 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.154 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 13.155 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 13.155 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.155 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.156 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 13.156 * [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))) 13.156 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.156 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.156 * [taylor]: Taking taylor expansion of -1 in k 13.156 * [backup-simplify]: Simplify -1 into -1 13.156 * [taylor]: Taking taylor expansion of k in k 13.156 * [backup-simplify]: Simplify 0 into 0 13.156 * [backup-simplify]: Simplify 1 into 1 13.156 * [backup-simplify]: Simplify (/ -1 1) into -1 13.157 * [backup-simplify]: Simplify (sqrt 0) into 0 13.158 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.158 * [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)))) 13.159 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 13.159 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 13.159 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 13.159 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 13.159 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 13.159 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.159 * [taylor]: Taking taylor expansion of 1/2 in n 13.159 * [backup-simplify]: Simplify 1/2 into 1/2 13.159 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.159 * [taylor]: Taking taylor expansion of k in n 13.159 * [backup-simplify]: Simplify k into k 13.159 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.159 * [taylor]: Taking taylor expansion of 1/2 in n 13.159 * [backup-simplify]: Simplify 1/2 into 1/2 13.159 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 13.159 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.159 * [taylor]: Taking taylor expansion of -2 in n 13.159 * [backup-simplify]: Simplify -2 into -2 13.159 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.159 * [taylor]: Taking taylor expansion of PI in n 13.159 * [backup-simplify]: Simplify PI into PI 13.159 * [taylor]: Taking taylor expansion of n in n 13.159 * [backup-simplify]: Simplify 0 into 0 13.159 * [backup-simplify]: Simplify 1 into 1 13.160 * [backup-simplify]: Simplify (/ PI 1) into PI 13.160 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.161 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.161 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.161 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 13.163 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.164 * [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))) 13.165 * [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)))) 13.165 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 13.165 * [taylor]: Taking taylor expansion of (/ -1 k) in n 13.165 * [taylor]: Taking taylor expansion of -1 in n 13.165 * [backup-simplify]: Simplify -1 into -1 13.165 * [taylor]: Taking taylor expansion of k in n 13.165 * [backup-simplify]: Simplify k into k 13.165 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 13.165 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 13.165 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 13.165 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 13.167 * [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))) 13.167 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 13.167 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 13.167 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 13.167 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 13.167 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 13.167 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.167 * [taylor]: Taking taylor expansion of 1/2 in n 13.167 * [backup-simplify]: Simplify 1/2 into 1/2 13.167 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.167 * [taylor]: Taking taylor expansion of k in n 13.167 * [backup-simplify]: Simplify k into k 13.167 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.167 * [taylor]: Taking taylor expansion of 1/2 in n 13.167 * [backup-simplify]: Simplify 1/2 into 1/2 13.167 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 13.167 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.167 * [taylor]: Taking taylor expansion of -2 in n 13.167 * [backup-simplify]: Simplify -2 into -2 13.167 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.167 * [taylor]: Taking taylor expansion of PI in n 13.167 * [backup-simplify]: Simplify PI into PI 13.167 * [taylor]: Taking taylor expansion of n in n 13.167 * [backup-simplify]: Simplify 0 into 0 13.167 * [backup-simplify]: Simplify 1 into 1 13.168 * [backup-simplify]: Simplify (/ PI 1) into PI 13.168 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.169 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.169 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.169 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 13.171 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.172 * [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))) 13.173 * [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)))) 13.173 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 13.173 * [taylor]: Taking taylor expansion of (/ -1 k) in n 13.173 * [taylor]: Taking taylor expansion of -1 in n 13.173 * [backup-simplify]: Simplify -1 into -1 13.173 * [taylor]: Taking taylor expansion of k in n 13.173 * [backup-simplify]: Simplify k into k 13.173 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 13.173 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 13.173 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 13.173 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 13.175 * [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))) 13.175 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 13.175 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 13.175 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 13.175 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 13.175 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.175 * [taylor]: Taking taylor expansion of 1/2 in k 13.175 * [backup-simplify]: Simplify 1/2 into 1/2 13.175 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.175 * [taylor]: Taking taylor expansion of k in k 13.175 * [backup-simplify]: Simplify 0 into 0 13.175 * [backup-simplify]: Simplify 1 into 1 13.175 * [backup-simplify]: Simplify (/ 1 1) into 1 13.175 * [taylor]: Taking taylor expansion of 1/2 in k 13.175 * [backup-simplify]: Simplify 1/2 into 1/2 13.175 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 13.175 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 13.175 * [taylor]: Taking taylor expansion of (* -2 PI) in k 13.176 * [taylor]: Taking taylor expansion of -2 in k 13.176 * [backup-simplify]: Simplify -2 into -2 13.176 * [taylor]: Taking taylor expansion of PI in k 13.176 * [backup-simplify]: Simplify PI into PI 13.176 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.177 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.177 * [taylor]: Taking taylor expansion of (log n) in k 13.177 * [taylor]: Taking taylor expansion of n in k 13.177 * [backup-simplify]: Simplify n into n 13.177 * [backup-simplify]: Simplify (log n) into (log n) 13.178 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.178 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.178 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.179 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 13.180 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 13.181 * [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)))) 13.181 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.181 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.181 * [taylor]: Taking taylor expansion of -1 in k 13.181 * [backup-simplify]: Simplify -1 into -1 13.181 * [taylor]: Taking taylor expansion of k in k 13.181 * [backup-simplify]: Simplify 0 into 0 13.181 * [backup-simplify]: Simplify 1 into 1 13.182 * [backup-simplify]: Simplify (/ -1 1) into -1 13.182 * [backup-simplify]: Simplify (sqrt 0) into 0 13.183 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.185 * [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))))) 13.186 * [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))))) 13.187 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.188 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 13.189 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 13.190 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.190 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 13.190 * [backup-simplify]: Simplify (+ 0 0) into 0 13.192 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.193 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 13.195 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.196 * [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 13.196 * [taylor]: Taking taylor expansion of 0 in k 13.196 * [backup-simplify]: Simplify 0 into 0 13.196 * [backup-simplify]: Simplify 0 into 0 13.197 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 13.200 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.202 * [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)))))) 13.203 * [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)))))) 13.205 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.206 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 13.210 * [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 13.210 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.211 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 13.211 * [backup-simplify]: Simplify (+ 0 0) into 0 13.213 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.214 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 13.217 * [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 13.217 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.218 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 13.219 * [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 13.219 * [taylor]: Taking taylor expansion of 0 in k 13.219 * [backup-simplify]: Simplify 0 into 0 13.219 * [backup-simplify]: Simplify 0 into 0 13.219 * [backup-simplify]: Simplify 0 into 0 13.220 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.227 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.230 * [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)))))) 13.231 * [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)))))) 13.234 * [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))))))))))) 13.234 * * * * [progress]: [ 4 / 4 ] generating series at (2 1) 13.234 * [backup-simplify]: Simplify (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) into (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 13.234 * [approximate]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 13.234 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 13.234 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 13.234 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 13.234 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 13.234 * [taylor]: Taking taylor expansion of 1/4 in k 13.234 * [backup-simplify]: Simplify 1/4 into 1/4 13.234 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 13.234 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.234 * [taylor]: Taking taylor expansion of k in k 13.234 * [backup-simplify]: Simplify 0 into 0 13.234 * [backup-simplify]: Simplify 1 into 1 13.235 * [backup-simplify]: Simplify (/ 1 1) into 1 13.235 * [backup-simplify]: Simplify (log 1) into 0 13.235 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 13.235 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 13.235 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 13.235 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 13.235 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 13.235 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 13.235 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 13.235 * [taylor]: Taking taylor expansion of 1/2 in k 13.235 * [backup-simplify]: Simplify 1/2 into 1/2 13.235 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 13.235 * [taylor]: Taking taylor expansion of 1/2 in k 13.235 * [backup-simplify]: Simplify 1/2 into 1/2 13.235 * [taylor]: Taking taylor expansion of k in k 13.235 * [backup-simplify]: Simplify 0 into 0 13.235 * [backup-simplify]: Simplify 1 into 1 13.235 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 13.235 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 13.235 * [taylor]: Taking taylor expansion of 2 in k 13.235 * [backup-simplify]: Simplify 2 into 2 13.235 * [taylor]: Taking taylor expansion of (* n PI) in k 13.235 * [taylor]: Taking taylor expansion of n in k 13.235 * [backup-simplify]: Simplify n into n 13.235 * [taylor]: Taking taylor expansion of PI in k 13.236 * [backup-simplify]: Simplify PI into PI 13.236 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.236 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 13.236 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 13.236 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.236 * [backup-simplify]: Simplify (- 0) into 0 13.236 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.236 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 13.237 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 13.237 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 13.237 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in n 13.237 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in n 13.237 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in n 13.237 * [taylor]: Taking taylor expansion of 1/4 in n 13.237 * [backup-simplify]: Simplify 1/4 into 1/4 13.237 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in n 13.237 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.237 * [taylor]: Taking taylor expansion of k in n 13.237 * [backup-simplify]: Simplify k into k 13.237 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.237 * [backup-simplify]: Simplify (log (/ 1 k)) into (log (/ 1 k)) 13.237 * [backup-simplify]: Simplify (* 1/4 (log (/ 1 k))) into (* 1/4 (log (/ 1 k))) 13.237 * [backup-simplify]: Simplify (exp (* 1/4 (log (/ 1 k)))) into (pow (/ 1 k) 1/4) 13.237 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 13.237 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 13.237 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 13.237 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 13.237 * [taylor]: Taking taylor expansion of 1/2 in n 13.237 * [backup-simplify]: Simplify 1/2 into 1/2 13.237 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 13.237 * [taylor]: Taking taylor expansion of 1/2 in n 13.237 * [backup-simplify]: Simplify 1/2 into 1/2 13.237 * [taylor]: Taking taylor expansion of k in n 13.237 * [backup-simplify]: Simplify k into k 13.237 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.237 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.237 * [taylor]: Taking taylor expansion of 2 in n 13.237 * [backup-simplify]: Simplify 2 into 2 13.237 * [taylor]: Taking taylor expansion of (* n PI) in n 13.237 * [taylor]: Taking taylor expansion of n in n 13.237 * [backup-simplify]: Simplify 0 into 0 13.237 * [backup-simplify]: Simplify 1 into 1 13.237 * [taylor]: Taking taylor expansion of PI in n 13.237 * [backup-simplify]: Simplify PI into PI 13.237 * [backup-simplify]: Simplify (* 0 PI) into 0 13.238 * [backup-simplify]: Simplify (* 2 0) into 0 13.239 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.240 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.240 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.240 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 13.240 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 13.240 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 13.241 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.242 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 13.242 * [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))))) 13.242 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 13.242 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in n 13.242 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in n 13.243 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in n 13.243 * [taylor]: Taking taylor expansion of 1/4 in n 13.243 * [backup-simplify]: Simplify 1/4 into 1/4 13.243 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in n 13.243 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.243 * [taylor]: Taking taylor expansion of k in n 13.243 * [backup-simplify]: Simplify k into k 13.243 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.243 * [backup-simplify]: Simplify (log (/ 1 k)) into (log (/ 1 k)) 13.243 * [backup-simplify]: Simplify (* 1/4 (log (/ 1 k))) into (* 1/4 (log (/ 1 k))) 13.243 * [backup-simplify]: Simplify (exp (* 1/4 (log (/ 1 k)))) into (pow (/ 1 k) 1/4) 13.243 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 13.243 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 13.243 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 13.243 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 13.243 * [taylor]: Taking taylor expansion of 1/2 in n 13.243 * [backup-simplify]: Simplify 1/2 into 1/2 13.243 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 13.243 * [taylor]: Taking taylor expansion of 1/2 in n 13.243 * [backup-simplify]: Simplify 1/2 into 1/2 13.243 * [taylor]: Taking taylor expansion of k in n 13.243 * [backup-simplify]: Simplify k into k 13.243 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.243 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.243 * [taylor]: Taking taylor expansion of 2 in n 13.243 * [backup-simplify]: Simplify 2 into 2 13.243 * [taylor]: Taking taylor expansion of (* n PI) in n 13.243 * [taylor]: Taking taylor expansion of n in n 13.243 * [backup-simplify]: Simplify 0 into 0 13.243 * [backup-simplify]: Simplify 1 into 1 13.243 * [taylor]: Taking taylor expansion of PI in n 13.243 * [backup-simplify]: Simplify PI into PI 13.243 * [backup-simplify]: Simplify (* 0 PI) into 0 13.244 * [backup-simplify]: Simplify (* 2 0) into 0 13.245 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.245 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.246 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.246 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 13.246 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 13.246 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 13.247 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.248 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 13.248 * [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))))) 13.249 * [backup-simplify]: Simplify (* (pow (/ 1 k) 1/4) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) 13.249 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) in k 13.249 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 13.249 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 13.249 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 13.249 * [taylor]: Taking taylor expansion of 1/2 in k 13.249 * [backup-simplify]: Simplify 1/2 into 1/2 13.249 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 13.249 * [taylor]: Taking taylor expansion of 1/2 in k 13.249 * [backup-simplify]: Simplify 1/2 into 1/2 13.249 * [taylor]: Taking taylor expansion of k in k 13.249 * [backup-simplify]: Simplify 0 into 0 13.249 * [backup-simplify]: Simplify 1 into 1 13.249 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 13.249 * [taylor]: Taking taylor expansion of (log n) in k 13.249 * [taylor]: Taking taylor expansion of n in k 13.249 * [backup-simplify]: Simplify n into n 13.249 * [backup-simplify]: Simplify (log n) into (log n) 13.249 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 13.250 * [taylor]: Taking taylor expansion of (* 2 PI) in k 13.250 * [taylor]: Taking taylor expansion of 2 in k 13.250 * [backup-simplify]: Simplify 2 into 2 13.250 * [taylor]: Taking taylor expansion of PI in k 13.250 * [backup-simplify]: Simplify PI into PI 13.250 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.250 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.251 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.251 * [backup-simplify]: Simplify (- 0) into 0 13.251 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.252 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.253 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 13.253 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 13.253 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 13.253 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 13.253 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 13.253 * [taylor]: Taking taylor expansion of 1/4 in k 13.253 * [backup-simplify]: Simplify 1/4 into 1/4 13.253 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 13.253 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.253 * [taylor]: Taking taylor expansion of k in k 13.253 * [backup-simplify]: Simplify 0 into 0 13.253 * [backup-simplify]: Simplify 1 into 1 13.254 * [backup-simplify]: Simplify (/ 1 1) into 1 13.254 * [backup-simplify]: Simplify (log 1) into 0 13.254 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 13.254 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 13.254 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 13.255 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k -1/4)) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) 13.256 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) 13.256 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.257 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 13.258 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 13.259 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 13.259 * [backup-simplify]: Simplify (- 0) into 0 13.259 * [backup-simplify]: Simplify (+ 0 0) into 0 13.261 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.261 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 13.263 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.263 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.264 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (/ 1 k) 1)))) 1) into 0 13.264 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log (/ 1 k)))) into 0 13.265 * [backup-simplify]: Simplify (* (exp (* 1/4 (log (/ 1 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.266 * [backup-simplify]: Simplify (+ (* (pow (/ 1 k) 1/4) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 13.266 * [taylor]: Taking taylor expansion of 0 in k 13.266 * [backup-simplify]: Simplify 0 into 0 13.266 * [backup-simplify]: Simplify 0 into 0 13.267 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 13.268 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 13.269 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 13.269 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 13.270 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 13.271 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 13.272 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 13.273 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 13.274 * [backup-simplify]: Simplify (+ 0 0) into 0 13.275 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 13.275 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.275 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.277 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 13.280 * [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))))))) 13.284 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (pow k -1/4))) into (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (/ 1 k) 1/4))))) 13.288 * [backup-simplify]: Simplify (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (/ 1 k) 1/4))))) into (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (/ 1 k) 1/4))))) 13.289 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.290 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.293 * [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 13.294 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 13.295 * [backup-simplify]: Simplify (- 0) into 0 13.295 * [backup-simplify]: Simplify (+ 0 0) into 0 13.296 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.297 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 13.298 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.298 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.299 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (/ 1 k) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (/ 1 k) 1)))) 2) into 0 13.300 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log (/ 1 k))))) into 0 13.301 * [backup-simplify]: Simplify (* (exp (* 1/4 (log (/ 1 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.302 * [backup-simplify]: Simplify (+ (* (pow (/ 1 k) 1/4) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 13.302 * [taylor]: Taking taylor expansion of 0 in k 13.302 * [backup-simplify]: Simplify 0 into 0 13.302 * [backup-simplify]: Simplify 0 into 0 13.302 * [backup-simplify]: Simplify 0 into 0 13.303 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.304 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 13.304 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 13.305 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 13.306 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.307 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 13.307 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 13.309 * [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 13.309 * [backup-simplify]: Simplify (+ 0 0) into 0 13.310 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 13.310 * [backup-simplify]: Simplify (- 0) into 0 13.310 * [backup-simplify]: Simplify (+ 0 0) into 0 13.312 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 13.314 * [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))))) 13.319 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 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))))) (pow k -1/4)))) into (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (* 1/4 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) 13.323 * [backup-simplify]: Simplify (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (* 1/4 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) into (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (* 1/4 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) 13.337 * [backup-simplify]: Simplify (+ (* (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/8 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (* 1/4 (* (pow (/ 1 k) 1/4) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))) (pow (* k 1) 2)) (+ (* (- (+ (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (/ 1 k) 1/4))))) (* k 1)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)))) into (- (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (/ 1 k) 1/4)) (+ (* 1/8 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2)) (pow (pow k 7) 1/4))) (+ (* 1/4 (* (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))) (pow (pow k 7) 1/4))) (* 1/8 (* (* (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (pow k 7) 1/4)))))) (+ (* 1/2 (* (* (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (pow (pow k 3) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)) (pow (pow k 3) 1/4))))) 13.338 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (sqrt (/ 1 k)))) into (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 13.338 * [approximate]: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 13.338 * [taylor]: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 13.338 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 13.338 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 13.338 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 13.338 * [taylor]: Taking taylor expansion of 1/4 in k 13.338 * [backup-simplify]: Simplify 1/4 into 1/4 13.338 * [taylor]: Taking taylor expansion of (log k) in k 13.338 * [taylor]: Taking taylor expansion of k in k 13.338 * [backup-simplify]: Simplify 0 into 0 13.338 * [backup-simplify]: Simplify 1 into 1 13.339 * [backup-simplify]: Simplify (log 1) into 0 13.339 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.339 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 13.339 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 13.339 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 13.339 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 13.339 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 13.339 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 13.339 * [taylor]: Taking taylor expansion of 1/2 in k 13.339 * [backup-simplify]: Simplify 1/2 into 1/2 13.339 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.339 * [taylor]: Taking taylor expansion of 1/2 in k 13.339 * [backup-simplify]: Simplify 1/2 into 1/2 13.339 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.339 * [taylor]: Taking taylor expansion of k in k 13.339 * [backup-simplify]: Simplify 0 into 0 13.339 * [backup-simplify]: Simplify 1 into 1 13.339 * [backup-simplify]: Simplify (/ 1 1) into 1 13.340 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 13.340 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 13.340 * [taylor]: Taking taylor expansion of 2 in k 13.340 * [backup-simplify]: Simplify 2 into 2 13.340 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.340 * [taylor]: Taking taylor expansion of PI in k 13.340 * [backup-simplify]: Simplify PI into PI 13.340 * [taylor]: Taking taylor expansion of n in k 13.340 * [backup-simplify]: Simplify n into n 13.340 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.340 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 13.340 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 13.340 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.340 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.341 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.341 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 13.341 * [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)))) 13.341 * [taylor]: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 13.341 * [taylor]: Taking taylor expansion of (pow k 1/4) in n 13.341 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in n 13.341 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in n 13.341 * [taylor]: Taking taylor expansion of 1/4 in n 13.341 * [backup-simplify]: Simplify 1/4 into 1/4 13.341 * [taylor]: Taking taylor expansion of (log k) in n 13.341 * [taylor]: Taking taylor expansion of k in n 13.341 * [backup-simplify]: Simplify k into k 13.341 * [backup-simplify]: Simplify (log k) into (log k) 13.341 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 13.341 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 13.341 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 13.341 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 13.341 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 13.341 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 13.341 * [taylor]: Taking taylor expansion of 1/2 in n 13.341 * [backup-simplify]: Simplify 1/2 into 1/2 13.341 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.341 * [taylor]: Taking taylor expansion of 1/2 in n 13.341 * [backup-simplify]: Simplify 1/2 into 1/2 13.341 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.341 * [taylor]: Taking taylor expansion of k in n 13.341 * [backup-simplify]: Simplify k into k 13.341 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.341 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 13.341 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.341 * [taylor]: Taking taylor expansion of 2 in n 13.341 * [backup-simplify]: Simplify 2 into 2 13.341 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.341 * [taylor]: Taking taylor expansion of PI in n 13.341 * [backup-simplify]: Simplify PI into PI 13.341 * [taylor]: Taking taylor expansion of n in n 13.341 * [backup-simplify]: Simplify 0 into 0 13.341 * [backup-simplify]: Simplify 1 into 1 13.342 * [backup-simplify]: Simplify (/ PI 1) into PI 13.342 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.343 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.343 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.343 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 13.343 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 13.344 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.344 * [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))) 13.345 * [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)))) 13.345 * [taylor]: Taking taylor expansion of (* (pow k 1/4) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 13.345 * [taylor]: Taking taylor expansion of (pow k 1/4) in n 13.345 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in n 13.345 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in n 13.345 * [taylor]: Taking taylor expansion of 1/4 in n 13.345 * [backup-simplify]: Simplify 1/4 into 1/4 13.345 * [taylor]: Taking taylor expansion of (log k) in n 13.345 * [taylor]: Taking taylor expansion of k in n 13.345 * [backup-simplify]: Simplify k into k 13.345 * [backup-simplify]: Simplify (log k) into (log k) 13.345 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 13.345 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 13.345 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 13.345 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 13.345 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 13.345 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 13.345 * [taylor]: Taking taylor expansion of 1/2 in n 13.345 * [backup-simplify]: Simplify 1/2 into 1/2 13.345 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.345 * [taylor]: Taking taylor expansion of 1/2 in n 13.345 * [backup-simplify]: Simplify 1/2 into 1/2 13.345 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.345 * [taylor]: Taking taylor expansion of k in n 13.345 * [backup-simplify]: Simplify k into k 13.345 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.345 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 13.345 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.345 * [taylor]: Taking taylor expansion of 2 in n 13.345 * [backup-simplify]: Simplify 2 into 2 13.346 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.346 * [taylor]: Taking taylor expansion of PI in n 13.346 * [backup-simplify]: Simplify PI into PI 13.346 * [taylor]: Taking taylor expansion of n in n 13.346 * [backup-simplify]: Simplify 0 into 0 13.346 * [backup-simplify]: Simplify 1 into 1 13.346 * [backup-simplify]: Simplify (/ PI 1) into PI 13.346 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.347 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.347 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.347 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 13.347 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 13.348 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.348 * [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))) 13.349 * [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)))) 13.350 * [backup-simplify]: Simplify (* (pow k 1/4) (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)))) (pow k 1/4)) 13.350 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) in k 13.350 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 13.350 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 13.350 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 13.350 * [taylor]: Taking taylor expansion of 1/2 in k 13.350 * [backup-simplify]: Simplify 1/2 into 1/2 13.350 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.350 * [taylor]: Taking taylor expansion of 1/2 in k 13.350 * [backup-simplify]: Simplify 1/2 into 1/2 13.350 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.350 * [taylor]: Taking taylor expansion of k in k 13.350 * [backup-simplify]: Simplify 0 into 0 13.350 * [backup-simplify]: Simplify 1 into 1 13.350 * [backup-simplify]: Simplify (/ 1 1) into 1 13.350 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 13.350 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 13.350 * [taylor]: Taking taylor expansion of (* 2 PI) in k 13.350 * [taylor]: Taking taylor expansion of 2 in k 13.350 * [backup-simplify]: Simplify 2 into 2 13.350 * [taylor]: Taking taylor expansion of PI in k 13.350 * [backup-simplify]: Simplify PI into PI 13.351 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.351 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.351 * [taylor]: Taking taylor expansion of (log n) in k 13.351 * [taylor]: Taking taylor expansion of n in k 13.351 * [backup-simplify]: Simplify n into n 13.351 * [backup-simplify]: Simplify (log n) into (log n) 13.352 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.352 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.352 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.353 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.353 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 13.354 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 13.354 * [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)))) 13.354 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 13.354 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 13.354 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 13.354 * [taylor]: Taking taylor expansion of 1/4 in k 13.354 * [backup-simplify]: Simplify 1/4 into 1/4 13.354 * [taylor]: Taking taylor expansion of (log k) in k 13.355 * [taylor]: Taking taylor expansion of k in k 13.355 * [backup-simplify]: Simplify 0 into 0 13.355 * [backup-simplify]: Simplify 1 into 1 13.355 * [backup-simplify]: Simplify (log 1) into 0 13.355 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.355 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 13.355 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 13.356 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) 13.357 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (pow k 1/4)) 13.357 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.358 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 13.358 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 13.359 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.359 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 13.359 * [backup-simplify]: Simplify (- 0) into 0 13.359 * [backup-simplify]: Simplify (+ 0 0) into 0 13.360 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.361 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 13.362 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.362 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow k 1)))) 1) into 0 13.363 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 13.363 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 13.364 * [backup-simplify]: Simplify (+ (* (pow k 1/4) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 13.364 * [taylor]: Taking taylor expansion of 0 in k 13.364 * [backup-simplify]: Simplify 0 into 0 13.364 * [backup-simplify]: Simplify 0 into 0 13.365 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 13.365 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.366 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 13.366 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 13.367 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (* 0 (pow k 1/4))) into 0 13.367 * [backup-simplify]: Simplify 0 into 0 13.368 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.368 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 13.370 * [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 13.370 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.371 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 13.371 * [backup-simplify]: Simplify (- 0) into 0 13.371 * [backup-simplify]: Simplify (+ 0 0) into 0 13.373 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.374 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 13.377 * [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 13.379 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow k 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow k 1)))) 2) into 0 13.380 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 13.381 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.382 * [backup-simplify]: Simplify (+ (* (pow k 1/4) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 13.383 * [taylor]: Taking taylor expansion of 0 in k 13.383 * [backup-simplify]: Simplify 0 into 0 13.383 * [backup-simplify]: Simplify 0 into 0 13.383 * [backup-simplify]: Simplify 0 into 0 13.386 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 13.386 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 13.387 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 13.388 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.390 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0 13.390 * [backup-simplify]: Simplify 0 into 0 13.391 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.392 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.398 * [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 13.399 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.400 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 13.400 * [backup-simplify]: Simplify (- 0) into 0 13.401 * [backup-simplify]: Simplify (+ 0 0) into 0 13.403 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.404 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 13.407 * [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 13.410 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow k 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow k 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow k 1)))) 6) into 0 13.411 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 13.413 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.415 * [backup-simplify]: Simplify (+ (* (pow k 1/4) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 13.415 * [taylor]: Taking taylor expansion of 0 in k 13.415 * [backup-simplify]: Simplify 0 into 0 13.415 * [backup-simplify]: Simplify 0 into 0 13.416 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) (pow (/ 1 k) 1/4)) into (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow (/ 1 k) 1/4)) 13.417 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (sqrt (/ 1 (- k))))) into (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 13.417 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0 13.417 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 13.417 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 13.417 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 13.417 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.417 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.417 * [taylor]: Taking taylor expansion of -1 in k 13.417 * [backup-simplify]: Simplify -1 into -1 13.417 * [taylor]: Taking taylor expansion of k in k 13.417 * [backup-simplify]: Simplify 0 into 0 13.417 * [backup-simplify]: Simplify 1 into 1 13.418 * [backup-simplify]: Simplify (/ -1 1) into -1 13.418 * [backup-simplify]: Simplify (sqrt 0) into 0 13.419 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.420 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 13.420 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 13.420 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 13.422 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.423 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 13.425 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 13.425 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 13.425 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 13.425 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 13.425 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 13.425 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.425 * [taylor]: Taking taylor expansion of 1/2 in k 13.425 * [backup-simplify]: Simplify 1/2 into 1/2 13.425 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.425 * [taylor]: Taking taylor expansion of k in k 13.425 * [backup-simplify]: Simplify 0 into 0 13.425 * [backup-simplify]: Simplify 1 into 1 13.425 * [backup-simplify]: Simplify (/ 1 1) into 1 13.425 * [taylor]: Taking taylor expansion of 1/2 in k 13.425 * [backup-simplify]: Simplify 1/2 into 1/2 13.425 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 13.425 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 13.425 * [taylor]: Taking taylor expansion of -2 in k 13.425 * [backup-simplify]: Simplify -2 into -2 13.425 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.425 * [taylor]: Taking taylor expansion of PI in k 13.425 * [backup-simplify]: Simplify PI into PI 13.425 * [taylor]: Taking taylor expansion of n in k 13.425 * [backup-simplify]: Simplify n into n 13.425 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.425 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 13.426 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 13.426 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.426 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.426 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 13.427 * [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))) 13.427 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 13.427 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in n 13.427 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in n 13.427 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 13.427 * [taylor]: Taking taylor expansion of (/ -1 k) in n 13.427 * [taylor]: Taking taylor expansion of -1 in n 13.427 * [backup-simplify]: Simplify -1 into -1 13.427 * [taylor]: Taking taylor expansion of k in n 13.427 * [backup-simplify]: Simplify k into k 13.427 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 13.427 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 13.427 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 13.427 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 13.427 * [backup-simplify]: Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) 13.427 * [backup-simplify]: Simplify (sqrt (/ 1 (sqrt (/ -1 k)))) into (sqrt (/ 1 (sqrt (/ -1 k)))) 13.427 * [backup-simplify]: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 13.427 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 13.427 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 13.427 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 13.427 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 13.427 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 13.427 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.427 * [taylor]: Taking taylor expansion of 1/2 in n 13.427 * [backup-simplify]: Simplify 1/2 into 1/2 13.427 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.427 * [taylor]: Taking taylor expansion of k in n 13.427 * [backup-simplify]: Simplify k into k 13.427 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.428 * [taylor]: Taking taylor expansion of 1/2 in n 13.428 * [backup-simplify]: Simplify 1/2 into 1/2 13.428 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 13.428 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.428 * [taylor]: Taking taylor expansion of -2 in n 13.428 * [backup-simplify]: Simplify -2 into -2 13.428 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.428 * [taylor]: Taking taylor expansion of PI in n 13.428 * [backup-simplify]: Simplify PI into PI 13.428 * [taylor]: Taking taylor expansion of n in n 13.428 * [backup-simplify]: Simplify 0 into 0 13.428 * [backup-simplify]: Simplify 1 into 1 13.428 * [backup-simplify]: Simplify (/ PI 1) into PI 13.428 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.429 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.429 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.429 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 13.430 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.431 * [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))) 13.431 * [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)))) 13.431 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 13.431 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in n 13.431 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in n 13.431 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 13.431 * [taylor]: Taking taylor expansion of (/ -1 k) in n 13.431 * [taylor]: Taking taylor expansion of -1 in n 13.431 * [backup-simplify]: Simplify -1 into -1 13.431 * [taylor]: Taking taylor expansion of k in n 13.431 * [backup-simplify]: Simplify k into k 13.431 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 13.431 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 13.432 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 13.432 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 13.432 * [backup-simplify]: Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) 13.432 * [backup-simplify]: Simplify (sqrt (/ 1 (sqrt (/ -1 k)))) into (sqrt (/ 1 (sqrt (/ -1 k)))) 13.432 * [backup-simplify]: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 13.432 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 13.432 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 13.432 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 13.432 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 13.432 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 13.432 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.432 * [taylor]: Taking taylor expansion of 1/2 in n 13.432 * [backup-simplify]: Simplify 1/2 into 1/2 13.432 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.432 * [taylor]: Taking taylor expansion of k in n 13.432 * [backup-simplify]: Simplify k into k 13.432 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.432 * [taylor]: Taking taylor expansion of 1/2 in n 13.432 * [backup-simplify]: Simplify 1/2 into 1/2 13.432 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 13.432 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.432 * [taylor]: Taking taylor expansion of -2 in n 13.432 * [backup-simplify]: Simplify -2 into -2 13.432 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.432 * [taylor]: Taking taylor expansion of PI in n 13.432 * [backup-simplify]: Simplify PI into PI 13.432 * [taylor]: Taking taylor expansion of n in n 13.432 * [backup-simplify]: Simplify 0 into 0 13.432 * [backup-simplify]: Simplify 1 into 1 13.433 * [backup-simplify]: Simplify (/ PI 1) into PI 13.433 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.434 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.434 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.434 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 13.435 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.435 * [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))) 13.438 * [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)))) 13.439 * [backup-simplify]: Simplify (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 13.439 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k 13.439 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 13.439 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 13.439 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.439 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.439 * [taylor]: Taking taylor expansion of -1 in k 13.439 * [backup-simplify]: Simplify -1 into -1 13.439 * [taylor]: Taking taylor expansion of k in k 13.439 * [backup-simplify]: Simplify 0 into 0 13.439 * [backup-simplify]: Simplify 1 into 1 13.439 * [backup-simplify]: Simplify (/ -1 1) into -1 13.440 * [backup-simplify]: Simplify (sqrt 0) into 0 13.440 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.441 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 13.441 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 13.442 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 13.443 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.445 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 13.446 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 13.446 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 13.446 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 13.446 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 13.446 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.446 * [taylor]: Taking taylor expansion of 1/2 in k 13.446 * [backup-simplify]: Simplify 1/2 into 1/2 13.446 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.446 * [taylor]: Taking taylor expansion of k in k 13.446 * [backup-simplify]: Simplify 0 into 0 13.446 * [backup-simplify]: Simplify 1 into 1 13.446 * [backup-simplify]: Simplify (/ 1 1) into 1 13.446 * [taylor]: Taking taylor expansion of 1/2 in k 13.446 * [backup-simplify]: Simplify 1/2 into 1/2 13.446 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 13.446 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 13.446 * [taylor]: Taking taylor expansion of (* -2 PI) in k 13.446 * [taylor]: Taking taylor expansion of -2 in k 13.446 * [backup-simplify]: Simplify -2 into -2 13.446 * [taylor]: Taking taylor expansion of PI in k 13.446 * [backup-simplify]: Simplify PI into PI 13.447 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.448 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.448 * [taylor]: Taking taylor expansion of (log n) in k 13.448 * [taylor]: Taking taylor expansion of n in k 13.448 * [backup-simplify]: Simplify n into n 13.448 * [backup-simplify]: Simplify (log n) into (log n) 13.448 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.449 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.449 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.450 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 13.451 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 13.452 * [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)))) 13.454 * [backup-simplify]: Simplify (* (sqrt +nan.0) (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)))) (sqrt +nan.0)) 13.456 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)) 13.457 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.457 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 13.459 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 13.459 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.460 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 13.460 * [backup-simplify]: Simplify (+ 0 0) into 0 13.462 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.463 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 13.465 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.466 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (sqrt (/ -1 k)))) 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 13.466 * [taylor]: Taking taylor expansion of 0 in k 13.466 * [backup-simplify]: Simplify 0 into 0 13.466 * [backup-simplify]: Simplify 0 into 0 13.468 * [backup-simplify]: Simplify (+ (* (sqrt +nan.0) 0) (* (/ +nan.0 (sqrt +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)))) (sqrt +nan.0)))) 13.469 * [backup-simplify]: Simplify (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))) into (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))) 13.469 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.470 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 13.472 * [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 13.472 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.473 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 13.473 * [backup-simplify]: Simplify (+ 0 0) into 0 13.474 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.475 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 13.476 * [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 13.476 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.477 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 13.477 * [backup-simplify]: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 13.477 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 13.478 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (sqrt (/ -1 k)))) 0) (+ (* 0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into 0 13.478 * [taylor]: Taking taylor expansion of 0 in k 13.478 * [backup-simplify]: Simplify 0 into 0 13.478 * [backup-simplify]: Simplify 0 into 0 13.478 * [backup-simplify]: Simplify 0 into 0 13.479 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.481 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.483 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 13.487 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) 13.492 * [backup-simplify]: Simplify (+ (* (sqrt +nan.0) 0) (+ (* (/ +nan.0 (sqrt +nan.0)) 0) (* (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))))) 13.495 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))))) into (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt +nan.0)))))) 13.499 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) (sqrt +nan.0)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) (sqrt +nan.0)))) (* (/ 1 (- k)) 1)) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) (sqrt +nan.0)))) into (- (* (sqrt +nan.0) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt +nan.0) (pow k 2))))))))) 13.499 * * * [progress]: simplifying candidates 13.499 * * * * [progress]: [ 1 / 4800 ] simplifiying candidate # 13.500 * * * * [progress]: [ 2 / 4800 ] simplifiying candidate # 13.500 * * * * [progress]: [ 3 / 4800 ] simplifiying candidate # 13.500 * * * * [progress]: [ 4 / 4800 ] simplifiying candidate # 13.500 * * * * [progress]: [ 5 / 4800 ] simplifiying candidate # 13.500 * * * * [progress]: [ 6 / 4800 ] simplifiying candidate # 13.500 * * * * [progress]: [ 7 / 4800 ] simplifiying candidate # 13.500 * * * * [progress]: [ 8 / 4800 ] 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simplifiying candidate # 13.502 * * * * [progress]: [ 39 / 4800 ] simplifiying candidate # 13.502 * * * * [progress]: [ 40 / 4800 ] simplifiying candidate # 13.502 * * * * [progress]: [ 41 / 4800 ] simplifiying candidate # 13.502 * * * * [progress]: [ 42 / 4800 ] simplifiying candidate # 13.502 * * * * [progress]: [ 43 / 4800 ] simplifiying candidate # 13.502 * * * * [progress]: [ 44 / 4800 ] simplifiying candidate # 13.502 * * * * [progress]: [ 45 / 4800 ] simplifiying candidate # 13.502 * * * * [progress]: [ 46 / 4800 ] simplifiying candidate # 13.502 * * * * [progress]: [ 47 / 4800 ] simplifiying candidate # 13.502 * * * * [progress]: [ 48 / 4800 ] simplifiying candidate # 13.502 * * * * [progress]: [ 49 / 4800 ] simplifiying candidate # 13.502 * * * * [progress]: [ 50 / 4800 ] simplifiying candidate # 13.502 * * * * [progress]: [ 51 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 52 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 53 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 54 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 55 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 56 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 57 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 58 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 59 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 60 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 61 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 62 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 63 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 64 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 65 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 66 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 67 / 4800 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (sqrt (sqrt k))))> 13.503 * * * * [progress]: [ 68 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 69 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 70 / 4800 ] simplifiying candidate # 13.503 * * * * [progress]: [ 71 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 72 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 73 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 74 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 75 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 76 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 77 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 78 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 79 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 80 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 81 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 82 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 83 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 84 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 85 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 86 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 87 / 4800 ] simplifiying candidate #real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))> 13.504 * * * * [progress]: [ 88 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 89 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 90 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 91 / 4800 ] simplifiying candidate # 13.504 * * * * [progress]: [ 92 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 93 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 94 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 95 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 96 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 97 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 98 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 99 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 100 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 101 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 102 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 103 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 104 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 105 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 106 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 107 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 108 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 109 / 4800 ] simplifiying candidate # 13.505 * * * * [progress]: [ 110 / 4800 ] simplifiying candidate # 13.506 * * * * 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candidate # 13.907 * * * * [progress]: [ 4772 / 4800 ] simplifiying candidate # 13.907 * * * * [progress]: [ 4773 / 4800 ] simplifiying candidate # 13.907 * * * * [progress]: [ 4774 / 4800 ] simplifiying candidate # 13.907 * * * * [progress]: [ 4775 / 4800 ] simplifiying candidate # 13.907 * * * * [progress]: [ 4776 / 4800 ] simplifiying candidate # 13.907 * * * * [progress]: [ 4777 / 4800 ] simplifiying candidate # 13.907 * * * * [progress]: [ 4778 / 4800 ] simplifiying candidate # 13.907 * * * * [progress]: [ 4779 / 4800 ] simplifiying candidate # 13.907 * * * * [progress]: [ 4780 / 4800 ] simplifiying candidate # 13.908 * * * * [progress]: [ 4781 / 4800 ] simplifiying candidate # 13.908 * * * * [progress]: [ 4782 / 4800 ] simplifiying candidate # 13.908 * * * * [progress]: [ 4783 / 4800 ] simplifiying candidate # 13.908 * * * * [progress]: [ 4784 / 4800 ] simplifiying candidate # 13.908 * * * * [progress]: [ 4785 / 4800 ] simplifiying candidate # 13.908 * * * * [progress]: [ 4786 / 4800 ] simplifiying candidate # 13.908 * * * * [progress]: [ 4787 / 4800 ] simplifiying candidate # 13.908 * * * * [progress]: [ 4788 / 4800 ] simplifiying candidate #real (real->posit16 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) (sqrt (sqrt k))))> 13.908 * * * * [progress]: [ 4789 / 4800 ] simplifiying candidate # 13.908 * * * * [progress]: [ 4790 / 4800 ] simplifiying candidate # 13.908 * * * * [progress]: [ 4791 / 4800 ] simplifiying candidate # 13.908 * * * * [progress]: [ 4792 / 4800 ] simplifiying candidate # 13.908 * * * * [progress]: [ 4793 / 4800 ] simplifiying candidate # 13.909 * * * * [progress]: [ 4794 / 4800 ] simplifiying candidate # 13.909 * * * * [progress]: [ 4795 / 4800 ] simplifiying candidate # 13.909 * * * * [progress]: [ 4796 / 4800 ] simplifiying candidate # 13.909 * * * * [progress]: [ 4797 / 4800 ] simplifiying candidate # 13.909 * * * * [progress]: [ 4798 / 4800 ] simplifiying candidate # 13.909 * * * * [progress]: [ 4799 / 4800 ] simplifiying candidate # 13.909 * * * * [progress]: [ 4800 / 4800 ] simplifiying candidate # 14.106 * [simplify]: Simplifying: (expm1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log1p (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2)) (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n (* 2 PI)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* 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2 PI))))) (log n)) (pow (pow k 3) 1/4))))) (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow (/ 1 k) 1/4)) (- (* (sqrt +nan.0) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (sqrt +nan.0) (pow k 2))))))))) 14.367 * * [simplify]: iteration 1: (3687 enodes) 19.575 * * [simplify]: Extracting #0: cost 1578 inf + 0 19.592 * * [simplify]: Extracting #1: cost 3671 inf + 1 19.630 * * [simplify]: Extracting #2: cost 3897 inf + 1400 19.658 * * [simplify]: Extracting #3: cost 4024 inf + 7287 19.708 * * [simplify]: Extracting #4: cost 3747 inf + 128331 19.857 * * [simplify]: Extracting #5: cost 2727 inf + 738500 20.224 * * [simplify]: Extracting #6: cost 1501 inf + 1705758 20.644 * * [simplify]: Extracting #7: cost 571 inf + 2489845 21.210 * * [simplify]: Extracting #8: cost 199 inf + 2820387 21.803 * * [simplify]: Extracting #9: cost 67 inf + 2947095 22.476 * * [simplify]: Extracting #10: cost 51 inf + 2972427 23.135 * * [simplify]: Extracting #11: cost 42 inf + 2980636 23.763 * * [simplify]: Extracting #12: cost 32 inf + 2987895 24.419 * * [simplify]: Extracting #13: cost 24 inf + 2997023 25.027 * * [simplify]: Extracting #14: cost 20 inf + 3002127 25.671 * * [simplify]: Extracting #15: cost 3 inf + 3027709 26.347 * * [simplify]: Extracting #16: cost 0 inf + 3032767 27.101 * [simplify]: Simplified to: (expm1 (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (log1p (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (/ k 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k)))))))))))) (- (- (* (/ (exp (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2)))) (* (* k k) k)) +nan.0) (- (* (/ (exp (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2)))) k) +nan.0) (* +nan.0 (/ (exp (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2)))) (* k k)))))) (- (- (* (/ (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))) (* (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) +nan.0)))) (- (fma (exp (* 1/2 (log (* (* PI 2) n)))) (pow (/ 1 k) 1/4) (fma 1/8 (* (* (exp (* 1/2 (log (* (* PI 2) n)))) (* (log n) (log n))) (pow (pow k 7) 1/4)) (fma 1/4 (* (* (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))) (log n)) (pow (pow k 7) 1/4)) (* (* (pow (pow k 7) 1/4) (* (* (log (* PI 2)) (log (* PI 2))) (exp (* 1/2 (log (* (* PI 2) n)))))) 1/8)))) (* 1/2 (+ (* (pow (* (* k k) k) 1/4) (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n)))))) (* (* (log n) (exp (* 1/2 (log (* (* PI 2) n))))) (pow (* (* k k) k) 1/4))))) (* (exp (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2)))) (pow (/ 1 k) 1/4)) (- (* (sqrt +nan.0) (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2))))) (- (* +nan.0 (/ (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (* (sqrt +nan.0) k))) (- (/ (* (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) +nan.0) (* (* k k) (* (sqrt +nan.0) (* (sqrt +nan.0) (sqrt +nan.0))))) (/ (* (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) +nan.0) (* (* k k) (sqrt +nan.0)))))) 28.968 * * * [progress]: adding candidates to table 127.028 * * [progress]: iteration 3 / 4 127.028 * * * [progress]: picking best candidate 127.074 * * * * [pick]: Picked # 127.074 * * * [progress]: localizing error 127.131 * * * [progress]: generating rewritten candidates 127.132 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1) 127.163 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1) 127.192 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1) 127.217 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1) 127.232 * * * [progress]: generating series expansions 127.232 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1) 127.233 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) 127.233 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0 127.233 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k 127.233 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k 127.233 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k 127.233 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k 127.233 * [taylor]: Taking taylor expansion of 1/2 in k 127.233 * [backup-simplify]: Simplify 1/2 into 1/2 127.233 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 127.233 * [taylor]: Taking taylor expansion of 1/2 in k 127.233 * [backup-simplify]: Simplify 1/2 into 1/2 127.233 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 127.233 * [taylor]: Taking taylor expansion of 1/2 in k 127.233 * [backup-simplify]: Simplify 1/2 into 1/2 127.233 * [taylor]: Taking taylor expansion of k in k 127.233 * [backup-simplify]: Simplify 0 into 0 127.233 * [backup-simplify]: Simplify 1 into 1 127.233 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 127.233 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 127.233 * [taylor]: Taking taylor expansion of 2 in k 127.233 * [backup-simplify]: Simplify 2 into 2 127.233 * [taylor]: Taking taylor expansion of (* n PI) in k 127.233 * [taylor]: Taking taylor expansion of n in k 127.233 * [backup-simplify]: Simplify n into n 127.233 * [taylor]: Taking taylor expansion of PI in k 127.233 * [backup-simplify]: Simplify PI into PI 127.233 * [backup-simplify]: Simplify (* n PI) into (* n PI) 127.234 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 127.234 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 127.234 * [backup-simplify]: Simplify (* 1/2 0) into 0 127.234 * [backup-simplify]: Simplify (- 0) into 0 127.234 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 127.235 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4 127.235 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI)))) 127.235 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4) 127.235 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n 127.235 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n 127.235 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n 127.235 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n 127.235 * [taylor]: Taking taylor expansion of 1/2 in n 127.235 * [backup-simplify]: Simplify 1/2 into 1/2 127.235 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 127.235 * [taylor]: Taking taylor expansion of 1/2 in n 127.235 * [backup-simplify]: Simplify 1/2 into 1/2 127.235 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 127.235 * [taylor]: Taking taylor expansion of 1/2 in n 127.235 * [backup-simplify]: Simplify 1/2 into 1/2 127.235 * [taylor]: Taking taylor expansion of k in n 127.235 * [backup-simplify]: Simplify k into k 127.235 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 127.235 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 127.235 * [taylor]: Taking taylor expansion of 2 in n 127.235 * [backup-simplify]: Simplify 2 into 2 127.235 * [taylor]: Taking taylor expansion of (* n PI) in n 127.235 * [taylor]: Taking taylor expansion of n in n 127.235 * [backup-simplify]: Simplify 0 into 0 127.235 * [backup-simplify]: Simplify 1 into 1 127.235 * [taylor]: Taking taylor expansion of PI in n 127.235 * [backup-simplify]: Simplify PI into PI 127.236 * [backup-simplify]: Simplify (* 0 PI) into 0 127.236 * [backup-simplify]: Simplify (* 2 0) into 0 127.237 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 127.238 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 127.238 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 127.239 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 127.239 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 127.239 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 127.239 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k))) 127.240 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 127.240 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 127.241 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 127.241 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n 127.241 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n 127.241 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n 127.241 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n 127.241 * [taylor]: Taking taylor expansion of 1/2 in n 127.241 * [backup-simplify]: Simplify 1/2 into 1/2 127.241 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 127.241 * [taylor]: Taking taylor expansion of 1/2 in n 127.241 * [backup-simplify]: Simplify 1/2 into 1/2 127.241 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 127.241 * [taylor]: Taking taylor expansion of 1/2 in n 127.241 * [backup-simplify]: Simplify 1/2 into 1/2 127.241 * [taylor]: Taking taylor expansion of k in n 127.241 * [backup-simplify]: Simplify k into k 127.241 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 127.241 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 127.241 * [taylor]: Taking taylor expansion of 2 in n 127.241 * [backup-simplify]: Simplify 2 into 2 127.241 * [taylor]: Taking taylor expansion of (* n PI) in n 127.241 * [taylor]: Taking taylor expansion of n in n 127.241 * [backup-simplify]: Simplify 0 into 0 127.241 * [backup-simplify]: Simplify 1 into 1 127.241 * [taylor]: Taking taylor expansion of PI in n 127.241 * [backup-simplify]: Simplify PI into PI 127.242 * [backup-simplify]: Simplify (* 0 PI) into 0 127.242 * [backup-simplify]: Simplify (* 2 0) into 0 127.243 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 127.244 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 127.244 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 127.245 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 127.245 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 127.245 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 127.245 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k))) 127.246 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 127.246 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 127.247 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 127.247 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k 127.247 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 127.247 * [taylor]: Taking taylor expansion of 1/2 in k 127.247 * [backup-simplify]: Simplify 1/2 into 1/2 127.247 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 127.247 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 127.247 * [taylor]: Taking taylor expansion of 1/2 in k 127.247 * [backup-simplify]: Simplify 1/2 into 1/2 127.247 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 127.247 * [taylor]: Taking taylor expansion of 1/2 in k 127.247 * [backup-simplify]: Simplify 1/2 into 1/2 127.247 * [taylor]: Taking taylor expansion of k in k 127.247 * [backup-simplify]: Simplify 0 into 0 127.247 * [backup-simplify]: Simplify 1 into 1 127.247 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 127.247 * [taylor]: Taking taylor expansion of (log n) in k 127.247 * [taylor]: Taking taylor expansion of n in k 127.247 * [backup-simplify]: Simplify n into n 127.247 * [backup-simplify]: Simplify (log n) into (log n) 127.247 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 127.247 * [taylor]: Taking taylor expansion of (* 2 PI) in k 127.247 * [taylor]: Taking taylor expansion of 2 in k 127.247 * [backup-simplify]: Simplify 2 into 2 127.247 * [taylor]: Taking taylor expansion of PI in k 127.247 * [backup-simplify]: Simplify PI into PI 127.248 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 127.248 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 127.249 * [backup-simplify]: Simplify (* 1/2 0) into 0 127.249 * [backup-simplify]: Simplify (- 0) into 0 127.249 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 127.250 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 127.250 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 127.251 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI)))) 127.252 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 127.252 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 127.253 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 127.254 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 127.255 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 127.255 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 127.255 * [backup-simplify]: Simplify (- 0) into 0 127.256 * [backup-simplify]: Simplify (+ 0 0) into 0 127.256 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0 127.258 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 127.259 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 127.261 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 127.261 * [taylor]: Taking taylor expansion of 0 in k 127.261 * [backup-simplify]: Simplify 0 into 0 127.261 * [backup-simplify]: Simplify 0 into 0 127.262 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 127.263 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 127.264 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 127.265 * [backup-simplify]: Simplify (+ 0 0) into 0 127.265 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 127.266 * [backup-simplify]: Simplify (- 1/2) into -1/2 127.266 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 127.268 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 127.271 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI)))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 127.273 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) 127.276 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) 127.278 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 127.279 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 127.283 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 127.284 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 127.284 * [backup-simplify]: Simplify (- 0) into 0 127.285 * [backup-simplify]: Simplify (+ 0 0) into 0 127.286 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0 127.288 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 127.290 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 127.292 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 127.292 * [taylor]: Taking taylor expansion of 0 in k 127.292 * [backup-simplify]: Simplify 0 into 0 127.292 * [backup-simplify]: Simplify 0 into 0 127.292 * [backup-simplify]: Simplify 0 into 0 127.294 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 127.295 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 127.298 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 127.299 * [backup-simplify]: Simplify (+ 0 0) into 0 127.300 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 127.300 * [backup-simplify]: Simplify (- 0) into 0 127.301 * [backup-simplify]: Simplify (+ 0 0) into 0 127.303 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 127.310 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI))))))) into 0 127.314 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) 127.320 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) 127.329 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) 127.330 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) 127.330 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 127.330 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k 127.330 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k 127.330 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k 127.330 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k 127.330 * [taylor]: Taking taylor expansion of 1/2 in k 127.330 * [backup-simplify]: Simplify 1/2 into 1/2 127.330 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 127.330 * [taylor]: Taking taylor expansion of 1/2 in k 127.330 * [backup-simplify]: Simplify 1/2 into 1/2 127.330 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 127.330 * [taylor]: Taking taylor expansion of 1/2 in k 127.330 * [backup-simplify]: Simplify 1/2 into 1/2 127.331 * [taylor]: Taking taylor expansion of (/ 1 k) in k 127.331 * [taylor]: Taking taylor expansion of k in k 127.331 * [backup-simplify]: Simplify 0 into 0 127.331 * [backup-simplify]: Simplify 1 into 1 127.331 * [backup-simplify]: Simplify (/ 1 1) into 1 127.331 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 127.331 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 127.331 * [taylor]: Taking taylor expansion of 2 in k 127.331 * [backup-simplify]: Simplify 2 into 2 127.331 * [taylor]: Taking taylor expansion of (/ PI n) in k 127.331 * [taylor]: Taking taylor expansion of PI in k 127.331 * [backup-simplify]: Simplify PI into PI 127.331 * [taylor]: Taking taylor expansion of n in k 127.331 * [backup-simplify]: Simplify n into n 127.331 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 127.331 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 127.331 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 127.331 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 127.332 * [backup-simplify]: Simplify (- 1/2) into -1/2 127.332 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 127.332 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4 127.332 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n)))) 127.332 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))))) 127.332 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n 127.332 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n 127.333 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n 127.333 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n 127.333 * [taylor]: Taking taylor expansion of 1/2 in n 127.333 * [backup-simplify]: Simplify 1/2 into 1/2 127.333 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 127.333 * [taylor]: Taking taylor expansion of 1/2 in n 127.333 * [backup-simplify]: Simplify 1/2 into 1/2 127.333 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 127.333 * [taylor]: Taking taylor expansion of 1/2 in n 127.333 * [backup-simplify]: Simplify 1/2 into 1/2 127.333 * [taylor]: Taking taylor expansion of (/ 1 k) in n 127.333 * [taylor]: Taking taylor expansion of k in n 127.333 * [backup-simplify]: Simplify k into k 127.333 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 127.333 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 127.333 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 127.333 * [taylor]: Taking taylor expansion of 2 in n 127.333 * [backup-simplify]: Simplify 2 into 2 127.333 * [taylor]: Taking taylor expansion of (/ PI n) in n 127.333 * [taylor]: Taking taylor expansion of PI in n 127.333 * [backup-simplify]: Simplify PI into PI 127.333 * [taylor]: Taking taylor expansion of n in n 127.333 * [backup-simplify]: Simplify 0 into 0 127.333 * [backup-simplify]: Simplify 1 into 1 127.333 * [backup-simplify]: Simplify (/ PI 1) into PI 127.333 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 127.334 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 127.334 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 127.334 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 127.334 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 127.334 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 127.335 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 127.336 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 127.337 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 127.337 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n 127.337 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n 127.337 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n 127.337 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n 127.337 * [taylor]: Taking taylor expansion of 1/2 in n 127.337 * [backup-simplify]: Simplify 1/2 into 1/2 127.337 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 127.337 * [taylor]: Taking taylor expansion of 1/2 in n 127.337 * [backup-simplify]: Simplify 1/2 into 1/2 127.337 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 127.337 * [taylor]: Taking taylor expansion of 1/2 in n 127.337 * [backup-simplify]: Simplify 1/2 into 1/2 127.337 * [taylor]: Taking taylor expansion of (/ 1 k) in n 127.337 * [taylor]: Taking taylor expansion of k in n 127.337 * [backup-simplify]: Simplify k into k 127.337 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 127.337 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 127.337 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 127.337 * [taylor]: Taking taylor expansion of 2 in n 127.337 * [backup-simplify]: Simplify 2 into 2 127.337 * [taylor]: Taking taylor expansion of (/ PI n) in n 127.337 * [taylor]: Taking taylor expansion of PI in n 127.337 * [backup-simplify]: Simplify PI into PI 127.337 * [taylor]: Taking taylor expansion of n in n 127.337 * [backup-simplify]: Simplify 0 into 0 127.337 * [backup-simplify]: Simplify 1 into 1 127.337 * [backup-simplify]: Simplify (/ PI 1) into PI 127.338 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 127.338 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 127.338 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 127.338 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 127.338 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 127.338 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 127.339 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 127.340 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 127.341 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 127.341 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k 127.341 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 127.341 * [taylor]: Taking taylor expansion of 1/2 in k 127.341 * [backup-simplify]: Simplify 1/2 into 1/2 127.341 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 127.341 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 127.341 * [taylor]: Taking taylor expansion of 1/2 in k 127.341 * [backup-simplify]: Simplify 1/2 into 1/2 127.341 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 127.341 * [taylor]: Taking taylor expansion of 1/2 in k 127.341 * [backup-simplify]: Simplify 1/2 into 1/2 127.341 * [taylor]: Taking taylor expansion of (/ 1 k) in k 127.341 * [taylor]: Taking taylor expansion of k in k 127.341 * [backup-simplify]: Simplify 0 into 0 127.341 * [backup-simplify]: Simplify 1 into 1 127.341 * [backup-simplify]: Simplify (/ 1 1) into 1 127.341 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 127.341 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 127.341 * [taylor]: Taking taylor expansion of (* 2 PI) in k 127.341 * [taylor]: Taking taylor expansion of 2 in k 127.341 * [backup-simplify]: Simplify 2 into 2 127.341 * [taylor]: Taking taylor expansion of PI in k 127.341 * [backup-simplify]: Simplify PI into PI 127.342 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 127.342 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 127.342 * [taylor]: Taking taylor expansion of (log n) in k 127.342 * [taylor]: Taking taylor expansion of n in k 127.342 * [backup-simplify]: Simplify n into n 127.342 * [backup-simplify]: Simplify (log n) into (log n) 127.343 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 127.343 * [backup-simplify]: Simplify (- 1/2) into -1/2 127.343 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 127.343 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 127.344 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 127.344 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 127.345 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n))) 127.346 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 127.346 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 127.347 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 127.347 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 127.348 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 127.348 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 127.349 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 127.349 * [backup-simplify]: Simplify (- 0) into 0 127.349 * [backup-simplify]: Simplify (+ 0 0) into 0 127.349 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0 127.350 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 127.351 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 127.352 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 127.352 * [taylor]: Taking taylor expansion of 0 in k 127.352 * [backup-simplify]: Simplify 0 into 0 127.352 * [backup-simplify]: Simplify 0 into 0 127.352 * [backup-simplify]: Simplify 0 into 0 127.353 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.354 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 127.355 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 127.356 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 127.356 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 127.356 * [backup-simplify]: Simplify (- 0) into 0 127.357 * [backup-simplify]: Simplify (+ 0 0) into 0 127.357 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0 127.358 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 127.359 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 127.360 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 127.360 * [taylor]: Taking taylor expansion of 0 in k 127.360 * [backup-simplify]: Simplify 0 into 0 127.360 * [backup-simplify]: Simplify 0 into 0 127.360 * [backup-simplify]: Simplify 0 into 0 127.360 * [backup-simplify]: Simplify 0 into 0 127.361 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.362 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 127.367 * [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 0 127.367 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 127.368 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 127.369 * [backup-simplify]: Simplify (- 0) into 0 127.369 * [backup-simplify]: Simplify (+ 0 0) into 0 127.370 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0 127.372 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 127.374 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 127.376 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 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 0 127.377 * [taylor]: Taking taylor expansion of 0 in k 127.377 * [backup-simplify]: Simplify 0 into 0 127.377 * [backup-simplify]: Simplify 0 into 0 127.378 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 127.379 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) 127.379 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0 127.379 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k 127.379 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k 127.379 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k 127.379 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 127.379 * [taylor]: Taking taylor expansion of 1/2 in k 127.379 * [backup-simplify]: Simplify 1/2 into 1/2 127.379 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 127.379 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 127.379 * [taylor]: Taking taylor expansion of 1/2 in k 127.379 * [backup-simplify]: Simplify 1/2 into 1/2 127.379 * [taylor]: Taking taylor expansion of (/ 1 k) in k 127.379 * [taylor]: Taking taylor expansion of k in k 127.379 * [backup-simplify]: Simplify 0 into 0 127.379 * [backup-simplify]: Simplify 1 into 1 127.380 * [backup-simplify]: Simplify (/ 1 1) into 1 127.380 * [taylor]: Taking taylor expansion of 1/2 in k 127.380 * [backup-simplify]: Simplify 1/2 into 1/2 127.380 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 127.380 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 127.380 * [taylor]: Taking taylor expansion of -2 in k 127.380 * [backup-simplify]: Simplify -2 into -2 127.380 * [taylor]: Taking taylor expansion of (/ PI n) in k 127.380 * [taylor]: Taking taylor expansion of PI in k 127.380 * [backup-simplify]: Simplify PI into PI 127.380 * [taylor]: Taking taylor expansion of n in k 127.380 * [backup-simplify]: Simplify n into n 127.380 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 127.380 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 127.380 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 127.381 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 127.381 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 127.381 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4 127.381 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n)))) 127.382 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 127.382 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n 127.382 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n 127.382 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n 127.382 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 127.382 * [taylor]: Taking taylor expansion of 1/2 in n 127.382 * [backup-simplify]: Simplify 1/2 into 1/2 127.382 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 127.382 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 127.382 * [taylor]: Taking taylor expansion of 1/2 in n 127.382 * [backup-simplify]: Simplify 1/2 into 1/2 127.382 * [taylor]: Taking taylor expansion of (/ 1 k) in n 127.382 * [taylor]: Taking taylor expansion of k in n 127.382 * [backup-simplify]: Simplify k into k 127.382 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 127.382 * [taylor]: Taking taylor expansion of 1/2 in n 127.382 * [backup-simplify]: Simplify 1/2 into 1/2 127.382 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 127.382 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 127.382 * [taylor]: Taking taylor expansion of -2 in n 127.382 * [backup-simplify]: Simplify -2 into -2 127.382 * [taylor]: Taking taylor expansion of (/ PI n) in n 127.382 * [taylor]: Taking taylor expansion of PI in n 127.382 * [backup-simplify]: Simplify PI into PI 127.382 * [taylor]: Taking taylor expansion of n in n 127.382 * [backup-simplify]: Simplify 0 into 0 127.382 * [backup-simplify]: Simplify 1 into 1 127.383 * [backup-simplify]: Simplify (/ PI 1) into PI 127.383 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 127.384 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 127.384 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 127.384 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 127.385 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 127.386 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 127.387 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 127.388 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 127.388 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n 127.388 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n 127.388 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n 127.388 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 127.388 * [taylor]: Taking taylor expansion of 1/2 in n 127.388 * [backup-simplify]: Simplify 1/2 into 1/2 127.388 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 127.388 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 127.388 * [taylor]: Taking taylor expansion of 1/2 in n 127.388 * [backup-simplify]: Simplify 1/2 into 1/2 127.388 * [taylor]: Taking taylor expansion of (/ 1 k) in n 127.388 * [taylor]: Taking taylor expansion of k in n 127.388 * [backup-simplify]: Simplify k into k 127.389 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 127.389 * [taylor]: Taking taylor expansion of 1/2 in n 127.389 * [backup-simplify]: Simplify 1/2 into 1/2 127.389 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 127.389 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 127.389 * [taylor]: Taking taylor expansion of -2 in n 127.389 * [backup-simplify]: Simplify -2 into -2 127.389 * [taylor]: Taking taylor expansion of (/ PI n) in n 127.389 * [taylor]: Taking taylor expansion of PI in n 127.389 * [backup-simplify]: Simplify PI into PI 127.389 * [taylor]: Taking taylor expansion of n in n 127.389 * [backup-simplify]: Simplify 0 into 0 127.389 * [backup-simplify]: Simplify 1 into 1 127.389 * [backup-simplify]: Simplify (/ PI 1) into PI 127.390 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 127.391 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 127.391 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 127.391 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 127.391 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 127.392 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 127.394 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 127.395 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 127.395 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k 127.395 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 127.395 * [taylor]: Taking taylor expansion of 1/2 in k 127.395 * [backup-simplify]: Simplify 1/2 into 1/2 127.395 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 127.395 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 127.395 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 127.395 * [taylor]: Taking taylor expansion of 1/2 in k 127.395 * [backup-simplify]: Simplify 1/2 into 1/2 127.395 * [taylor]: Taking taylor expansion of (/ 1 k) in k 127.395 * [taylor]: Taking taylor expansion of k in k 127.395 * [backup-simplify]: Simplify 0 into 0 127.395 * [backup-simplify]: Simplify 1 into 1 127.396 * [backup-simplify]: Simplify (/ 1 1) into 1 127.396 * [taylor]: Taking taylor expansion of 1/2 in k 127.396 * [backup-simplify]: Simplify 1/2 into 1/2 127.396 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 127.396 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 127.396 * [taylor]: Taking taylor expansion of (* -2 PI) in k 127.396 * [taylor]: Taking taylor expansion of -2 in k 127.396 * [backup-simplify]: Simplify -2 into -2 127.396 * [taylor]: Taking taylor expansion of PI in k 127.396 * [backup-simplify]: Simplify PI into PI 127.396 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 127.397 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 127.397 * [taylor]: Taking taylor expansion of (log n) in k 127.397 * [taylor]: Taking taylor expansion of n in k 127.397 * [backup-simplify]: Simplify n into n 127.398 * [backup-simplify]: Simplify (log n) into (log n) 127.399 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 127.399 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 127.399 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 127.400 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 127.401 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 127.402 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n))) 127.403 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 127.404 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 127.405 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 127.406 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 127.408 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 127.408 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 127.409 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 127.409 * [backup-simplify]: Simplify (+ 0 0) into 0 127.409 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 127.411 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 127.412 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 127.414 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 127.414 * [taylor]: Taking taylor expansion of 0 in k 127.414 * [backup-simplify]: Simplify 0 into 0 127.414 * [backup-simplify]: Simplify 0 into 0 127.414 * [backup-simplify]: Simplify 0 into 0 127.415 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.416 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 127.420 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 127.420 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 127.421 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 127.421 * [backup-simplify]: Simplify (+ 0 0) into 0 127.422 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 127.423 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 127.425 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 127.430 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 127.430 * [taylor]: Taking taylor expansion of 0 in k 127.430 * [backup-simplify]: Simplify 0 into 0 127.430 * [backup-simplify]: Simplify 0 into 0 127.430 * [backup-simplify]: Simplify 0 into 0 127.430 * [backup-simplify]: Simplify 0 into 0 127.431 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.432 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 127.439 * [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 0 127.439 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 127.441 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 127.441 * [backup-simplify]: Simplify (+ 0 0) into 0 127.442 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 127.444 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 127.446 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 127.450 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 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 0 127.450 * [taylor]: Taking taylor expansion of 0 in k 127.450 * [backup-simplify]: Simplify 0 into 0 127.450 * [backup-simplify]: Simplify 0 into 0 127.451 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 127.451 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1) 127.452 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) 127.452 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0 127.452 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k 127.452 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k 127.452 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k 127.452 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k 127.452 * [taylor]: Taking taylor expansion of 1/2 in k 127.453 * [backup-simplify]: Simplify 1/2 into 1/2 127.453 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 127.453 * [taylor]: Taking taylor expansion of 1/2 in k 127.453 * [backup-simplify]: Simplify 1/2 into 1/2 127.453 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 127.453 * [taylor]: Taking taylor expansion of 1/2 in k 127.453 * [backup-simplify]: Simplify 1/2 into 1/2 127.453 * [taylor]: Taking taylor expansion of k in k 127.453 * [backup-simplify]: Simplify 0 into 0 127.453 * [backup-simplify]: Simplify 1 into 1 127.453 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 127.453 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 127.453 * [taylor]: Taking taylor expansion of 2 in k 127.453 * [backup-simplify]: Simplify 2 into 2 127.453 * [taylor]: Taking taylor expansion of (* n PI) in k 127.453 * [taylor]: Taking taylor expansion of n in k 127.453 * [backup-simplify]: Simplify n into n 127.453 * [taylor]: Taking taylor expansion of PI in k 127.453 * [backup-simplify]: Simplify PI into PI 127.453 * [backup-simplify]: Simplify (* n PI) into (* n PI) 127.453 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 127.453 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 127.454 * [backup-simplify]: Simplify (* 1/2 0) into 0 127.454 * [backup-simplify]: Simplify (- 0) into 0 127.455 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 127.455 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4 127.455 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI)))) 127.455 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4) 127.455 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n 127.455 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n 127.455 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n 127.455 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n 127.455 * [taylor]: Taking taylor expansion of 1/2 in n 127.455 * [backup-simplify]: Simplify 1/2 into 1/2 127.456 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 127.456 * [taylor]: Taking taylor expansion of 1/2 in n 127.456 * [backup-simplify]: Simplify 1/2 into 1/2 127.456 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 127.456 * [taylor]: Taking taylor expansion of 1/2 in n 127.456 * [backup-simplify]: Simplify 1/2 into 1/2 127.456 * [taylor]: Taking taylor expansion of k in n 127.456 * [backup-simplify]: Simplify k into k 127.456 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 127.456 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 127.456 * [taylor]: Taking taylor expansion of 2 in n 127.456 * [backup-simplify]: Simplify 2 into 2 127.456 * [taylor]: Taking taylor expansion of (* n PI) in n 127.456 * [taylor]: Taking taylor expansion of n in n 127.456 * [backup-simplify]: Simplify 0 into 0 127.456 * [backup-simplify]: Simplify 1 into 1 127.456 * [taylor]: Taking taylor expansion of PI in n 127.456 * [backup-simplify]: Simplify PI into PI 127.456 * [backup-simplify]: Simplify (* 0 PI) into 0 127.457 * [backup-simplify]: Simplify (* 2 0) into 0 127.458 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 127.460 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 127.461 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 127.461 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 127.461 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 127.461 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 127.461 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k))) 127.462 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 127.463 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 127.464 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 127.465 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n 127.465 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n 127.465 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n 127.465 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n 127.465 * [taylor]: Taking taylor expansion of 1/2 in n 127.465 * [backup-simplify]: Simplify 1/2 into 1/2 127.465 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 127.465 * [taylor]: Taking taylor expansion of 1/2 in n 127.465 * [backup-simplify]: Simplify 1/2 into 1/2 127.465 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 127.465 * [taylor]: Taking taylor expansion of 1/2 in n 127.465 * [backup-simplify]: Simplify 1/2 into 1/2 127.465 * [taylor]: Taking taylor expansion of k in n 127.465 * [backup-simplify]: Simplify k into k 127.465 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 127.465 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 127.465 * [taylor]: Taking taylor expansion of 2 in n 127.465 * [backup-simplify]: Simplify 2 into 2 127.465 * [taylor]: Taking taylor expansion of (* n PI) in n 127.465 * [taylor]: Taking taylor expansion of n in n 127.465 * [backup-simplify]: Simplify 0 into 0 127.465 * [backup-simplify]: Simplify 1 into 1 127.465 * [taylor]: Taking taylor expansion of PI in n 127.465 * [backup-simplify]: Simplify PI into PI 127.466 * [backup-simplify]: Simplify (* 0 PI) into 0 127.466 * [backup-simplify]: Simplify (* 2 0) into 0 127.468 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 127.469 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 127.470 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 127.470 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 127.470 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 127.470 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 127.470 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k))) 127.472 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 127.473 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 127.474 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 127.475 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k 127.475 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 127.475 * [taylor]: Taking taylor expansion of 1/2 in k 127.475 * [backup-simplify]: Simplify 1/2 into 1/2 127.475 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 127.475 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 127.475 * [taylor]: Taking taylor expansion of 1/2 in k 127.475 * [backup-simplify]: Simplify 1/2 into 1/2 127.475 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 127.475 * [taylor]: Taking taylor expansion of 1/2 in k 127.475 * [backup-simplify]: Simplify 1/2 into 1/2 127.475 * [taylor]: Taking taylor expansion of k in k 127.475 * [backup-simplify]: Simplify 0 into 0 127.475 * [backup-simplify]: Simplify 1 into 1 127.475 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 127.475 * [taylor]: Taking taylor expansion of (log n) in k 127.475 * [taylor]: Taking taylor expansion of n in k 127.475 * [backup-simplify]: Simplify n into n 127.475 * [backup-simplify]: Simplify (log n) into (log n) 127.475 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 127.475 * [taylor]: Taking taylor expansion of (* 2 PI) in k 127.475 * [taylor]: Taking taylor expansion of 2 in k 127.475 * [backup-simplify]: Simplify 2 into 2 127.475 * [taylor]: Taking taylor expansion of PI in k 127.475 * [backup-simplify]: Simplify PI into PI 127.476 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 127.477 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 127.477 * [backup-simplify]: Simplify (* 1/2 0) into 0 127.478 * [backup-simplify]: Simplify (- 0) into 0 127.478 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 127.479 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 127.480 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 127.481 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI)))) 127.482 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 127.483 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 127.485 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 127.486 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 127.488 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 127.488 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 127.488 * [backup-simplify]: Simplify (- 0) into 0 127.489 * [backup-simplify]: Simplify (+ 0 0) into 0 127.489 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0 127.491 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 127.492 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 127.494 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0 127.494 * [taylor]: Taking taylor expansion of 0 in k 127.494 * [backup-simplify]: Simplify 0 into 0 127.494 * [backup-simplify]: Simplify 0 into 0 127.495 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 127.496 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 127.498 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 127.498 * [backup-simplify]: Simplify (+ 0 0) into 0 127.499 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 127.500 * [backup-simplify]: Simplify (- 1/2) into -1/2 127.500 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 127.501 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 127.505 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI)))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 127.508 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) 127.511 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) 127.512 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 127.514 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 127.517 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 127.518 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 127.518 * [backup-simplify]: Simplify (- 0) into 0 127.519 * [backup-simplify]: Simplify (+ 0 0) into 0 127.520 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0 127.521 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 127.523 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 127.525 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 127.525 * [taylor]: Taking taylor expansion of 0 in k 127.526 * [backup-simplify]: Simplify 0 into 0 127.526 * [backup-simplify]: Simplify 0 into 0 127.526 * [backup-simplify]: Simplify 0 into 0 127.527 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 127.528 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 127.532 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 127.533 * [backup-simplify]: Simplify (+ 0 0) into 0 127.534 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 127.534 * [backup-simplify]: Simplify (- 0) into 0 127.535 * [backup-simplify]: Simplify (+ 0 0) into 0 127.536 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 127.540 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI))))))) into 0 127.544 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) 127.549 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) 127.559 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) 127.560 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) 127.560 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 127.560 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k 127.560 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k 127.560 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k 127.560 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k 127.560 * [taylor]: Taking taylor expansion of 1/2 in k 127.560 * [backup-simplify]: Simplify 1/2 into 1/2 127.560 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 127.560 * [taylor]: Taking taylor expansion of 1/2 in k 127.560 * [backup-simplify]: Simplify 1/2 into 1/2 127.560 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 127.560 * [taylor]: Taking taylor expansion of 1/2 in k 127.560 * [backup-simplify]: Simplify 1/2 into 1/2 127.560 * [taylor]: Taking taylor expansion of (/ 1 k) in k 127.560 * [taylor]: Taking taylor expansion of k in k 127.560 * [backup-simplify]: Simplify 0 into 0 127.560 * [backup-simplify]: Simplify 1 into 1 127.561 * [backup-simplify]: Simplify (/ 1 1) into 1 127.561 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 127.561 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 127.561 * [taylor]: Taking taylor expansion of 2 in k 127.561 * [backup-simplify]: Simplify 2 into 2 127.561 * [taylor]: Taking taylor expansion of (/ PI n) in k 127.561 * [taylor]: Taking taylor expansion of PI in k 127.561 * [backup-simplify]: Simplify PI into PI 127.561 * [taylor]: Taking taylor expansion of n in k 127.561 * [backup-simplify]: Simplify n into n 127.561 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 127.561 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 127.561 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 127.562 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 127.562 * [backup-simplify]: Simplify (- 1/2) into -1/2 127.562 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 127.563 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4 127.563 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n)))) 127.563 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))))) 127.563 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n 127.563 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n 127.563 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n 127.563 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n 127.563 * [taylor]: Taking taylor expansion of 1/2 in n 127.563 * [backup-simplify]: Simplify 1/2 into 1/2 127.563 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 127.563 * [taylor]: Taking taylor expansion of 1/2 in n 127.563 * [backup-simplify]: Simplify 1/2 into 1/2 127.563 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 127.563 * [taylor]: Taking taylor expansion of 1/2 in n 127.563 * [backup-simplify]: Simplify 1/2 into 1/2 127.563 * [taylor]: Taking taylor expansion of (/ 1 k) in n 127.563 * [taylor]: Taking taylor expansion of k in n 127.563 * [backup-simplify]: Simplify k into k 127.563 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 127.563 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 127.563 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 127.563 * [taylor]: Taking taylor expansion of 2 in n 127.563 * [backup-simplify]: Simplify 2 into 2 127.563 * [taylor]: Taking taylor expansion of (/ PI n) in n 127.563 * [taylor]: Taking taylor expansion of PI in n 127.563 * [backup-simplify]: Simplify PI into PI 127.563 * [taylor]: Taking taylor expansion of n in n 127.563 * [backup-simplify]: Simplify 0 into 0 127.563 * [backup-simplify]: Simplify 1 into 1 127.564 * [backup-simplify]: Simplify (/ PI 1) into PI 127.564 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 127.565 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 127.565 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 127.565 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 127.565 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 127.565 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 127.566 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 127.566 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 127.567 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 127.567 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n 127.567 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n 127.567 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n 127.567 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n 127.567 * [taylor]: Taking taylor expansion of 1/2 in n 127.567 * [backup-simplify]: Simplify 1/2 into 1/2 127.567 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 127.567 * [taylor]: Taking taylor expansion of 1/2 in n 127.567 * [backup-simplify]: Simplify 1/2 into 1/2 127.567 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 127.567 * [taylor]: Taking taylor expansion of 1/2 in n 127.567 * [backup-simplify]: Simplify 1/2 into 1/2 127.567 * [taylor]: Taking taylor expansion of (/ 1 k) in n 127.567 * [taylor]: Taking taylor expansion of k in n 127.567 * [backup-simplify]: Simplify k into k 127.567 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 127.567 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 127.567 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 127.567 * [taylor]: Taking taylor expansion of 2 in n 127.567 * [backup-simplify]: Simplify 2 into 2 127.567 * [taylor]: Taking taylor expansion of (/ PI n) in n 127.567 * [taylor]: Taking taylor expansion of PI in n 127.567 * [backup-simplify]: Simplify PI into PI 127.567 * [taylor]: Taking taylor expansion of n in n 127.567 * [backup-simplify]: Simplify 0 into 0 127.567 * [backup-simplify]: Simplify 1 into 1 127.568 * [backup-simplify]: Simplify (/ PI 1) into PI 127.568 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 127.569 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 127.569 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 127.569 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 127.569 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 127.569 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 127.571 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 127.572 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 127.572 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 127.573 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k 127.573 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 127.573 * [taylor]: Taking taylor expansion of 1/2 in k 127.573 * [backup-simplify]: Simplify 1/2 into 1/2 127.573 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 127.573 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 127.573 * [taylor]: Taking taylor expansion of 1/2 in k 127.573 * [backup-simplify]: Simplify 1/2 into 1/2 127.573 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 127.573 * [taylor]: Taking taylor expansion of 1/2 in k 127.573 * [backup-simplify]: Simplify 1/2 into 1/2 127.573 * [taylor]: Taking taylor expansion of (/ 1 k) in k 127.573 * [taylor]: Taking taylor expansion of k in k 127.573 * [backup-simplify]: Simplify 0 into 0 127.573 * [backup-simplify]: Simplify 1 into 1 127.573 * [backup-simplify]: Simplify (/ 1 1) into 1 127.573 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 127.573 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 127.573 * [taylor]: Taking taylor expansion of (* 2 PI) in k 127.573 * [taylor]: Taking taylor expansion of 2 in k 127.573 * [backup-simplify]: Simplify 2 into 2 127.573 * [taylor]: Taking taylor expansion of PI in k 127.573 * [backup-simplify]: Simplify PI into PI 127.573 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 127.574 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 127.574 * [taylor]: Taking taylor expansion of (log n) in k 127.574 * [taylor]: Taking taylor expansion of n in k 127.574 * [backup-simplify]: Simplify n into n 127.574 * [backup-simplify]: Simplify (log n) into (log n) 127.574 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 127.575 * [backup-simplify]: Simplify (- 1/2) into -1/2 127.575 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 127.575 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 127.576 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 127.576 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 127.577 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n))) 127.577 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 127.578 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 127.579 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 127.579 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 127.580 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 127.580 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 127.581 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 127.581 * [backup-simplify]: Simplify (- 0) into 0 127.581 * [backup-simplify]: Simplify (+ 0 0) into 0 127.581 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0 127.582 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 127.583 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 127.584 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 127.584 * [taylor]: Taking taylor expansion of 0 in k 127.584 * [backup-simplify]: Simplify 0 into 0 127.584 * [backup-simplify]: Simplify 0 into 0 127.584 * [backup-simplify]: Simplify 0 into 0 127.585 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.586 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 127.588 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 127.588 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 127.588 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 127.588 * [backup-simplify]: Simplify (- 0) into 0 127.589 * [backup-simplify]: Simplify (+ 0 0) into 0 127.589 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0 127.590 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 127.591 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 127.593 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 127.593 * [taylor]: Taking taylor expansion of 0 in k 127.593 * [backup-simplify]: Simplify 0 into 0 127.593 * [backup-simplify]: Simplify 0 into 0 127.593 * [backup-simplify]: Simplify 0 into 0 127.593 * [backup-simplify]: Simplify 0 into 0 127.593 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.594 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 127.597 * [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 0 127.598 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 127.598 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 127.599 * [backup-simplify]: Simplify (- 0) into 0 127.599 * [backup-simplify]: Simplify (+ 0 0) into 0 127.600 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0 127.601 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 127.602 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 127.604 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 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 0 127.604 * [taylor]: Taking taylor expansion of 0 in k 127.604 * [backup-simplify]: Simplify 0 into 0 127.604 * [backup-simplify]: Simplify 0 into 0 127.605 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 127.605 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) 127.605 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0 127.605 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k 127.605 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k 127.605 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k 127.606 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 127.606 * [taylor]: Taking taylor expansion of 1/2 in k 127.606 * [backup-simplify]: Simplify 1/2 into 1/2 127.606 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 127.606 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 127.606 * [taylor]: Taking taylor expansion of 1/2 in k 127.606 * [backup-simplify]: Simplify 1/2 into 1/2 127.606 * [taylor]: Taking taylor expansion of (/ 1 k) in k 127.606 * [taylor]: Taking taylor expansion of k in k 127.606 * [backup-simplify]: Simplify 0 into 0 127.606 * [backup-simplify]: Simplify 1 into 1 127.606 * [backup-simplify]: Simplify (/ 1 1) into 1 127.606 * [taylor]: Taking taylor expansion of 1/2 in k 127.606 * [backup-simplify]: Simplify 1/2 into 1/2 127.606 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 127.606 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 127.606 * [taylor]: Taking taylor expansion of -2 in k 127.606 * [backup-simplify]: Simplify -2 into -2 127.606 * [taylor]: Taking taylor expansion of (/ PI n) in k 127.606 * [taylor]: Taking taylor expansion of PI in k 127.606 * [backup-simplify]: Simplify PI into PI 127.606 * [taylor]: Taking taylor expansion of n in k 127.606 * [backup-simplify]: Simplify n into n 127.606 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 127.606 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 127.606 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 127.606 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 127.607 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 127.607 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4 127.607 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n)))) 127.607 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 127.607 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n 127.607 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n 127.607 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n 127.607 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 127.607 * [taylor]: Taking taylor expansion of 1/2 in n 127.607 * [backup-simplify]: Simplify 1/2 into 1/2 127.607 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 127.607 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 127.607 * [taylor]: Taking taylor expansion of 1/2 in n 127.607 * [backup-simplify]: Simplify 1/2 into 1/2 127.607 * [taylor]: Taking taylor expansion of (/ 1 k) in n 127.607 * [taylor]: Taking taylor expansion of k in n 127.607 * [backup-simplify]: Simplify k into k 127.607 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 127.607 * [taylor]: Taking taylor expansion of 1/2 in n 127.608 * [backup-simplify]: Simplify 1/2 into 1/2 127.608 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 127.608 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 127.608 * [taylor]: Taking taylor expansion of -2 in n 127.608 * [backup-simplify]: Simplify -2 into -2 127.608 * [taylor]: Taking taylor expansion of (/ PI n) in n 127.608 * [taylor]: Taking taylor expansion of PI in n 127.608 * [backup-simplify]: Simplify PI into PI 127.608 * [taylor]: Taking taylor expansion of n in n 127.608 * [backup-simplify]: Simplify 0 into 0 127.608 * [backup-simplify]: Simplify 1 into 1 127.608 * [backup-simplify]: Simplify (/ PI 1) into PI 127.608 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 127.609 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 127.609 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 127.609 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 127.609 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 127.610 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 127.611 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 127.611 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 127.611 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n 127.611 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n 127.611 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n 127.611 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 127.611 * [taylor]: Taking taylor expansion of 1/2 in n 127.611 * [backup-simplify]: Simplify 1/2 into 1/2 127.611 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 127.611 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 127.611 * [taylor]: Taking taylor expansion of 1/2 in n 127.611 * [backup-simplify]: Simplify 1/2 into 1/2 127.611 * [taylor]: Taking taylor expansion of (/ 1 k) in n 127.611 * [taylor]: Taking taylor expansion of k in n 127.611 * [backup-simplify]: Simplify k into k 127.611 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 127.612 * [taylor]: Taking taylor expansion of 1/2 in n 127.612 * [backup-simplify]: Simplify 1/2 into 1/2 127.612 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 127.612 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 127.612 * [taylor]: Taking taylor expansion of -2 in n 127.612 * [backup-simplify]: Simplify -2 into -2 127.612 * [taylor]: Taking taylor expansion of (/ PI n) in n 127.612 * [taylor]: Taking taylor expansion of PI in n 127.612 * [backup-simplify]: Simplify PI into PI 127.612 * [taylor]: Taking taylor expansion of n in n 127.612 * [backup-simplify]: Simplify 0 into 0 127.612 * [backup-simplify]: Simplify 1 into 1 127.612 * [backup-simplify]: Simplify (/ PI 1) into PI 127.612 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 127.613 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 127.613 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 127.613 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 127.613 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 127.614 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 127.615 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 127.615 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 127.615 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k 127.615 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 127.615 * [taylor]: Taking taylor expansion of 1/2 in k 127.615 * [backup-simplify]: Simplify 1/2 into 1/2 127.615 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 127.615 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 127.615 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 127.615 * [taylor]: Taking taylor expansion of 1/2 in k 127.616 * [backup-simplify]: Simplify 1/2 into 1/2 127.616 * [taylor]: Taking taylor expansion of (/ 1 k) in k 127.616 * [taylor]: Taking taylor expansion of k in k 127.616 * [backup-simplify]: Simplify 0 into 0 127.616 * [backup-simplify]: Simplify 1 into 1 127.616 * [backup-simplify]: Simplify (/ 1 1) into 1 127.616 * [taylor]: Taking taylor expansion of 1/2 in k 127.616 * [backup-simplify]: Simplify 1/2 into 1/2 127.616 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 127.616 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 127.616 * [taylor]: Taking taylor expansion of (* -2 PI) in k 127.616 * [taylor]: Taking taylor expansion of -2 in k 127.616 * [backup-simplify]: Simplify -2 into -2 127.616 * [taylor]: Taking taylor expansion of PI in k 127.616 * [backup-simplify]: Simplify PI into PI 127.616 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 127.617 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 127.617 * [taylor]: Taking taylor expansion of (log n) in k 127.617 * [taylor]: Taking taylor expansion of n in k 127.617 * [backup-simplify]: Simplify n into n 127.617 * [backup-simplify]: Simplify (log n) into (log n) 127.617 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 127.617 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 127.618 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 127.618 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 127.619 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 127.619 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n))) 127.620 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 127.621 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 127.621 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 127.622 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 127.623 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 127.623 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 127.623 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 127.624 * [backup-simplify]: Simplify (+ 0 0) into 0 127.624 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 127.625 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 127.625 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 127.627 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 127.627 * [taylor]: Taking taylor expansion of 0 in k 127.627 * [backup-simplify]: Simplify 0 into 0 127.627 * [backup-simplify]: Simplify 0 into 0 127.627 * [backup-simplify]: Simplify 0 into 0 127.628 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.629 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 127.632 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 127.632 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 127.633 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 127.633 * [backup-simplify]: Simplify (+ 0 0) into 0 127.634 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 127.635 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 127.637 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 127.639 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 127.639 * [taylor]: Taking taylor expansion of 0 in k 127.639 * [backup-simplify]: Simplify 0 into 0 127.639 * [backup-simplify]: Simplify 0 into 0 127.639 * [backup-simplify]: Simplify 0 into 0 127.639 * [backup-simplify]: Simplify 0 into 0 127.640 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.642 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 127.648 * [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 0 127.648 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 127.650 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 127.650 * [backup-simplify]: Simplify (+ 0 0) into 0 127.651 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 127.652 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 127.653 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 127.654 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 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 0 127.654 * [taylor]: Taking taylor expansion of 0 in k 127.654 * [backup-simplify]: Simplify 0 into 0 127.654 * [backup-simplify]: Simplify 0 into 0 127.655 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 127.655 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1) 127.656 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 127.656 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 127.656 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 127.656 * [taylor]: Taking taylor expansion of 2 in n 127.656 * [backup-simplify]: Simplify 2 into 2 127.656 * [taylor]: Taking taylor expansion of (* n PI) in n 127.656 * [taylor]: Taking taylor expansion of n in n 127.656 * [backup-simplify]: Simplify 0 into 0 127.656 * [backup-simplify]: Simplify 1 into 1 127.656 * [taylor]: Taking taylor expansion of PI in n 127.656 * [backup-simplify]: Simplify PI into PI 127.656 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 127.656 * [taylor]: Taking taylor expansion of 2 in n 127.656 * [backup-simplify]: Simplify 2 into 2 127.656 * [taylor]: Taking taylor expansion of (* n PI) in n 127.656 * [taylor]: Taking taylor expansion of n in n 127.656 * [backup-simplify]: Simplify 0 into 0 127.656 * [backup-simplify]: Simplify 1 into 1 127.656 * [taylor]: Taking taylor expansion of PI in n 127.656 * [backup-simplify]: Simplify PI into PI 127.656 * [backup-simplify]: Simplify (* 0 PI) into 0 127.657 * [backup-simplify]: Simplify (* 2 0) into 0 127.657 * [backup-simplify]: Simplify 0 into 0 127.657 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 127.658 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 127.659 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 127.659 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 127.660 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 127.660 * [backup-simplify]: Simplify 0 into 0 127.660 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 127.661 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 127.661 * [backup-simplify]: Simplify 0 into 0 127.662 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 127.663 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 127.663 * [backup-simplify]: Simplify 0 into 0 127.663 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 127.666 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 127.666 * [backup-simplify]: Simplify 0 into 0 127.667 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 127.668 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 127.668 * [backup-simplify]: Simplify 0 into 0 127.669 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 127.670 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 127.670 * [backup-simplify]: Simplify 0 into 0 127.671 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 127.671 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 127.671 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 127.671 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 127.671 * [taylor]: Taking taylor expansion of 2 in n 127.671 * [backup-simplify]: Simplify 2 into 2 127.671 * [taylor]: Taking taylor expansion of (/ PI n) in n 127.671 * [taylor]: Taking taylor expansion of PI in n 127.671 * [backup-simplify]: Simplify PI into PI 127.671 * [taylor]: Taking taylor expansion of n in n 127.671 * [backup-simplify]: Simplify 0 into 0 127.671 * [backup-simplify]: Simplify 1 into 1 127.671 * [backup-simplify]: Simplify (/ PI 1) into PI 127.671 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 127.671 * [taylor]: Taking taylor expansion of 2 in n 127.671 * [backup-simplify]: Simplify 2 into 2 127.671 * [taylor]: Taking taylor expansion of (/ PI n) in n 127.672 * [taylor]: Taking taylor expansion of PI in n 127.672 * [backup-simplify]: Simplify PI into PI 127.672 * [taylor]: Taking taylor expansion of n in n 127.672 * [backup-simplify]: Simplify 0 into 0 127.672 * [backup-simplify]: Simplify 1 into 1 127.672 * [backup-simplify]: Simplify (/ PI 1) into PI 127.672 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 127.673 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 127.673 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 127.674 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 127.674 * [backup-simplify]: Simplify 0 into 0 127.674 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.675 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 127.675 * [backup-simplify]: Simplify 0 into 0 127.675 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.676 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 127.676 * [backup-simplify]: Simplify 0 into 0 127.677 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.677 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 127.677 * [backup-simplify]: Simplify 0 into 0 127.678 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.679 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 127.679 * [backup-simplify]: Simplify 0 into 0 127.680 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.680 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 127.681 * [backup-simplify]: Simplify 0 into 0 127.681 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 127.681 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 127.681 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 127.681 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 127.681 * [taylor]: Taking taylor expansion of -2 in n 127.681 * [backup-simplify]: Simplify -2 into -2 127.681 * [taylor]: Taking taylor expansion of (/ PI n) in n 127.681 * [taylor]: Taking taylor expansion of PI in n 127.681 * [backup-simplify]: Simplify PI into PI 127.681 * [taylor]: Taking taylor expansion of n in n 127.681 * [backup-simplify]: Simplify 0 into 0 127.681 * [backup-simplify]: Simplify 1 into 1 127.682 * [backup-simplify]: Simplify (/ PI 1) into PI 127.682 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 127.682 * [taylor]: Taking taylor expansion of -2 in n 127.682 * [backup-simplify]: Simplify -2 into -2 127.682 * [taylor]: Taking taylor expansion of (/ PI n) in n 127.682 * [taylor]: Taking taylor expansion of PI in n 127.682 * [backup-simplify]: Simplify PI into PI 127.682 * [taylor]: Taking taylor expansion of n in n 127.682 * [backup-simplify]: Simplify 0 into 0 127.682 * [backup-simplify]: Simplify 1 into 1 127.682 * [backup-simplify]: Simplify (/ PI 1) into PI 127.682 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 127.683 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 127.684 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 127.685 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 127.685 * [backup-simplify]: Simplify 0 into 0 127.686 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.687 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 127.687 * [backup-simplify]: Simplify 0 into 0 127.688 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.689 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 127.689 * [backup-simplify]: Simplify 0 into 0 127.690 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.691 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 127.691 * [backup-simplify]: Simplify 0 into 0 127.691 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.692 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 127.692 * [backup-simplify]: Simplify 0 into 0 127.693 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.694 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 127.694 * [backup-simplify]: Simplify 0 into 0 127.694 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 127.694 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1) 127.695 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 127.695 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 127.695 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 127.695 * [taylor]: Taking taylor expansion of 2 in n 127.695 * [backup-simplify]: Simplify 2 into 2 127.695 * [taylor]: Taking taylor expansion of (* n PI) in n 127.695 * [taylor]: Taking taylor expansion of n in n 127.695 * [backup-simplify]: Simplify 0 into 0 127.695 * [backup-simplify]: Simplify 1 into 1 127.695 * [taylor]: Taking taylor expansion of PI in n 127.695 * [backup-simplify]: Simplify PI into PI 127.695 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 127.695 * [taylor]: Taking taylor expansion of 2 in n 127.695 * [backup-simplify]: Simplify 2 into 2 127.695 * [taylor]: Taking taylor expansion of (* n PI) in n 127.695 * [taylor]: Taking taylor expansion of n in n 127.695 * [backup-simplify]: Simplify 0 into 0 127.695 * [backup-simplify]: Simplify 1 into 1 127.695 * [taylor]: Taking taylor expansion of PI in n 127.695 * [backup-simplify]: Simplify PI into PI 127.695 * [backup-simplify]: Simplify (* 0 PI) into 0 127.696 * [backup-simplify]: Simplify (* 2 0) into 0 127.696 * [backup-simplify]: Simplify 0 into 0 127.696 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 127.697 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 127.698 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 127.698 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 127.699 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 127.699 * [backup-simplify]: Simplify 0 into 0 127.699 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 127.700 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 127.700 * [backup-simplify]: Simplify 0 into 0 127.701 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 127.702 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 127.702 * [backup-simplify]: Simplify 0 into 0 127.703 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 127.704 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 127.704 * [backup-simplify]: Simplify 0 into 0 127.705 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 127.706 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 127.706 * [backup-simplify]: Simplify 0 into 0 127.707 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 127.708 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 127.708 * [backup-simplify]: Simplify 0 into 0 127.708 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 127.708 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 127.708 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 127.708 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 127.708 * [taylor]: Taking taylor expansion of 2 in n 127.708 * [backup-simplify]: Simplify 2 into 2 127.708 * [taylor]: Taking taylor expansion of (/ PI n) in n 127.708 * [taylor]: Taking taylor expansion of PI in n 127.709 * [backup-simplify]: Simplify PI into PI 127.709 * [taylor]: Taking taylor expansion of n in n 127.709 * [backup-simplify]: Simplify 0 into 0 127.709 * [backup-simplify]: Simplify 1 into 1 127.709 * [backup-simplify]: Simplify (/ PI 1) into PI 127.709 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 127.709 * [taylor]: Taking taylor expansion of 2 in n 127.709 * [backup-simplify]: Simplify 2 into 2 127.709 * [taylor]: Taking taylor expansion of (/ PI n) in n 127.709 * [taylor]: Taking taylor expansion of PI in n 127.709 * [backup-simplify]: Simplify PI into PI 127.709 * [taylor]: Taking taylor expansion of n in n 127.709 * [backup-simplify]: Simplify 0 into 0 127.709 * [backup-simplify]: Simplify 1 into 1 127.709 * [backup-simplify]: Simplify (/ PI 1) into PI 127.710 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 127.710 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 127.710 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 127.711 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 127.711 * [backup-simplify]: Simplify 0 into 0 127.711 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.712 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 127.712 * [backup-simplify]: Simplify 0 into 0 127.713 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.713 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 127.713 * [backup-simplify]: Simplify 0 into 0 127.714 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.715 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 127.715 * [backup-simplify]: Simplify 0 into 0 127.715 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.716 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 127.716 * [backup-simplify]: Simplify 0 into 0 127.717 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.718 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 127.718 * [backup-simplify]: Simplify 0 into 0 127.718 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 127.718 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 127.718 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 127.718 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 127.719 * [taylor]: Taking taylor expansion of -2 in n 127.719 * [backup-simplify]: Simplify -2 into -2 127.719 * [taylor]: Taking taylor expansion of (/ PI n) in n 127.719 * [taylor]: Taking taylor expansion of PI in n 127.719 * [backup-simplify]: Simplify PI into PI 127.719 * [taylor]: Taking taylor expansion of n in n 127.719 * [backup-simplify]: Simplify 0 into 0 127.719 * [backup-simplify]: Simplify 1 into 1 127.719 * [backup-simplify]: Simplify (/ PI 1) into PI 127.719 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 127.719 * [taylor]: Taking taylor expansion of -2 in n 127.719 * [backup-simplify]: Simplify -2 into -2 127.719 * [taylor]: Taking taylor expansion of (/ PI n) in n 127.719 * [taylor]: Taking taylor expansion of PI in n 127.719 * [backup-simplify]: Simplify PI into PI 127.719 * [taylor]: Taking taylor expansion of n in n 127.719 * [backup-simplify]: Simplify 0 into 0 127.719 * [backup-simplify]: Simplify 1 into 1 127.719 * [backup-simplify]: Simplify (/ PI 1) into PI 127.720 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 127.720 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 127.720 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 127.721 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 127.721 * [backup-simplify]: Simplify 0 into 0 127.722 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.722 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 127.722 * [backup-simplify]: Simplify 0 into 0 127.723 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.724 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 127.724 * [backup-simplify]: Simplify 0 into 0 127.725 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.726 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 127.726 * [backup-simplify]: Simplify 0 into 0 127.728 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.729 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 127.729 * [backup-simplify]: Simplify 0 into 0 127.730 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 127.732 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 127.732 * [backup-simplify]: Simplify 0 into 0 127.733 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 127.733 * * * [progress]: simplifying candidates 127.733 * * * * [progress]: [ 1 / 138 ] simplifiying candidate # 127.733 * * * * [progress]: [ 2 / 138 ] simplifiying candidate # 127.733 * * * * [progress]: [ 3 / 138 ] simplifiying candidate # 127.733 * * * * [progress]: [ 4 / 138 ] simplifiying candidate # 127.733 * * * * [progress]: [ 5 / 138 ] simplifiying candidate # 127.733 * * * * [progress]: [ 6 / 138 ] simplifiying candidate # 127.733 * * * * [progress]: [ 7 / 138 ] simplifiying candidate # 127.733 * * * * [progress]: [ 8 / 138 ] simplifiying candidate # 127.733 * * * * [progress]: [ 9 / 138 ] simplifiying candidate # 127.733 * * * * [progress]: [ 10 / 138 ] simplifiying candidate # 127.734 * * * * [progress]: [ 11 / 138 ] simplifiying candidate # 127.734 * * * * [progress]: [ 12 / 138 ] simplifiying candidate # 127.734 * * * * [progress]: [ 13 / 138 ] simplifiying candidate # 127.734 * * * * [progress]: [ 14 / 138 ] simplifiying candidate # 127.734 * * * * [progress]: [ 15 / 138 ] simplifiying candidate # 127.734 * * * * [progress]: [ 16 / 138 ] simplifiying candidate # 127.734 * * * * [progress]: [ 17 / 138 ] simplifiying candidate # 127.734 * * * * [progress]: [ 18 / 138 ] simplifiying candidate # 127.734 * * * * [progress]: [ 19 / 138 ] simplifiying candidate # 127.734 * * * * [progress]: [ 20 / 138 ] simplifiying candidate # 127.734 * * * * [progress]: [ 21 / 138 ] simplifiying candidate # 127.734 * * * * [progress]: [ 22 / 138 ] simplifiying candidate # 127.734 * * * * [progress]: [ 23 / 138 ] simplifiying candidate # 127.735 * * * * [progress]: [ 24 / 138 ] simplifiying candidate # 127.735 * * * * [progress]: [ 25 / 138 ] simplifiying candidate # 127.735 * * * * [progress]: [ 26 / 138 ] simplifiying candidate # 127.735 * * * * [progress]: [ 27 / 138 ] simplifiying candidate # 127.735 * * * * [progress]: [ 28 / 138 ] simplifiying candidate # 127.735 * * * * [progress]: [ 29 / 138 ] simplifiying candidate # 127.735 * * * * [progress]: [ 30 / 138 ] simplifiying candidate # 127.735 * * * * [progress]: [ 31 / 138 ] simplifiying candidate # 127.735 * * * * [progress]: [ 32 / 138 ] simplifiying candidate # 127.735 * * * * [progress]: [ 33 / 138 ] simplifiying candidate # 127.735 * * * * [progress]: [ 34 / 138 ] simplifiying candidate # 127.735 * * * * [progress]: [ 35 / 138 ] simplifiying candidate # 127.736 * * * * [progress]: [ 36 / 138 ] simplifiying candidate # 127.736 * * * * [progress]: [ 37 / 138 ] simplifiying candidate # 127.736 * * * * [progress]: [ 38 / 138 ] simplifiying candidate # 127.736 * * * * [progress]: [ 39 / 138 ] simplifiying candidate # 127.736 * * * * [progress]: [ 40 / 138 ] simplifiying candidate # 127.736 * * * * [progress]: [ 41 / 138 ] simplifiying candidate # 127.736 * * * * [progress]: [ 42 / 138 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))> 127.736 * * * * [progress]: [ 43 / 138 ] simplifiying candidate # 127.736 * * * * [progress]: [ 44 / 138 ] simplifiying candidate # 127.736 * * * * [progress]: [ 45 / 138 ] simplifiying candidate # 127.736 * * * * [progress]: [ 46 / 138 ] simplifiying candidate # 127.736 * * * * [progress]: [ 47 / 138 ] simplifiying candidate # 127.736 * * * * [progress]: [ 48 / 138 ] simplifiying candidate # 127.737 * * * * [progress]: [ 49 / 138 ] simplifiying candidate # 127.737 * * * * [progress]: [ 50 / 138 ] simplifiying candidate # 127.737 * * * * [progress]: [ 51 / 138 ] simplifiying candidate # 127.737 * * * * [progress]: [ 52 / 138 ] simplifiying candidate # 127.738 * * * * [progress]: [ 53 / 138 ] simplifiying candidate # 127.738 * * * * [progress]: [ 54 / 138 ] simplifiying candidate # 127.738 * * * * [progress]: [ 55 / 138 ] simplifiying candidate # 127.738 * * * * [progress]: [ 56 / 138 ] simplifiying candidate # 127.738 * * * * [progress]: [ 57 / 138 ] simplifiying candidate # 127.738 * * * * [progress]: [ 58 / 138 ] simplifiying candidate # 127.738 * * * * [progress]: [ 59 / 138 ] simplifiying candidate # 127.738 * * * * [progress]: [ 60 / 138 ] simplifiying candidate # 127.738 * * * * [progress]: [ 61 / 138 ] simplifiying candidate # 127.738 * * * * [progress]: [ 62 / 138 ] simplifiying candidate # 127.739 * * * * [progress]: [ 63 / 138 ] simplifiying candidate # 127.739 * * * * [progress]: [ 64 / 138 ] simplifiying candidate # 127.739 * * * * [progress]: [ 65 / 138 ] simplifiying candidate # 127.739 * * * * [progress]: [ 66 / 138 ] simplifiying candidate # 127.739 * * * * [progress]: [ 67 / 138 ] simplifiying candidate # 127.739 * * * * [progress]: [ 68 / 138 ] simplifiying candidate # 127.739 * * * * [progress]: [ 69 / 138 ] simplifiying candidate # 127.739 * * * * [progress]: [ 70 / 138 ] simplifiying candidate # 127.739 * * * * [progress]: [ 71 / 138 ] simplifiying candidate # 127.739 * * * * [progress]: [ 72 / 138 ] simplifiying candidate # 127.739 * * * * [progress]: [ 73 / 138 ] simplifiying candidate # 127.739 * * * * [progress]: [ 74 / 138 ] simplifiying candidate # 127.740 * * * * [progress]: [ 75 / 138 ] simplifiying candidate # 127.740 * * * * [progress]: [ 76 / 138 ] simplifiying candidate # 127.740 * * * * [progress]: [ 77 / 138 ] simplifiying candidate # 127.740 * * * * [progress]: [ 78 / 138 ] simplifiying candidate # 127.740 * * * * [progress]: [ 79 / 138 ] simplifiying candidate # 127.740 * * * * [progress]: [ 80 / 138 ] simplifiying candidate # 127.740 * * * * [progress]: [ 81 / 138 ] simplifiying candidate # 127.740 * * * * [progress]: [ 82 / 138 ] simplifiying candidate # 127.740 * * * * [progress]: [ 83 / 138 ] simplifiying candidate # 127.740 * * * * [progress]: [ 84 / 138 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))> 127.740 * * * * [progress]: [ 85 / 138 ] simplifiying candidate # 127.740 * * * * [progress]: [ 86 / 138 ] simplifiying candidate # 127.740 * * * * [progress]: [ 87 / 138 ] simplifiying candidate # 127.741 * * * * [progress]: [ 88 / 138 ] simplifiying candidate # 127.741 * * * * [progress]: [ 89 / 138 ] simplifiying candidate # 127.741 * * * * [progress]: [ 90 / 138 ] simplifiying candidate # 127.741 * * * * [progress]: [ 91 / 138 ] simplifiying candidate # 127.741 * * * * [progress]: [ 92 / 138 ] simplifiying candidate # 127.741 * * * * [progress]: [ 93 / 138 ] simplifiying candidate # 127.741 * * * * [progress]: [ 94 / 138 ] simplifiying candidate # 127.741 * * * * [progress]: [ 95 / 138 ] simplifiying candidate # 127.741 * * * * [progress]: [ 96 / 138 ] simplifiying candidate # 127.741 * * * * [progress]: [ 97 / 138 ] simplifiying candidate # 127.741 * * * * [progress]: [ 98 / 138 ] simplifiying candidate # 127.741 * * * * [progress]: [ 99 / 138 ] simplifiying candidate # 127.741 * * * * [progress]: [ 100 / 138 ] simplifiying candidate # 127.741 * * * * [progress]: [ 101 / 138 ] simplifiying candidate # 127.742 * * * * [progress]: [ 102 / 138 ] simplifiying candidate # 127.742 * * * * [progress]: [ 103 / 138 ] simplifiying candidate # 127.742 * * * * [progress]: [ 104 / 138 ] simplifiying candidate #real (real->posit16 (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))> 127.742 * * * * [progress]: [ 105 / 138 ] simplifiying candidate # 127.742 * * * * [progress]: [ 106 / 138 ] simplifiying candidate # 127.742 * * * * [progress]: [ 107 / 138 ] simplifiying candidate # 127.742 * * * * [progress]: [ 108 / 138 ] simplifiying candidate # 127.742 * * * * [progress]: [ 109 / 138 ] simplifiying candidate # 127.742 * * * * [progress]: [ 110 / 138 ] simplifiying candidate # 127.742 * * * * [progress]: [ 111 / 138 ] simplifiying candidate # 127.742 * * * * [progress]: [ 112 / 138 ] simplifiying candidate # 127.742 * * * * [progress]: [ 113 / 138 ] simplifiying candidate # 127.742 * * * * [progress]: [ 114 / 138 ] simplifiying candidate # 127.742 * * * * [progress]: [ 115 / 138 ] simplifiying candidate # 127.743 * * * * [progress]: [ 116 / 138 ] simplifiying candidate # 127.743 * * * * [progress]: [ 117 / 138 ] simplifiying candidate # 127.743 * * * * [progress]: [ 118 / 138 ] simplifiying candidate # 127.743 * * * * [progress]: [ 119 / 138 ] simplifiying candidate # 127.743 * * * * [progress]: [ 120 / 138 ] simplifiying candidate # 127.743 * * * * [progress]: [ 121 / 138 ] simplifiying candidate # 127.743 * * * * [progress]: [ 122 / 138 ] simplifiying candidate # 127.743 * * * * [progress]: [ 123 / 138 ] simplifiying candidate # 127.743 * * * * [progress]: [ 124 / 138 ] simplifiying candidate # 127.743 * * * * [progress]: [ 125 / 138 ] simplifiying candidate #real (real->posit16 (* n (* 2 PI)))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))> 127.743 * * * * [progress]: [ 126 / 138 ] simplifiying candidate # 127.743 * * * * [progress]: [ 127 / 138 ] simplifiying candidate # 127.743 * * * * [progress]: [ 128 / 138 ] simplifiying candidate # 127.744 * * * * [progress]: [ 129 / 138 ] simplifiying candidate # 127.744 * * * * [progress]: [ 130 / 138 ] simplifiying candidate # 127.744 * * * * [progress]: [ 131 / 138 ] simplifiying candidate # 127.744 * * * * [progress]: [ 132 / 138 ] simplifiying candidate # 127.744 * * * * [progress]: [ 133 / 138 ] simplifiying candidate # 127.744 * * * * [progress]: [ 134 / 138 ] simplifiying candidate # 127.744 * * * * [progress]: [ 135 / 138 ] simplifiying candidate # 127.744 * * * * [progress]: [ 136 / 138 ] simplifiying candidate # 127.744 * * * * [progress]: [ 137 / 138 ] simplifiying candidate # 127.744 * * * * [progress]: [ 138 / 138 ] simplifiying candidate # 127.746 * [simplify]: Simplifying: (expm1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log1p (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2)) (pow (* n (* 2 PI)) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))) (pow (* n (* 2 PI)) (sqrt (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) 1)) (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (pow (* n (* 2 PI)) (/ 1 1)) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)) (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (pow (* n (* 2 PI)) (/ 1 1)) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (exp (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (expm1 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (log1p (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (* (+ (log n) (log (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* (log (* n (* 2 PI))) (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (* 1 (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ 1/2 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2)) (pow (* n (* 2 PI)) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))) (pow (* n (* 2 PI)) (sqrt (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (sqrt (- 1/2 (/ k 2))) 1)) (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (pow (* n (* 2 PI)) (/ 1 1)) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (pow (* n (* 2 PI)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)) (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (pow (* n (* 2 PI)) (/ 1 1)) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (log (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (exp (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (* (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (real->posit16 (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (expm1 (* n (* 2 PI))) (log1p (* n (* 2 PI))) (* n (* 2 PI)) (* n (* 2 PI)) (+ (log n) (+ (log 2) (log PI))) (+ (log n) (log (* 2 PI))) (log (* n (* 2 PI))) (exp (* n (* 2 PI))) (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI))) (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 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 n) (* 2 PI)) (* (sqrt n) (* 2 PI)) (* n (* 2 PI)) (real->posit16 (* n (* 2 PI))) (expm1 (* n (* 2 PI))) (log1p (* n (* 2 PI))) (* n (* 2 PI)) (* n (* 2 PI)) (+ (log n) (+ (log 2) (log PI))) (+ (log n) (log (* 2 PI))) (log (* n (* 2 PI))) (exp (* n (* 2 PI))) (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI))) (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 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 n) (* 2 PI)) (* (sqrt n) (* 2 PI)) (* n (* 2 PI)) (real->posit16 (* n (* 2 PI))) (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) 127.750 * * [simplify]: iteration 1: (165 enodes) 127.833 * * [simplify]: iteration 2: (752 enodes) 128.026 * * [simplify]: iteration 3: (1966 enodes) 129.141 * * [simplify]: Extracting #0: cost 48 inf + 0 129.142 * * [simplify]: Extracting #1: cost 524 inf + 0 129.148 * * [simplify]: Extracting #2: cost 1524 inf + 10544 129.175 * * [simplify]: Extracting #3: cost 1840 inf + 58499 129.256 * * [simplify]: Extracting #4: cost 1030 inf + 300841 129.371 * * [simplify]: Extracting #5: cost 383 inf + 576598 129.549 * * [simplify]: Extracting #6: cost 110 inf + 700641 129.776 * * [simplify]: Extracting #7: cost 4 inf + 745570 130.002 * * [simplify]: Extracting #8: cost 0 inf + 748026 130.199 * [simplify]: Simplified to: (expm1 (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (log1p (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))) (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))) (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))) (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))) (- 1/4 (* k 1/4)) (- 1/4 (* k 1/4)) (- 1/4 (* k 1/4)) (exp (* (log (* (* PI 2) n)) 1/4)) (pow (* (* PI 2) n) (* k 1/4)) (pow (* (* PI 2) n) (* (cbrt (- 1/4 (* k 1/4))) (cbrt (- 1/4 (* k 1/4))))) (pow (* (* PI 2) n) (sqrt (- 1/4 (* k 1/4)))) (pow (* (* PI 2) n) (* (/ (cbrt (fma k -1/2 1/2)) (cbrt 2)) (/ (cbrt (fma k -1/2 1/2)) (cbrt 2)))) (pow (* (* PI 2) n) (/ (* (cbrt (fma k -1/2 1/2)) (cbrt (fma k -1/2 1/2))) (sqrt 2))) (pow (* (* PI 2) n) (* (cbrt (fma k -1/2 1/2)) (cbrt (fma k -1/2 1/2)))) (pow (* (* PI 2) n) (/ (sqrt (fma k -1/2 1/2)) (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ (sqrt (fma k -1/2 1/2)) (sqrt 2))) (pow (* (* PI 2) n) (sqrt (fma k -1/2 1/2))) (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ 1 (sqrt 2))) (* (* PI 2) n) (pow (* (* PI 2) n) (/ (/ (+ (sqrt 1/2) (sqrt (* 1/2 k))) (cbrt 2)) (cbrt 2))) (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (sqrt (* 1/2 k))) (sqrt 2))) (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (* 1/2 k)))) (pow (* (* PI 2) n) (/ (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2)) (cbrt 2))) (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (pow (* (* PI 2) n) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ 1 (sqrt 2))) (* (* PI 2) n) (* (* PI 2) n) (exp (* (log (* (* PI 2) n)) (fma k -1/2 1/2))) (pow n (- 1/4 (* k 1/4))) (pow (* PI 2) (- 1/4 (* k 1/4))) (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))) (exp (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (* (cbrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (cbrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4)))))) (cbrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (* (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4)))) (exp (* (log (* (* PI 2) n)) (fma k -1/2 1/2)))) (sqrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (sqrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (pow (* (* PI 2) n) (- 1/8 (/ k 8))) (pow (* (* PI 2) n) (- 1/8 (/ k 8))) (real->posit16 (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (expm1 (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (log1p (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))) (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))) (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))) (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))) (- 1/4 (* k 1/4)) (- 1/4 (* k 1/4)) (- 1/4 (* k 1/4)) (exp (* (log (* (* PI 2) n)) 1/4)) (pow (* (* PI 2) n) (* k 1/4)) (pow (* (* PI 2) n) (* (cbrt (- 1/4 (* k 1/4))) (cbrt (- 1/4 (* k 1/4))))) (pow (* (* PI 2) n) (sqrt (- 1/4 (* k 1/4)))) (pow (* (* PI 2) n) (* (/ (cbrt (fma k -1/2 1/2)) (cbrt 2)) (/ (cbrt (fma k -1/2 1/2)) (cbrt 2)))) (pow (* (* PI 2) n) (/ (* (cbrt (fma k -1/2 1/2)) (cbrt (fma k -1/2 1/2))) (sqrt 2))) (pow (* (* PI 2) n) (* (cbrt (fma k -1/2 1/2)) (cbrt (fma k -1/2 1/2)))) (pow (* (* PI 2) n) (/ (sqrt (fma k -1/2 1/2)) (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ (sqrt (fma k -1/2 1/2)) (sqrt 2))) (pow (* (* PI 2) n) (sqrt (fma k -1/2 1/2))) (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ 1 (sqrt 2))) (* (* PI 2) n) (pow (* (* PI 2) n) (/ (/ (+ (sqrt 1/2) (sqrt (* 1/2 k))) (cbrt 2)) (cbrt 2))) (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (sqrt (* 1/2 k))) (sqrt 2))) (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (* 1/2 k)))) (pow (* (* PI 2) n) (/ (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2)) (cbrt 2))) (pow (* (* PI 2) n) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (pow (* (* PI 2) n) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* PI 2) n) (/ 1 (sqrt 2))) (* (* PI 2) n) (* (* PI 2) n) (exp (* (log (* (* PI 2) n)) (fma k -1/2 1/2))) (pow n (- 1/4 (* k 1/4))) (pow (* PI 2) (- 1/4 (* k 1/4))) (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))) (exp (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (* (cbrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (cbrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4)))))) (cbrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (* (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4)))) (exp (* (log (* (* PI 2) n)) (fma k -1/2 1/2)))) (sqrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (sqrt (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (pow (* (* PI 2) n) (- 1/8 (/ k 8))) (pow (* (* PI 2) n) (- 1/8 (/ k 8))) (real->posit16 (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4))))) (expm1 (* (* PI 2) n)) (log1p (* (* PI 2) n)) (* (* PI 2) n) (* (* PI 2) n) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (exp (+ (* n PI) (* n PI))) (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n))) (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n))) (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n))) (cbrt (* (* PI 2) n)) (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n))) (sqrt (* (* PI 2) n)) (sqrt (* (* PI 2) n)) (* n 2) (* (cbrt n) (* PI 2)) (* PI (* 2 (sqrt n))) (* (* PI 2) n) (real->posit16 (* (* PI 2) n)) (expm1 (* (* PI 2) n)) (log1p (* (* PI 2) n)) (* (* PI 2) n) (* (* PI 2) n) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (exp (+ (* n PI) (* n PI))) (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n))) (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n))) (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n))) (cbrt (* (* PI 2) n)) (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n))) (sqrt (* (* PI 2) n)) (sqrt (* (* PI 2) n)) (* n 2) (* (cbrt n) (* PI 2)) (* PI (* 2 (sqrt n))) (* (* PI 2) n) (real->posit16 (* (* PI 2) n)) (fma -1/4 (* k (* (exp (* (log (* (* PI 2) n)) 1/4)) (log (* (* PI 2) n)))) (fma (* (log (* PI 2)) (* 1/16 (exp (* (log (* (* PI 2) n)) 1/4)))) (* k (* (log n) k)) (fma 1/32 (* (exp (* (log (* (* PI 2) n)) 1/4)) (+ (* (* k (log (* PI 2))) (* k (log (* PI 2)))) (* (* (log n) k) (* (log n) k)))) (exp (* (log (* (* PI 2) n)) 1/4))))) (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4)))) (exp (* (- 1/4 (* k 1/4)) (- (log (* PI -2)) (log (/ -1 n))))) (fma -1/4 (* k (* (exp (* (log (* (* PI 2) n)) 1/4)) (log (* (* PI 2) n)))) (fma (* (log (* PI 2)) (* 1/16 (exp (* (log (* (* PI 2) n)) 1/4)))) (* k (* (log n) k)) (fma 1/32 (* (exp (* (log (* (* PI 2) n)) 1/4)) (+ (* (* k (log (* PI 2))) (* k (log (* PI 2)))) (* (* (log n) k) (* (log n) k)))) (exp (* (log (* (* PI 2) n)) 1/4))))) (exp (* (log (* (* PI 2) n)) (- 1/4 (* k 1/4)))) (exp (* (- 1/4 (* k 1/4)) (- (log (* PI -2)) (log (/ -1 n))))) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) 130.223 * * * [progress]: adding candidates to table 132.089 * * [progress]: iteration 4 / 4 132.089 * * * [progress]: picking best candidate 132.137 * * * * [pick]: Picked # 132.137 * * * [progress]: localizing error 132.184 * * * [progress]: generating rewritten candidates 132.184 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1) 132.200 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1) 132.224 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1 1) 132.255 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1 1) 132.272 * * * [progress]: generating series expansions 132.272 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1) 132.272 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 132.272 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 132.272 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 132.272 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 132.272 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 132.272 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 132.272 * [taylor]: Taking taylor expansion of 1/2 in k 132.272 * [backup-simplify]: Simplify 1/2 into 1/2 132.272 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 132.272 * [taylor]: Taking taylor expansion of 1/2 in k 132.272 * [backup-simplify]: Simplify 1/2 into 1/2 132.273 * [taylor]: Taking taylor expansion of k in k 132.273 * [backup-simplify]: Simplify 0 into 0 132.273 * [backup-simplify]: Simplify 1 into 1 132.273 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 132.273 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 132.273 * [taylor]: Taking taylor expansion of 2 in k 132.273 * [backup-simplify]: Simplify 2 into 2 132.273 * [taylor]: Taking taylor expansion of (* n PI) in k 132.273 * [taylor]: Taking taylor expansion of n in k 132.273 * [backup-simplify]: Simplify n into n 132.273 * [taylor]: Taking taylor expansion of PI in k 132.273 * [backup-simplify]: Simplify PI into PI 132.273 * [backup-simplify]: Simplify (* n PI) into (* n PI) 132.273 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 132.273 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 132.273 * [backup-simplify]: Simplify (* 1/2 0) into 0 132.273 * [backup-simplify]: Simplify (- 0) into 0 132.274 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 132.274 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 132.274 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 132.274 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 132.274 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 132.274 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 132.274 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 132.274 * [taylor]: Taking taylor expansion of 1/2 in n 132.274 * [backup-simplify]: Simplify 1/2 into 1/2 132.274 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 132.274 * [taylor]: Taking taylor expansion of 1/2 in n 132.274 * [backup-simplify]: Simplify 1/2 into 1/2 132.274 * [taylor]: Taking taylor expansion of k in n 132.274 * [backup-simplify]: Simplify k into k 132.274 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 132.274 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 132.274 * [taylor]: Taking taylor expansion of 2 in n 132.274 * [backup-simplify]: Simplify 2 into 2 132.274 * [taylor]: Taking taylor expansion of (* n PI) in n 132.274 * [taylor]: Taking taylor expansion of n in n 132.274 * [backup-simplify]: Simplify 0 into 0 132.274 * [backup-simplify]: Simplify 1 into 1 132.274 * [taylor]: Taking taylor expansion of PI in n 132.274 * [backup-simplify]: Simplify PI into PI 132.274 * [backup-simplify]: Simplify (* 0 PI) into 0 132.275 * [backup-simplify]: Simplify (* 2 0) into 0 132.276 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 132.276 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 132.277 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 132.277 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 132.277 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 132.277 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 132.278 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 132.279 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 132.279 * [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))))) 132.279 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 132.279 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 132.279 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 132.279 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 132.279 * [taylor]: Taking taylor expansion of 1/2 in n 132.279 * [backup-simplify]: Simplify 1/2 into 1/2 132.279 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 132.279 * [taylor]: Taking taylor expansion of 1/2 in n 132.280 * [backup-simplify]: Simplify 1/2 into 1/2 132.280 * [taylor]: Taking taylor expansion of k in n 132.280 * [backup-simplify]: Simplify k into k 132.280 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 132.280 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 132.280 * [taylor]: Taking taylor expansion of 2 in n 132.280 * [backup-simplify]: Simplify 2 into 2 132.280 * [taylor]: Taking taylor expansion of (* n PI) in n 132.280 * [taylor]: Taking taylor expansion of n in n 132.280 * [backup-simplify]: Simplify 0 into 0 132.280 * [backup-simplify]: Simplify 1 into 1 132.280 * [taylor]: Taking taylor expansion of PI in n 132.280 * [backup-simplify]: Simplify PI into PI 132.280 * [backup-simplify]: Simplify (* 0 PI) into 0 132.280 * [backup-simplify]: Simplify (* 2 0) into 0 132.281 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 132.282 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 132.283 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 132.283 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 132.283 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 132.283 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 132.284 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 132.284 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 132.285 * [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))))) 132.285 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 132.285 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 132.285 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 132.285 * [taylor]: Taking taylor expansion of 1/2 in k 132.285 * [backup-simplify]: Simplify 1/2 into 1/2 132.285 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 132.285 * [taylor]: Taking taylor expansion of 1/2 in k 132.285 * [backup-simplify]: Simplify 1/2 into 1/2 132.285 * [taylor]: Taking taylor expansion of k in k 132.285 * [backup-simplify]: Simplify 0 into 0 132.285 * [backup-simplify]: Simplify 1 into 1 132.285 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 132.285 * [taylor]: Taking taylor expansion of (log n) in k 132.285 * [taylor]: Taking taylor expansion of n in k 132.285 * [backup-simplify]: Simplify n into n 132.285 * [backup-simplify]: Simplify (log n) into (log n) 132.285 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 132.285 * [taylor]: Taking taylor expansion of (* 2 PI) in k 132.285 * [taylor]: Taking taylor expansion of 2 in k 132.285 * [backup-simplify]: Simplify 2 into 2 132.285 * [taylor]: Taking taylor expansion of PI in k 132.285 * [backup-simplify]: Simplify PI into PI 132.286 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 132.286 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 132.286 * [backup-simplify]: Simplify (* 1/2 0) into 0 132.287 * [backup-simplify]: Simplify (- 0) into 0 132.287 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 132.288 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 132.288 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 132.289 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 132.289 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 132.290 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 132.291 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 132.292 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 132.292 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 132.292 * [backup-simplify]: Simplify (- 0) into 0 132.293 * [backup-simplify]: Simplify (+ 0 0) into 0 132.293 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 132.294 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 132.295 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 132.295 * [taylor]: Taking taylor expansion of 0 in k 132.295 * [backup-simplify]: Simplify 0 into 0 132.295 * [backup-simplify]: Simplify 0 into 0 132.296 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 132.296 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 132.297 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 132.297 * [backup-simplify]: Simplify (+ 0 0) into 0 132.298 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 132.298 * [backup-simplify]: Simplify (- 1/2) into -1/2 132.298 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 132.299 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 132.301 * [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))))))) 132.302 * [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))))))) 132.303 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 132.304 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 132.306 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 132.306 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 132.306 * [backup-simplify]: Simplify (- 0) into 0 132.307 * [backup-simplify]: Simplify (+ 0 0) into 0 132.308 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 132.309 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 132.310 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 132.310 * [taylor]: Taking taylor expansion of 0 in k 132.310 * [backup-simplify]: Simplify 0 into 0 132.310 * [backup-simplify]: Simplify 0 into 0 132.310 * [backup-simplify]: Simplify 0 into 0 132.311 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 132.312 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 132.313 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 132.314 * [backup-simplify]: Simplify (+ 0 0) into 0 132.314 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 132.314 * [backup-simplify]: Simplify (- 0) into 0 132.315 * [backup-simplify]: Simplify (+ 0 0) into 0 132.316 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 132.318 * [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))))) 132.326 * [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))))) 132.335 * [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))))) 132.335 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 132.335 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 132.336 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 132.336 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 132.336 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 132.336 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 132.336 * [taylor]: Taking taylor expansion of 1/2 in k 132.336 * [backup-simplify]: Simplify 1/2 into 1/2 132.336 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 132.336 * [taylor]: Taking taylor expansion of 1/2 in k 132.336 * [backup-simplify]: Simplify 1/2 into 1/2 132.336 * [taylor]: Taking taylor expansion of (/ 1 k) in k 132.336 * [taylor]: Taking taylor expansion of k in k 132.336 * [backup-simplify]: Simplify 0 into 0 132.336 * [backup-simplify]: Simplify 1 into 1 132.336 * [backup-simplify]: Simplify (/ 1 1) into 1 132.336 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 132.336 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 132.336 * [taylor]: Taking taylor expansion of 2 in k 132.336 * [backup-simplify]: Simplify 2 into 2 132.336 * [taylor]: Taking taylor expansion of (/ PI n) in k 132.336 * [taylor]: Taking taylor expansion of PI in k 132.336 * [backup-simplify]: Simplify PI into PI 132.336 * [taylor]: Taking taylor expansion of n in k 132.336 * [backup-simplify]: Simplify n into n 132.337 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 132.337 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 132.337 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 132.337 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 132.338 * [backup-simplify]: Simplify (- 1/2) into -1/2 132.338 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 132.338 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 132.338 * [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)))) 132.338 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 132.338 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 132.338 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 132.338 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 132.338 * [taylor]: Taking taylor expansion of 1/2 in n 132.338 * [backup-simplify]: Simplify 1/2 into 1/2 132.338 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 132.339 * [taylor]: Taking taylor expansion of 1/2 in n 132.339 * [backup-simplify]: Simplify 1/2 into 1/2 132.339 * [taylor]: Taking taylor expansion of (/ 1 k) in n 132.339 * [taylor]: Taking taylor expansion of k in n 132.339 * [backup-simplify]: Simplify k into k 132.339 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 132.339 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 132.339 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 132.339 * [taylor]: Taking taylor expansion of 2 in n 132.339 * [backup-simplify]: Simplify 2 into 2 132.339 * [taylor]: Taking taylor expansion of (/ PI n) in n 132.339 * [taylor]: Taking taylor expansion of PI in n 132.339 * [backup-simplify]: Simplify PI into PI 132.339 * [taylor]: Taking taylor expansion of n in n 132.339 * [backup-simplify]: Simplify 0 into 0 132.339 * [backup-simplify]: Simplify 1 into 1 132.339 * [backup-simplify]: Simplify (/ PI 1) into PI 132.340 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 132.341 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 132.341 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 132.341 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 132.341 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 132.343 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 132.343 * [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))) 132.344 * [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)))) 132.344 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 132.344 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 132.344 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 132.344 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 132.344 * [taylor]: Taking taylor expansion of 1/2 in n 132.344 * [backup-simplify]: Simplify 1/2 into 1/2 132.344 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 132.344 * [taylor]: Taking taylor expansion of 1/2 in n 132.344 * [backup-simplify]: Simplify 1/2 into 1/2 132.344 * [taylor]: Taking taylor expansion of (/ 1 k) in n 132.344 * [taylor]: Taking taylor expansion of k in n 132.344 * [backup-simplify]: Simplify k into k 132.344 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 132.344 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 132.344 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 132.344 * [taylor]: Taking taylor expansion of 2 in n 132.344 * [backup-simplify]: Simplify 2 into 2 132.344 * [taylor]: Taking taylor expansion of (/ PI n) in n 132.344 * [taylor]: Taking taylor expansion of PI in n 132.344 * [backup-simplify]: Simplify PI into PI 132.344 * [taylor]: Taking taylor expansion of n in n 132.344 * [backup-simplify]: Simplify 0 into 0 132.344 * [backup-simplify]: Simplify 1 into 1 132.345 * [backup-simplify]: Simplify (/ PI 1) into PI 132.345 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 132.345 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 132.346 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 132.346 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 132.346 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 132.346 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 132.347 * [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))) 132.348 * [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)))) 132.348 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 132.348 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 132.348 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 132.348 * [taylor]: Taking taylor expansion of 1/2 in k 132.348 * [backup-simplify]: Simplify 1/2 into 1/2 132.348 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 132.348 * [taylor]: Taking taylor expansion of 1/2 in k 132.348 * [backup-simplify]: Simplify 1/2 into 1/2 132.348 * [taylor]: Taking taylor expansion of (/ 1 k) in k 132.348 * [taylor]: Taking taylor expansion of k in k 132.348 * [backup-simplify]: Simplify 0 into 0 132.348 * [backup-simplify]: Simplify 1 into 1 132.348 * [backup-simplify]: Simplify (/ 1 1) into 1 132.348 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 132.348 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 132.348 * [taylor]: Taking taylor expansion of (* 2 PI) in k 132.348 * [taylor]: Taking taylor expansion of 2 in k 132.348 * [backup-simplify]: Simplify 2 into 2 132.348 * [taylor]: Taking taylor expansion of PI in k 132.348 * [backup-simplify]: Simplify PI into PI 132.349 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 132.349 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 132.349 * [taylor]: Taking taylor expansion of (log n) in k 132.349 * [taylor]: Taking taylor expansion of n in k 132.349 * [backup-simplify]: Simplify n into n 132.349 * [backup-simplify]: Simplify (log n) into (log n) 132.350 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 132.350 * [backup-simplify]: Simplify (- 1/2) into -1/2 132.350 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 132.350 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 132.351 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 132.352 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 132.352 * [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)))) 132.353 * [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)))) 132.354 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 132.354 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 132.355 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 132.355 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 132.356 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 132.356 * [backup-simplify]: Simplify (- 0) into 0 132.356 * [backup-simplify]: Simplify (+ 0 0) into 0 132.357 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 132.358 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 132.359 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 132.359 * [taylor]: Taking taylor expansion of 0 in k 132.359 * [backup-simplify]: Simplify 0 into 0 132.359 * [backup-simplify]: Simplify 0 into 0 132.359 * [backup-simplify]: Simplify 0 into 0 132.360 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.360 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 132.362 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 132.362 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 132.363 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 132.363 * [backup-simplify]: Simplify (- 0) into 0 132.363 * [backup-simplify]: Simplify (+ 0 0) into 0 132.364 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 132.365 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 132.366 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 132.366 * [taylor]: Taking taylor expansion of 0 in k 132.366 * [backup-simplify]: Simplify 0 into 0 132.366 * [backup-simplify]: Simplify 0 into 0 132.366 * [backup-simplify]: Simplify 0 into 0 132.366 * [backup-simplify]: Simplify 0 into 0 132.367 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.368 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 132.371 * [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 0 132.371 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 132.372 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 132.372 * [backup-simplify]: Simplify (- 0) into 0 132.372 * [backup-simplify]: Simplify (+ 0 0) into 0 132.373 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 132.374 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 132.376 * [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 0 132.376 * [taylor]: Taking taylor expansion of 0 in k 132.376 * [backup-simplify]: Simplify 0 into 0 132.376 * [backup-simplify]: Simplify 0 into 0 132.377 * [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))))) 132.377 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 132.377 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 132.377 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 132.377 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 132.377 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 132.377 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 132.377 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 132.377 * [taylor]: Taking taylor expansion of 1/2 in k 132.377 * [backup-simplify]: Simplify 1/2 into 1/2 132.377 * [taylor]: Taking taylor expansion of (/ 1 k) in k 132.377 * [taylor]: Taking taylor expansion of k in k 132.377 * [backup-simplify]: Simplify 0 into 0 132.377 * [backup-simplify]: Simplify 1 into 1 132.377 * [backup-simplify]: Simplify (/ 1 1) into 1 132.377 * [taylor]: Taking taylor expansion of 1/2 in k 132.378 * [backup-simplify]: Simplify 1/2 into 1/2 132.378 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 132.378 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 132.378 * [taylor]: Taking taylor expansion of -2 in k 132.378 * [backup-simplify]: Simplify -2 into -2 132.378 * [taylor]: Taking taylor expansion of (/ PI n) in k 132.378 * [taylor]: Taking taylor expansion of PI in k 132.378 * [backup-simplify]: Simplify PI into PI 132.378 * [taylor]: Taking taylor expansion of n in k 132.378 * [backup-simplify]: Simplify n into n 132.378 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 132.378 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 132.378 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 132.378 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 132.378 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 132.378 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 132.379 * [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))) 132.379 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 132.379 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 132.379 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 132.379 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 132.379 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 132.379 * [taylor]: Taking taylor expansion of 1/2 in n 132.379 * [backup-simplify]: Simplify 1/2 into 1/2 132.379 * [taylor]: Taking taylor expansion of (/ 1 k) in n 132.379 * [taylor]: Taking taylor expansion of k in n 132.379 * [backup-simplify]: Simplify k into k 132.379 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 132.379 * [taylor]: Taking taylor expansion of 1/2 in n 132.379 * [backup-simplify]: Simplify 1/2 into 1/2 132.379 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 132.379 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 132.379 * [taylor]: Taking taylor expansion of -2 in n 132.379 * [backup-simplify]: Simplify -2 into -2 132.379 * [taylor]: Taking taylor expansion of (/ PI n) in n 132.379 * [taylor]: Taking taylor expansion of PI in n 132.379 * [backup-simplify]: Simplify PI into PI 132.379 * [taylor]: Taking taylor expansion of n in n 132.379 * [backup-simplify]: Simplify 0 into 0 132.379 * [backup-simplify]: Simplify 1 into 1 132.380 * [backup-simplify]: Simplify (/ PI 1) into PI 132.380 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 132.381 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 132.381 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 132.381 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 132.383 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 132.384 * [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))) 132.385 * [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)))) 132.385 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 132.385 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 132.385 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 132.385 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 132.385 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 132.385 * [taylor]: Taking taylor expansion of 1/2 in n 132.385 * [backup-simplify]: Simplify 1/2 into 1/2 132.386 * [taylor]: Taking taylor expansion of (/ 1 k) in n 132.386 * [taylor]: Taking taylor expansion of k in n 132.386 * [backup-simplify]: Simplify k into k 132.386 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 132.386 * [taylor]: Taking taylor expansion of 1/2 in n 132.386 * [backup-simplify]: Simplify 1/2 into 1/2 132.386 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 132.386 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 132.386 * [taylor]: Taking taylor expansion of -2 in n 132.386 * [backup-simplify]: Simplify -2 into -2 132.386 * [taylor]: Taking taylor expansion of (/ PI n) in n 132.386 * [taylor]: Taking taylor expansion of PI in n 132.386 * [backup-simplify]: Simplify PI into PI 132.386 * [taylor]: Taking taylor expansion of n in n 132.386 * [backup-simplify]: Simplify 0 into 0 132.386 * [backup-simplify]: Simplify 1 into 1 132.386 * [backup-simplify]: Simplify (/ PI 1) into PI 132.387 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 132.388 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 132.388 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 132.388 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 132.389 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 132.391 * [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))) 132.392 * [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)))) 132.392 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 132.392 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 132.392 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 132.392 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 132.392 * [taylor]: Taking taylor expansion of 1/2 in k 132.392 * [backup-simplify]: Simplify 1/2 into 1/2 132.392 * [taylor]: Taking taylor expansion of (/ 1 k) in k 132.392 * [taylor]: Taking taylor expansion of k in k 132.392 * [backup-simplify]: Simplify 0 into 0 132.392 * [backup-simplify]: Simplify 1 into 1 132.393 * [backup-simplify]: Simplify (/ 1 1) into 1 132.393 * [taylor]: Taking taylor expansion of 1/2 in k 132.393 * [backup-simplify]: Simplify 1/2 into 1/2 132.393 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 132.393 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 132.393 * [taylor]: Taking taylor expansion of (* -2 PI) in k 132.393 * [taylor]: Taking taylor expansion of -2 in k 132.393 * [backup-simplify]: Simplify -2 into -2 132.393 * [taylor]: Taking taylor expansion of PI in k 132.393 * [backup-simplify]: Simplify PI into PI 132.394 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 132.395 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 132.395 * [taylor]: Taking taylor expansion of (log n) in k 132.395 * [taylor]: Taking taylor expansion of n in k 132.395 * [backup-simplify]: Simplify n into n 132.395 * [backup-simplify]: Simplify (log n) into (log n) 132.396 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 132.396 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 132.396 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 132.397 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 132.398 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 132.399 * [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)))) 132.401 * [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)))) 132.402 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 132.402 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 132.404 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 132.405 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 132.405 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 132.405 * [backup-simplify]: Simplify (+ 0 0) into 0 132.407 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 132.408 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 132.410 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 132.410 * [taylor]: Taking taylor expansion of 0 in k 132.410 * [backup-simplify]: Simplify 0 into 0 132.410 * [backup-simplify]: Simplify 0 into 0 132.410 * [backup-simplify]: Simplify 0 into 0 132.412 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.413 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 132.416 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 132.416 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 132.417 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 132.417 * [backup-simplify]: Simplify (+ 0 0) into 0 132.419 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 132.420 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 132.423 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 132.423 * [taylor]: Taking taylor expansion of 0 in k 132.423 * [backup-simplify]: Simplify 0 into 0 132.423 * [backup-simplify]: Simplify 0 into 0 132.423 * [backup-simplify]: Simplify 0 into 0 132.423 * [backup-simplify]: Simplify 0 into 0 132.424 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.425 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 132.431 * [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 0 132.431 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 132.432 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 132.433 * [backup-simplify]: Simplify (+ 0 0) into 0 132.434 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 132.436 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 132.439 * [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 0 132.439 * [taylor]: Taking taylor expansion of 0 in k 132.439 * [backup-simplify]: Simplify 0 into 0 132.439 * [backup-simplify]: Simplify 0 into 0 132.446 * [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))))) 132.446 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1) 132.447 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 132.447 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 132.447 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 132.447 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 132.447 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 132.447 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 132.447 * [taylor]: Taking taylor expansion of 1/2 in k 132.447 * [backup-simplify]: Simplify 1/2 into 1/2 132.447 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 132.447 * [taylor]: Taking taylor expansion of 1/2 in k 132.447 * [backup-simplify]: Simplify 1/2 into 1/2 132.447 * [taylor]: Taking taylor expansion of k in k 132.447 * [backup-simplify]: Simplify 0 into 0 132.447 * [backup-simplify]: Simplify 1 into 1 132.447 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 132.447 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 132.447 * [taylor]: Taking taylor expansion of 2 in k 132.447 * [backup-simplify]: Simplify 2 into 2 132.447 * [taylor]: Taking taylor expansion of (* n PI) in k 132.447 * [taylor]: Taking taylor expansion of n in k 132.447 * [backup-simplify]: Simplify n into n 132.447 * [taylor]: Taking taylor expansion of PI in k 132.447 * [backup-simplify]: Simplify PI into PI 132.447 * [backup-simplify]: Simplify (* n PI) into (* n PI) 132.447 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 132.448 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 132.448 * [backup-simplify]: Simplify (* 1/2 0) into 0 132.448 * [backup-simplify]: Simplify (- 0) into 0 132.449 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 132.449 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 132.449 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 132.449 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 132.449 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 132.449 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 132.449 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 132.449 * [taylor]: Taking taylor expansion of 1/2 in n 132.449 * [backup-simplify]: Simplify 1/2 into 1/2 132.449 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 132.449 * [taylor]: Taking taylor expansion of 1/2 in n 132.449 * [backup-simplify]: Simplify 1/2 into 1/2 132.449 * [taylor]: Taking taylor expansion of k in n 132.449 * [backup-simplify]: Simplify k into k 132.449 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 132.449 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 132.449 * [taylor]: Taking taylor expansion of 2 in n 132.449 * [backup-simplify]: Simplify 2 into 2 132.449 * [taylor]: Taking taylor expansion of (* n PI) in n 132.449 * [taylor]: Taking taylor expansion of n in n 132.449 * [backup-simplify]: Simplify 0 into 0 132.450 * [backup-simplify]: Simplify 1 into 1 132.450 * [taylor]: Taking taylor expansion of PI in n 132.450 * [backup-simplify]: Simplify PI into PI 132.450 * [backup-simplify]: Simplify (* 0 PI) into 0 132.450 * [backup-simplify]: Simplify (* 2 0) into 0 132.452 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 132.453 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 132.454 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 132.454 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 132.454 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 132.455 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 132.456 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 132.457 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 132.458 * [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))))) 132.459 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 132.459 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 132.459 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 132.459 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 132.459 * [taylor]: Taking taylor expansion of 1/2 in n 132.459 * [backup-simplify]: Simplify 1/2 into 1/2 132.459 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 132.459 * [taylor]: Taking taylor expansion of 1/2 in n 132.459 * [backup-simplify]: Simplify 1/2 into 1/2 132.459 * [taylor]: Taking taylor expansion of k in n 132.459 * [backup-simplify]: Simplify k into k 132.459 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 132.459 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 132.459 * [taylor]: Taking taylor expansion of 2 in n 132.459 * [backup-simplify]: Simplify 2 into 2 132.459 * [taylor]: Taking taylor expansion of (* n PI) in n 132.459 * [taylor]: Taking taylor expansion of n in n 132.459 * [backup-simplify]: Simplify 0 into 0 132.459 * [backup-simplify]: Simplify 1 into 1 132.459 * [taylor]: Taking taylor expansion of PI in n 132.459 * [backup-simplify]: Simplify PI into PI 132.459 * [backup-simplify]: Simplify (* 0 PI) into 0 132.460 * [backup-simplify]: Simplify (* 2 0) into 0 132.461 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 132.463 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 132.464 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 132.464 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 132.464 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 132.464 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 132.465 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 132.467 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 132.468 * [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))))) 132.468 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 132.468 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 132.468 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 132.468 * [taylor]: Taking taylor expansion of 1/2 in k 132.468 * [backup-simplify]: Simplify 1/2 into 1/2 132.468 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 132.468 * [taylor]: Taking taylor expansion of 1/2 in k 132.468 * [backup-simplify]: Simplify 1/2 into 1/2 132.468 * [taylor]: Taking taylor expansion of k in k 132.468 * [backup-simplify]: Simplify 0 into 0 132.468 * [backup-simplify]: Simplify 1 into 1 132.468 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 132.468 * [taylor]: Taking taylor expansion of (log n) in k 132.468 * [taylor]: Taking taylor expansion of n in k 132.468 * [backup-simplify]: Simplify n into n 132.468 * [backup-simplify]: Simplify (log n) into (log n) 132.468 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 132.468 * [taylor]: Taking taylor expansion of (* 2 PI) in k 132.468 * [taylor]: Taking taylor expansion of 2 in k 132.468 * [backup-simplify]: Simplify 2 into 2 132.468 * [taylor]: Taking taylor expansion of PI in k 132.468 * [backup-simplify]: Simplify PI into PI 132.469 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 132.470 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 132.470 * [backup-simplify]: Simplify (* 1/2 0) into 0 132.471 * [backup-simplify]: Simplify (- 0) into 0 132.471 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 132.472 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 132.473 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 132.474 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 132.475 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 132.476 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 132.477 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 132.479 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 132.479 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 132.480 * [backup-simplify]: Simplify (- 0) into 0 132.480 * [backup-simplify]: Simplify (+ 0 0) into 0 132.481 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 132.482 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 132.484 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 132.484 * [taylor]: Taking taylor expansion of 0 in k 132.484 * [backup-simplify]: Simplify 0 into 0 132.484 * [backup-simplify]: Simplify 0 into 0 132.485 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 132.486 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 132.488 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 132.488 * [backup-simplify]: Simplify (+ 0 0) into 0 132.489 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 132.489 * [backup-simplify]: Simplify (- 1/2) into -1/2 132.490 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 132.491 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 132.494 * [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))))))) 132.497 * [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))))))) 132.498 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 132.499 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 132.502 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 132.503 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 132.504 * [backup-simplify]: Simplify (- 0) into 0 132.504 * [backup-simplify]: Simplify (+ 0 0) into 0 132.505 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 132.507 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 132.509 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 132.509 * [taylor]: Taking taylor expansion of 0 in k 132.509 * [backup-simplify]: Simplify 0 into 0 132.509 * [backup-simplify]: Simplify 0 into 0 132.509 * [backup-simplify]: Simplify 0 into 0 132.511 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 132.512 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 132.515 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 132.516 * [backup-simplify]: Simplify (+ 0 0) into 0 132.517 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 132.517 * [backup-simplify]: Simplify (- 0) into 0 132.517 * [backup-simplify]: Simplify (+ 0 0) into 0 132.519 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 132.523 * [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))))) 132.528 * [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))))) 132.538 * [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))))) 132.539 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 132.539 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 132.539 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 132.539 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 132.539 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 132.539 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 132.539 * [taylor]: Taking taylor expansion of 1/2 in k 132.539 * [backup-simplify]: Simplify 1/2 into 1/2 132.539 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 132.539 * [taylor]: Taking taylor expansion of 1/2 in k 132.539 * [backup-simplify]: Simplify 1/2 into 1/2 132.539 * [taylor]: Taking taylor expansion of (/ 1 k) in k 132.539 * [taylor]: Taking taylor expansion of k in k 132.539 * [backup-simplify]: Simplify 0 into 0 132.539 * [backup-simplify]: Simplify 1 into 1 132.540 * [backup-simplify]: Simplify (/ 1 1) into 1 132.540 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 132.540 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 132.540 * [taylor]: Taking taylor expansion of 2 in k 132.540 * [backup-simplify]: Simplify 2 into 2 132.540 * [taylor]: Taking taylor expansion of (/ PI n) in k 132.540 * [taylor]: Taking taylor expansion of PI in k 132.540 * [backup-simplify]: Simplify PI into PI 132.540 * [taylor]: Taking taylor expansion of n in k 132.540 * [backup-simplify]: Simplify n into n 132.540 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 132.540 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 132.540 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 132.541 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 132.541 * [backup-simplify]: Simplify (- 1/2) into -1/2 132.541 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 132.542 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 132.542 * [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)))) 132.542 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 132.542 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 132.542 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 132.542 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 132.542 * [taylor]: Taking taylor expansion of 1/2 in n 132.542 * [backup-simplify]: Simplify 1/2 into 1/2 132.542 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 132.542 * [taylor]: Taking taylor expansion of 1/2 in n 132.542 * [backup-simplify]: Simplify 1/2 into 1/2 132.542 * [taylor]: Taking taylor expansion of (/ 1 k) in n 132.542 * [taylor]: Taking taylor expansion of k in n 132.542 * [backup-simplify]: Simplify k into k 132.542 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 132.542 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 132.542 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 132.542 * [taylor]: Taking taylor expansion of 2 in n 132.542 * [backup-simplify]: Simplify 2 into 2 132.542 * [taylor]: Taking taylor expansion of (/ PI n) in n 132.542 * [taylor]: Taking taylor expansion of PI in n 132.542 * [backup-simplify]: Simplify PI into PI 132.542 * [taylor]: Taking taylor expansion of n in n 132.542 * [backup-simplify]: Simplify 0 into 0 132.542 * [backup-simplify]: Simplify 1 into 1 132.543 * [backup-simplify]: Simplify (/ PI 1) into PI 132.543 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 132.544 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 132.544 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 132.545 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 132.545 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 132.546 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 132.547 * [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))) 132.548 * [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)))) 132.548 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 132.548 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 132.548 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 132.548 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 132.549 * [taylor]: Taking taylor expansion of 1/2 in n 132.549 * [backup-simplify]: Simplify 1/2 into 1/2 132.549 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 132.549 * [taylor]: Taking taylor expansion of 1/2 in n 132.549 * [backup-simplify]: Simplify 1/2 into 1/2 132.549 * [taylor]: Taking taylor expansion of (/ 1 k) in n 132.549 * [taylor]: Taking taylor expansion of k in n 132.549 * [backup-simplify]: Simplify k into k 132.549 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 132.549 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 132.549 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 132.549 * [taylor]: Taking taylor expansion of 2 in n 132.549 * [backup-simplify]: Simplify 2 into 2 132.549 * [taylor]: Taking taylor expansion of (/ PI n) in n 132.549 * [taylor]: Taking taylor expansion of PI in n 132.549 * [backup-simplify]: Simplify PI into PI 132.549 * [taylor]: Taking taylor expansion of n in n 132.549 * [backup-simplify]: Simplify 0 into 0 132.549 * [backup-simplify]: Simplify 1 into 1 132.549 * [backup-simplify]: Simplify (/ PI 1) into PI 132.550 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 132.551 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 132.551 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 132.551 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 132.551 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 132.552 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 132.553 * [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))) 132.554 * [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)))) 132.555 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 132.555 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 132.555 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 132.555 * [taylor]: Taking taylor expansion of 1/2 in k 132.555 * [backup-simplify]: Simplify 1/2 into 1/2 132.555 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 132.555 * [taylor]: Taking taylor expansion of 1/2 in k 132.555 * [backup-simplify]: Simplify 1/2 into 1/2 132.555 * [taylor]: Taking taylor expansion of (/ 1 k) in k 132.555 * [taylor]: Taking taylor expansion of k in k 132.555 * [backup-simplify]: Simplify 0 into 0 132.555 * [backup-simplify]: Simplify 1 into 1 132.555 * [backup-simplify]: Simplify (/ 1 1) into 1 132.555 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 132.555 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 132.555 * [taylor]: Taking taylor expansion of (* 2 PI) in k 132.555 * [taylor]: Taking taylor expansion of 2 in k 132.555 * [backup-simplify]: Simplify 2 into 2 132.555 * [taylor]: Taking taylor expansion of PI in k 132.556 * [backup-simplify]: Simplify PI into PI 132.556 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 132.557 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 132.557 * [taylor]: Taking taylor expansion of (log n) in k 132.557 * [taylor]: Taking taylor expansion of n in k 132.557 * [backup-simplify]: Simplify n into n 132.557 * [backup-simplify]: Simplify (log n) into (log n) 132.557 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 132.558 * [backup-simplify]: Simplify (- 1/2) into -1/2 132.558 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 132.558 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 132.559 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 132.560 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 132.561 * [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)))) 132.563 * [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)))) 132.564 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 132.564 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 132.566 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 132.566 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 132.567 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 132.567 * [backup-simplify]: Simplify (- 0) into 0 132.567 * [backup-simplify]: Simplify (+ 0 0) into 0 132.569 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 132.570 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 132.572 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 132.572 * [taylor]: Taking taylor expansion of 0 in k 132.572 * [backup-simplify]: Simplify 0 into 0 132.572 * [backup-simplify]: Simplify 0 into 0 132.572 * [backup-simplify]: Simplify 0 into 0 132.573 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.574 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 132.578 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 132.578 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 132.579 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 132.579 * [backup-simplify]: Simplify (- 0) into 0 132.579 * [backup-simplify]: Simplify (+ 0 0) into 0 132.581 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 132.582 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 132.589 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 132.589 * [taylor]: Taking taylor expansion of 0 in k 132.589 * [backup-simplify]: Simplify 0 into 0 132.589 * [backup-simplify]: Simplify 0 into 0 132.589 * [backup-simplify]: Simplify 0 into 0 132.589 * [backup-simplify]: Simplify 0 into 0 132.591 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.592 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 132.597 * [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 0 132.598 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 132.599 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 132.599 * [backup-simplify]: Simplify (- 0) into 0 132.600 * [backup-simplify]: Simplify (+ 0 0) into 0 132.601 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 132.603 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 132.606 * [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 0 132.606 * [taylor]: Taking taylor expansion of 0 in k 132.606 * [backup-simplify]: Simplify 0 into 0 132.606 * [backup-simplify]: Simplify 0 into 0 132.607 * [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))))) 132.608 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 132.608 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 132.608 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 132.608 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 132.608 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 132.608 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 132.608 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 132.608 * [taylor]: Taking taylor expansion of 1/2 in k 132.608 * [backup-simplify]: Simplify 1/2 into 1/2 132.608 * [taylor]: Taking taylor expansion of (/ 1 k) in k 132.608 * [taylor]: Taking taylor expansion of k in k 132.608 * [backup-simplify]: Simplify 0 into 0 132.608 * [backup-simplify]: Simplify 1 into 1 132.608 * [backup-simplify]: Simplify (/ 1 1) into 1 132.609 * [taylor]: Taking taylor expansion of 1/2 in k 132.609 * [backup-simplify]: Simplify 1/2 into 1/2 132.609 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 132.609 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 132.609 * [taylor]: Taking taylor expansion of -2 in k 132.609 * [backup-simplify]: Simplify -2 into -2 132.609 * [taylor]: Taking taylor expansion of (/ PI n) in k 132.609 * [taylor]: Taking taylor expansion of PI in k 132.609 * [backup-simplify]: Simplify PI into PI 132.609 * [taylor]: Taking taylor expansion of n in k 132.609 * [backup-simplify]: Simplify n into n 132.609 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 132.609 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 132.609 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 132.609 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 132.610 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 132.610 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 132.610 * [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))) 132.610 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 132.610 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 132.610 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 132.610 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 132.610 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 132.611 * [taylor]: Taking taylor expansion of 1/2 in n 132.611 * [backup-simplify]: Simplify 1/2 into 1/2 132.611 * [taylor]: Taking taylor expansion of (/ 1 k) in n 132.611 * [taylor]: Taking taylor expansion of k in n 132.611 * [backup-simplify]: Simplify k into k 132.611 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 132.611 * [taylor]: Taking taylor expansion of 1/2 in n 132.611 * [backup-simplify]: Simplify 1/2 into 1/2 132.611 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 132.611 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 132.611 * [taylor]: Taking taylor expansion of -2 in n 132.611 * [backup-simplify]: Simplify -2 into -2 132.611 * [taylor]: Taking taylor expansion of (/ PI n) in n 132.611 * [taylor]: Taking taylor expansion of PI in n 132.611 * [backup-simplify]: Simplify PI into PI 132.611 * [taylor]: Taking taylor expansion of n in n 132.611 * [backup-simplify]: Simplify 0 into 0 132.611 * [backup-simplify]: Simplify 1 into 1 132.611 * [backup-simplify]: Simplify (/ PI 1) into PI 132.612 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 132.613 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 132.613 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 132.613 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 132.615 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 132.616 * [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))) 132.617 * [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)))) 132.617 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 132.617 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 132.617 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 132.617 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 132.617 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 132.617 * [taylor]: Taking taylor expansion of 1/2 in n 132.617 * [backup-simplify]: Simplify 1/2 into 1/2 132.617 * [taylor]: Taking taylor expansion of (/ 1 k) in n 132.617 * [taylor]: Taking taylor expansion of k in n 132.617 * [backup-simplify]: Simplify k into k 132.617 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 132.617 * [taylor]: Taking taylor expansion of 1/2 in n 132.617 * [backup-simplify]: Simplify 1/2 into 1/2 132.617 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 132.617 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 132.617 * [taylor]: Taking taylor expansion of -2 in n 132.617 * [backup-simplify]: Simplify -2 into -2 132.617 * [taylor]: Taking taylor expansion of (/ PI n) in n 132.617 * [taylor]: Taking taylor expansion of PI in n 132.617 * [backup-simplify]: Simplify PI into PI 132.618 * [taylor]: Taking taylor expansion of n in n 132.618 * [backup-simplify]: Simplify 0 into 0 132.618 * [backup-simplify]: Simplify 1 into 1 132.618 * [backup-simplify]: Simplify (/ PI 1) into PI 132.619 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 132.620 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 132.620 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 132.620 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 132.621 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 132.622 * [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))) 132.623 * [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)))) 132.623 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 132.624 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 132.624 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 132.624 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 132.624 * [taylor]: Taking taylor expansion of 1/2 in k 132.624 * [backup-simplify]: Simplify 1/2 into 1/2 132.624 * [taylor]: Taking taylor expansion of (/ 1 k) in k 132.624 * [taylor]: Taking taylor expansion of k in k 132.624 * [backup-simplify]: Simplify 0 into 0 132.624 * [backup-simplify]: Simplify 1 into 1 132.624 * [backup-simplify]: Simplify (/ 1 1) into 1 132.624 * [taylor]: Taking taylor expansion of 1/2 in k 132.624 * [backup-simplify]: Simplify 1/2 into 1/2 132.624 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 132.624 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 132.624 * [taylor]: Taking taylor expansion of (* -2 PI) in k 132.624 * [taylor]: Taking taylor expansion of -2 in k 132.624 * [backup-simplify]: Simplify -2 into -2 132.624 * [taylor]: Taking taylor expansion of PI in k 132.624 * [backup-simplify]: Simplify PI into PI 132.625 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 132.626 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 132.626 * [taylor]: Taking taylor expansion of (log n) in k 132.626 * [taylor]: Taking taylor expansion of n in k 132.626 * [backup-simplify]: Simplify n into n 132.626 * [backup-simplify]: Simplify (log n) into (log n) 132.626 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 132.627 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 132.627 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 132.628 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 132.629 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 132.630 * [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)))) 132.631 * [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)))) 132.632 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 132.633 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 132.635 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 132.635 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 132.635 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 132.636 * [backup-simplify]: Simplify (+ 0 0) into 0 132.637 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 132.638 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 132.640 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 132.640 * [taylor]: Taking taylor expansion of 0 in k 132.640 * [backup-simplify]: Simplify 0 into 0 132.640 * [backup-simplify]: Simplify 0 into 0 132.640 * [backup-simplify]: Simplify 0 into 0 132.641 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.642 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 132.646 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 132.646 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 132.647 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 132.648 * [backup-simplify]: Simplify (+ 0 0) into 0 132.649 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 132.650 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 132.653 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 132.653 * [taylor]: Taking taylor expansion of 0 in k 132.653 * [backup-simplify]: Simplify 0 into 0 132.653 * [backup-simplify]: Simplify 0 into 0 132.653 * [backup-simplify]: Simplify 0 into 0 132.653 * [backup-simplify]: Simplify 0 into 0 132.654 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.655 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 132.661 * [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 0 132.662 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 132.663 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 132.663 * [backup-simplify]: Simplify (+ 0 0) into 0 132.665 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 132.667 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 132.669 * [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 0 132.670 * [taylor]: Taking taylor expansion of 0 in k 132.670 * [backup-simplify]: Simplify 0 into 0 132.670 * [backup-simplify]: Simplify 0 into 0 132.671 * [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))))) 132.671 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1 1) 132.671 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 132.671 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 132.671 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 132.671 * [taylor]: Taking taylor expansion of 2 in n 132.671 * [backup-simplify]: Simplify 2 into 2 132.672 * [taylor]: Taking taylor expansion of (* n PI) in n 132.672 * [taylor]: Taking taylor expansion of n in n 132.672 * [backup-simplify]: Simplify 0 into 0 132.672 * [backup-simplify]: Simplify 1 into 1 132.672 * [taylor]: Taking taylor expansion of PI in n 132.672 * [backup-simplify]: Simplify PI into PI 132.672 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 132.672 * [taylor]: Taking taylor expansion of 2 in n 132.672 * [backup-simplify]: Simplify 2 into 2 132.672 * [taylor]: Taking taylor expansion of (* n PI) in n 132.672 * [taylor]: Taking taylor expansion of n in n 132.672 * [backup-simplify]: Simplify 0 into 0 132.672 * [backup-simplify]: Simplify 1 into 1 132.672 * [taylor]: Taking taylor expansion of PI in n 132.672 * [backup-simplify]: Simplify PI into PI 132.672 * [backup-simplify]: Simplify (* 0 PI) into 0 132.673 * [backup-simplify]: Simplify (* 2 0) into 0 132.673 * [backup-simplify]: Simplify 0 into 0 132.674 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 132.676 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 132.676 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 132.677 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 132.678 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 132.678 * [backup-simplify]: Simplify 0 into 0 132.679 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 132.681 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 132.681 * [backup-simplify]: Simplify 0 into 0 132.682 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 132.683 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 132.683 * [backup-simplify]: Simplify 0 into 0 132.685 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 132.686 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 132.686 * [backup-simplify]: Simplify 0 into 0 132.688 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 132.690 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 132.690 * [backup-simplify]: Simplify 0 into 0 132.692 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 132.694 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 132.694 * [backup-simplify]: Simplify 0 into 0 132.695 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 132.695 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 132.695 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 132.695 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 132.695 * [taylor]: Taking taylor expansion of 2 in n 132.695 * [backup-simplify]: Simplify 2 into 2 132.695 * [taylor]: Taking taylor expansion of (/ PI n) in n 132.695 * [taylor]: Taking taylor expansion of PI in n 132.695 * [backup-simplify]: Simplify PI into PI 132.695 * [taylor]: Taking taylor expansion of n in n 132.695 * [backup-simplify]: Simplify 0 into 0 132.696 * [backup-simplify]: Simplify 1 into 1 132.696 * [backup-simplify]: Simplify (/ PI 1) into PI 132.696 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 132.696 * [taylor]: Taking taylor expansion of 2 in n 132.696 * [backup-simplify]: Simplify 2 into 2 132.696 * [taylor]: Taking taylor expansion of (/ PI n) in n 132.696 * [taylor]: Taking taylor expansion of PI in n 132.696 * [backup-simplify]: Simplify PI into PI 132.696 * [taylor]: Taking taylor expansion of n in n 132.696 * [backup-simplify]: Simplify 0 into 0 132.696 * [backup-simplify]: Simplify 1 into 1 132.697 * [backup-simplify]: Simplify (/ PI 1) into PI 132.697 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 132.698 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 132.699 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 132.699 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 132.700 * [backup-simplify]: Simplify 0 into 0 132.701 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.702 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 132.702 * [backup-simplify]: Simplify 0 into 0 132.703 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.704 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 132.704 * [backup-simplify]: Simplify 0 into 0 132.705 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.707 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 132.707 * [backup-simplify]: Simplify 0 into 0 132.708 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.710 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 132.710 * [backup-simplify]: Simplify 0 into 0 132.711 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.713 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 132.713 * [backup-simplify]: Simplify 0 into 0 132.713 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 132.714 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 132.714 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 132.714 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 132.714 * [taylor]: Taking taylor expansion of -2 in n 132.714 * [backup-simplify]: Simplify -2 into -2 132.714 * [taylor]: Taking taylor expansion of (/ PI n) in n 132.714 * [taylor]: Taking taylor expansion of PI in n 132.714 * [backup-simplify]: Simplify PI into PI 132.714 * [taylor]: Taking taylor expansion of n in n 132.714 * [backup-simplify]: Simplify 0 into 0 132.714 * [backup-simplify]: Simplify 1 into 1 132.715 * [backup-simplify]: Simplify (/ PI 1) into PI 132.715 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 132.715 * [taylor]: Taking taylor expansion of -2 in n 132.715 * [backup-simplify]: Simplify -2 into -2 132.715 * [taylor]: Taking taylor expansion of (/ PI n) in n 132.715 * [taylor]: Taking taylor expansion of PI in n 132.715 * [backup-simplify]: Simplify PI into PI 132.715 * [taylor]: Taking taylor expansion of n in n 132.715 * [backup-simplify]: Simplify 0 into 0 132.715 * [backup-simplify]: Simplify 1 into 1 132.715 * [backup-simplify]: Simplify (/ PI 1) into PI 132.716 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 132.716 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 132.717 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 132.718 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 132.718 * [backup-simplify]: Simplify 0 into 0 132.719 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.720 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 132.720 * [backup-simplify]: Simplify 0 into 0 132.722 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.723 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 132.723 * [backup-simplify]: Simplify 0 into 0 132.724 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.725 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 132.725 * [backup-simplify]: Simplify 0 into 0 132.726 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.728 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 132.728 * [backup-simplify]: Simplify 0 into 0 132.729 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.730 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 132.730 * [backup-simplify]: Simplify 0 into 0 132.731 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 132.731 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1 1) 132.732 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI)) 132.732 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 132.732 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 132.732 * [taylor]: Taking taylor expansion of 2 in n 132.732 * [backup-simplify]: Simplify 2 into 2 132.732 * [taylor]: Taking taylor expansion of (* n PI) in n 132.732 * [taylor]: Taking taylor expansion of n in n 132.732 * [backup-simplify]: Simplify 0 into 0 132.732 * [backup-simplify]: Simplify 1 into 1 132.732 * [taylor]: Taking taylor expansion of PI in n 132.732 * [backup-simplify]: Simplify PI into PI 132.732 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 132.732 * [taylor]: Taking taylor expansion of 2 in n 132.732 * [backup-simplify]: Simplify 2 into 2 132.732 * [taylor]: Taking taylor expansion of (* n PI) in n 132.732 * [taylor]: Taking taylor expansion of n in n 132.732 * [backup-simplify]: Simplify 0 into 0 132.732 * [backup-simplify]: Simplify 1 into 1 132.732 * [taylor]: Taking taylor expansion of PI in n 132.732 * [backup-simplify]: Simplify PI into PI 132.733 * [backup-simplify]: Simplify (* 0 PI) into 0 132.733 * [backup-simplify]: Simplify (* 2 0) into 0 132.733 * [backup-simplify]: Simplify 0 into 0 132.735 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 132.741 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 132.742 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 132.743 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 132.744 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 132.744 * [backup-simplify]: Simplify 0 into 0 132.745 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 132.746 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 132.746 * [backup-simplify]: Simplify 0 into 0 132.748 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 132.749 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 132.749 * [backup-simplify]: Simplify 0 into 0 132.750 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 132.752 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 132.752 * [backup-simplify]: Simplify 0 into 0 132.754 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 132.755 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 132.755 * [backup-simplify]: Simplify 0 into 0 132.757 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 132.759 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 132.759 * [backup-simplify]: Simplify 0 into 0 132.760 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 132.760 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n)) 132.760 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 132.760 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 132.760 * [taylor]: Taking taylor expansion of 2 in n 132.760 * [backup-simplify]: Simplify 2 into 2 132.760 * [taylor]: Taking taylor expansion of (/ PI n) in n 132.760 * [taylor]: Taking taylor expansion of PI in n 132.760 * [backup-simplify]: Simplify PI into PI 132.760 * [taylor]: Taking taylor expansion of n in n 132.760 * [backup-simplify]: Simplify 0 into 0 132.760 * [backup-simplify]: Simplify 1 into 1 132.761 * [backup-simplify]: Simplify (/ PI 1) into PI 132.761 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 132.761 * [taylor]: Taking taylor expansion of 2 in n 132.761 * [backup-simplify]: Simplify 2 into 2 132.761 * [taylor]: Taking taylor expansion of (/ PI n) in n 132.761 * [taylor]: Taking taylor expansion of PI in n 132.761 * [backup-simplify]: Simplify PI into PI 132.761 * [taylor]: Taking taylor expansion of n in n 132.761 * [backup-simplify]: Simplify 0 into 0 132.761 * [backup-simplify]: Simplify 1 into 1 132.761 * [backup-simplify]: Simplify (/ PI 1) into PI 132.762 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 132.762 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 132.763 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 132.764 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 132.764 * [backup-simplify]: Simplify 0 into 0 132.765 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.766 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 132.766 * [backup-simplify]: Simplify 0 into 0 132.767 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.768 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 132.768 * [backup-simplify]: Simplify 0 into 0 132.770 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.771 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 132.771 * [backup-simplify]: Simplify 0 into 0 132.772 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.774 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 132.774 * [backup-simplify]: Simplify 0 into 0 132.775 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.777 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 132.777 * [backup-simplify]: Simplify 0 into 0 132.777 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 132.778 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n)) 132.778 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 132.778 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 132.778 * [taylor]: Taking taylor expansion of -2 in n 132.778 * [backup-simplify]: Simplify -2 into -2 132.778 * [taylor]: Taking taylor expansion of (/ PI n) in n 132.778 * [taylor]: Taking taylor expansion of PI in n 132.778 * [backup-simplify]: Simplify PI into PI 132.778 * [taylor]: Taking taylor expansion of n in n 132.778 * [backup-simplify]: Simplify 0 into 0 132.778 * [backup-simplify]: Simplify 1 into 1 132.779 * [backup-simplify]: Simplify (/ PI 1) into PI 132.779 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 132.779 * [taylor]: Taking taylor expansion of -2 in n 132.779 * [backup-simplify]: Simplify -2 into -2 132.779 * [taylor]: Taking taylor expansion of (/ PI n) in n 132.779 * [taylor]: Taking taylor expansion of PI in n 132.779 * [backup-simplify]: Simplify PI into PI 132.779 * [taylor]: Taking taylor expansion of n in n 132.779 * [backup-simplify]: Simplify 0 into 0 132.779 * [backup-simplify]: Simplify 1 into 1 132.779 * [backup-simplify]: Simplify (/ PI 1) into PI 132.780 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 132.780 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 132.781 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 132.782 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 132.782 * [backup-simplify]: Simplify 0 into 0 132.783 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.784 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 132.784 * [backup-simplify]: Simplify 0 into 0 132.785 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.786 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 132.786 * [backup-simplify]: Simplify 0 into 0 132.787 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.788 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 132.788 * [backup-simplify]: Simplify 0 into 0 132.789 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.791 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 132.791 * [backup-simplify]: Simplify 0 into 0 132.792 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 132.794 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 132.794 * [backup-simplify]: Simplify 0 into 0 132.794 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 132.794 * * * [progress]: simplifying candidates 132.794 * * * * [progress]: [ 1 / 188 ] simplifiying candidate # 132.795 * * * * [progress]: [ 2 / 188 ] simplifiying candidate # 132.795 * * * * [progress]: [ 3 / 188 ] simplifiying candidate # 132.795 * * * * [progress]: [ 4 / 188 ] simplifiying candidate # 132.795 * * * * [progress]: [ 5 / 188 ] simplifiying candidate # 132.795 * * * * [progress]: [ 6 / 188 ] simplifiying candidate # 132.795 * * * * [progress]: [ 7 / 188 ] simplifiying candidate # 132.795 * * * * [progress]: [ 8 / 188 ] simplifiying candidate # 132.795 * * * * [progress]: [ 9 / 188 ] simplifiying candidate # 132.795 * * * * [progress]: [ 10 / 188 ] simplifiying candidate # 132.795 * * * * [progress]: [ 11 / 188 ] simplifiying candidate # 132.795 * * * * [progress]: [ 12 / 188 ] simplifiying candidate # 132.795 * * * * [progress]: [ 13 / 188 ] simplifiying candidate # 132.795 * * * * [progress]: [ 14 / 188 ] simplifiying candidate # 132.795 * * * * [progress]: [ 15 / 188 ] simplifiying candidate # 132.796 * * * * [progress]: [ 16 / 188 ] simplifiying candidate # 132.796 * * * * [progress]: [ 17 / 188 ] simplifiying candidate # 132.796 * * * * [progress]: [ 18 / 188 ] simplifiying candidate # 132.796 * * * * [progress]: [ 19 / 188 ] simplifiying candidate # 132.796 * * * * [progress]: [ 20 / 188 ] simplifiying candidate # 132.796 * * * * [progress]: [ 21 / 188 ] simplifiying candidate # 132.796 * * * * [progress]: [ 22 / 188 ] simplifiying candidate # 132.796 * * * * [progress]: [ 23 / 188 ] simplifiying candidate # 132.796 * * * * [progress]: [ 24 / 188 ] simplifiying candidate # 132.796 * * * * [progress]: [ 25 / 188 ] simplifiying candidate # 132.796 * * * * [progress]: [ 26 / 188 ] simplifiying candidate # 132.797 * * * * [progress]: [ 27 / 188 ] simplifiying candidate # 132.797 * * * * [progress]: [ 28 / 188 ] simplifiying candidate # 132.797 * * * * [progress]: [ 29 / 188 ] simplifiying candidate # 132.797 * * * * [progress]: [ 30 / 188 ] simplifiying candidate # 132.797 * * * * [progress]: [ 31 / 188 ] simplifiying candidate # 132.797 * * * * [progress]: [ 32 / 188 ] simplifiying candidate # 132.797 * * * * [progress]: [ 33 / 188 ] simplifiying candidate # 132.797 * * * * [progress]: [ 34 / 188 ] simplifiying candidate # 132.797 * * * * [progress]: [ 35 / 188 ] simplifiying candidate # 132.797 * * * * [progress]: [ 36 / 188 ] simplifiying candidate # 132.797 * * * * [progress]: [ 37 / 188 ] simplifiying candidate # 132.798 * * * * [progress]: [ 38 / 188 ] simplifiying candidate # 132.798 * * * * [progress]: [ 39 / 188 ] simplifiying candidate # 132.798 * * * * [progress]: [ 40 / 188 ] simplifiying candidate # 132.798 * * * * [progress]: [ 41 / 188 ] simplifiying candidate # 132.798 * * * * 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[progress]: [ 57 / 188 ] simplifiying candidate # 132.799 * * * * [progress]: [ 58 / 188 ] simplifiying candidate # 132.799 * * * * [progress]: [ 59 / 188 ] simplifiying candidate # 132.800 * * * * [progress]: [ 60 / 188 ] simplifiying candidate # 132.800 * * * * [progress]: [ 61 / 188 ] simplifiying candidate # 132.800 * * * * [progress]: [ 62 / 188 ] simplifiying candidate # 132.800 * * * * [progress]: [ 63 / 188 ] simplifiying candidate # 132.800 * * * * [progress]: [ 64 / 188 ] simplifiying candidate # 132.800 * * * * [progress]: [ 65 / 188 ] simplifiying candidate # 132.800 * * * * [progress]: [ 66 / 188 ] simplifiying candidate # 132.800 * * * * [progress]: [ 67 / 188 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))))> 132.800 * * * * [progress]: [ 68 / 188 ] simplifiying candidate # 132.800 * * * * [progress]: [ 69 / 188 ] simplifiying candidate # 132.800 * * * * [progress]: [ 70 / 188 ] simplifiying candidate # 132.800 * * * * [progress]: [ 71 / 188 ] simplifiying candidate # 132.800 * * * * [progress]: [ 72 / 188 ] simplifiying candidate # 132.801 * * * * [progress]: [ 73 / 188 ] simplifiying candidate # 132.801 * * * * [progress]: [ 74 / 188 ] simplifiying candidate # 132.801 * * * * [progress]: [ 75 / 188 ] simplifiying candidate # 132.801 * * * * [progress]: [ 76 / 188 ] simplifiying candidate # 132.801 * * * * [progress]: [ 77 / 188 ] simplifiying candidate # 132.801 * * * * [progress]: [ 78 / 188 ] simplifiying candidate # 132.801 * * * * [progress]: [ 79 / 188 ] simplifiying candidate # 132.801 * * * * [progress]: [ 80 / 188 ] simplifiying candidate # 132.801 * * * * [progress]: [ 81 / 188 ] simplifiying candidate # 132.801 * * * * [progress]: [ 82 / 188 ] simplifiying candidate # 132.801 * * * * [progress]: [ 83 / 188 ] simplifiying candidate # 132.801 * * * * [progress]: [ 84 / 188 ] simplifiying candidate # 132.802 * * * * [progress]: [ 85 / 188 ] simplifiying candidate # 132.802 * * * * [progress]: [ 86 / 188 ] simplifiying candidate # 132.802 * * * * [progress]: [ 87 / 188 ] simplifiying candidate # 132.802 * * * * [progress]: [ 88 / 188 ] simplifiying candidate # 132.802 * * * * [progress]: [ 89 / 188 ] simplifiying candidate # 132.802 * * * * [progress]: [ 90 / 188 ] simplifiying candidate # 132.802 * * * * [progress]: [ 91 / 188 ] simplifiying candidate # 132.802 * * * * [progress]: [ 92 / 188 ] simplifiying candidate # 132.802 * * * * [progress]: [ 93 / 188 ] simplifiying candidate # 132.802 * * * * [progress]: [ 94 / 188 ] simplifiying candidate # 132.803 * * * * [progress]: [ 95 / 188 ] simplifiying candidate # 132.803 * * * * [progress]: [ 96 / 188 ] simplifiying candidate # 132.803 * * * * [progress]: [ 97 / 188 ] simplifiying candidate # 132.803 * * * * [progress]: [ 98 / 188 ] simplifiying candidate # 132.803 * * * * [progress]: [ 99 / 188 ] simplifiying candidate # 132.803 * * * * [progress]: [ 100 / 188 ] simplifiying candidate # 132.803 * * * * [progress]: [ 101 / 188 ] simplifiying candidate # 132.803 * * * * [progress]: [ 102 / 188 ] simplifiying candidate # 132.803 * * * * [progress]: [ 103 / 188 ] simplifiying candidate # 132.804 * * * * [progress]: [ 104 / 188 ] simplifiying candidate # 132.804 * * * * [progress]: [ 105 / 188 ] simplifiying candidate # 132.804 * * * * [progress]: [ 106 / 188 ] simplifiying candidate # 132.804 * * * * [progress]: [ 107 / 188 ] simplifiying candidate # 132.804 * * * * [progress]: [ 108 / 188 ] simplifiying candidate # 132.804 * * * * [progress]: [ 109 / 188 ] simplifiying candidate # 132.804 * * * * [progress]: [ 110 / 188 ] simplifiying candidate # 132.804 * * * * [progress]: [ 111 / 188 ] simplifiying candidate # 132.804 * * * * [progress]: [ 112 / 188 ] simplifiying candidate # 132.805 * * * * [progress]: [ 113 / 188 ] simplifiying candidate # 132.805 * * * * [progress]: [ 114 / 188 ] simplifiying candidate # 132.805 * * * * [progress]: [ 115 / 188 ] simplifiying candidate # 132.805 * * * * [progress]: [ 116 / 188 ] simplifiying candidate # 132.805 * * * * [progress]: [ 117 / 188 ] simplifiying candidate # 132.805 * * * * [progress]: [ 118 / 188 ] simplifiying candidate # 132.805 * * * * [progress]: [ 119 / 188 ] simplifiying candidate # 132.805 * * * * [progress]: [ 120 / 188 ] simplifiying candidate # 132.805 * * * * [progress]: [ 121 / 188 ] simplifiying candidate # 132.805 * * * * [progress]: [ 122 / 188 ] simplifiying candidate # 132.805 * * * * [progress]: [ 123 / 188 ] simplifiying candidate # 132.806 * * * * [progress]: [ 124 / 188 ] simplifiying candidate # 132.806 * * * * [progress]: [ 125 / 188 ] simplifiying candidate # 132.806 * * * * [progress]: [ 126 / 188 ] simplifiying candidate # 132.806 * * * * [progress]: [ 127 / 188 ] simplifiying candidate # 132.806 * * * * [progress]: [ 128 / 188 ] simplifiying candidate # 132.806 * * * * [progress]: [ 129 / 188 ] simplifiying candidate # 132.806 * * * * [progress]: [ 130 / 188 ] simplifiying candidate # 132.806 * * * * [progress]: [ 131 / 188 ] simplifiying candidate # 132.806 * * * * [progress]: [ 132 / 188 ] simplifiying candidate # 132.806 * * * * [progress]: [ 133 / 188 ] simplifiying candidate # 132.806 * * * * [progress]: [ 134 / 188 ] simplifiying candidate #real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))> 132.806 * * * * [progress]: [ 135 / 188 ] simplifiying candidate # 132.806 * * * * [progress]: [ 136 / 188 ] simplifiying candidate # 132.807 * * * * [progress]: [ 137 / 188 ] simplifiying candidate # 132.807 * * * * [progress]: [ 138 / 188 ] simplifiying candidate # 132.807 * * * * [progress]: [ 139 / 188 ] simplifiying candidate # 132.807 * * * * [progress]: [ 140 / 188 ] simplifiying candidate # 132.807 * * * * [progress]: [ 141 / 188 ] simplifiying candidate # 132.807 * * * * [progress]: [ 142 / 188 ] simplifiying candidate # 132.807 * * * * [progress]: [ 143 / 188 ] simplifiying candidate # 132.807 * * * * [progress]: [ 144 / 188 ] simplifiying candidate # 132.807 * * * * [progress]: [ 145 / 188 ] simplifiying candidate # 132.807 * * * * [progress]: [ 146 / 188 ] simplifiying candidate # 132.807 * * * * [progress]: [ 147 / 188 ] simplifiying candidate # 132.807 * * * * [progress]: [ 148 / 188 ] simplifiying candidate # 132.807 * * * * [progress]: [ 149 / 188 ] simplifiying candidate # 132.808 * * * * [progress]: [ 150 / 188 ] simplifiying candidate # 132.808 * * * * [progress]: [ 151 / 188 ] simplifiying candidate # 132.808 * * * * [progress]: [ 152 / 188 ] simplifiying candidate # 132.808 * * * * [progress]: [ 153 / 188 ] simplifiying candidate # 132.808 * * * * [progress]: [ 154 / 188 ] simplifiying candidate #real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))))> 132.808 * * * * [progress]: [ 155 / 188 ] simplifiying candidate # 132.808 * * * * [progress]: [ 156 / 188 ] simplifiying candidate # 132.808 * * * * [progress]: [ 157 / 188 ] simplifiying candidate # 132.808 * * * * [progress]: [ 158 / 188 ] simplifiying candidate # 132.808 * * * * [progress]: [ 159 / 188 ] simplifiying candidate # 132.808 * * * * [progress]: [ 160 / 188 ] simplifiying candidate # 132.808 * * * * [progress]: [ 161 / 188 ] simplifiying candidate # 132.808 * * * * [progress]: [ 162 / 188 ] simplifiying candidate # 132.808 * * * * [progress]: [ 163 / 188 ] simplifiying candidate # 132.809 * * * * [progress]: [ 164 / 188 ] simplifiying candidate # 132.809 * * * * [progress]: [ 165 / 188 ] simplifiying candidate # 132.809 * * * * [progress]: [ 166 / 188 ] simplifiying candidate # 132.809 * * * * [progress]: [ 167 / 188 ] simplifiying candidate # 132.809 * * * * [progress]: [ 168 / 188 ] simplifiying candidate # 132.809 * * * * [progress]: [ 169 / 188 ] simplifiying candidate # 132.809 * * * * [progress]: [ 170 / 188 ] simplifiying candidate # 132.809 * * * * [progress]: [ 171 / 188 ] simplifiying candidate # 132.809 * * * * [progress]: [ 172 / 188 ] simplifiying candidate # 132.809 * * * * [progress]: [ 173 / 188 ] simplifiying candidate # 132.809 * * * * [progress]: [ 174 / 188 ] simplifiying candidate # 132.809 * * * * [progress]: [ 175 / 188 ] simplifiying candidate #real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))> 132.809 * * * * [progress]: [ 176 / 188 ] simplifiying candidate # 132.809 * * * * [progress]: [ 177 / 188 ] simplifiying candidate # 132.810 * * * * [progress]: [ 178 / 188 ] simplifiying candidate # 132.810 * * * * [progress]: [ 179 / 188 ] simplifiying candidate # 132.810 * * * * [progress]: [ 180 / 188 ] simplifiying candidate # 132.810 * * * * [progress]: [ 181 / 188 ] simplifiying candidate # 132.810 * * * * [progress]: [ 182 / 188 ] simplifiying candidate # 132.810 * * * * [progress]: [ 183 / 188 ] simplifiying candidate # 132.810 * * * * [progress]: [ 184 / 188 ] simplifiying candidate # 132.810 * * * * [progress]: [ 185 / 188 ] simplifiying candidate # 132.810 * * * * [progress]: [ 186 / 188 ] simplifiying candidate # 132.810 * * * * [progress]: [ 187 / 188 ] simplifiying candidate # 132.810 * * * * [progress]: [ 188 / 188 ] simplifiying candidate # 132.813 * [simplify]: Simplifying: (expm1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log1p (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2)) (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* n (* 2 PI)) 1) (pow (* n (* 2 PI)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* 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(* n (* 2 PI))) (* n 2) (* (cbrt n) (* 2 PI)) (* (sqrt n) (* 2 PI)) (* n (* 2 PI)) (real->posit16 (* n (* 2 PI))) (- (+ (* 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))))) (- (+ (* 1/4 (* (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))))) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) 132.818 * * [simplify]: iteration 1: (292 enodes) 132.957 * * [simplify]: iteration 2: (1414 enodes) 133.458 * * [simplify]: Extracting #0: cost 61 inf + 0 133.460 * * [simplify]: Extracting #1: cost 462 inf + 0 133.465 * * [simplify]: Extracting #2: cost 975 inf + 3597 133.479 * * [simplify]: Extracting #3: cost 1158 inf + 34679 133.517 * * [simplify]: Extracting #4: cost 828 inf + 130600 133.586 * * [simplify]: Extracting #5: cost 426 inf + 259647 133.681 * * [simplify]: Extracting #6: cost 187 inf + 372104 133.769 * * [simplify]: Extracting #7: cost 50 inf + 446043 133.869 * * [simplify]: Extracting #8: cost 0 inf + 474820 133.966 * * [simplify]: Extracting #9: cost 0 inf + 474235 134.058 * [simplify]: Simplified to: (expm1 (pow (* (* PI 2) n) (- 1/2 (* 1/2 k)))) (log1p (pow (* (* PI 2) n) (- 1/2 (* 1/2 k)))) (* (log (* (* PI 2) n)) (- 1/2 (* 1/2 k))) (* (log (* (* PI 2) n)) (- 1/2 (* 1/2 k))) (* (log (* (* PI 2) n)) (- 1/2 (* 1/2 k))) (* (log (* (* PI 2) n)) (- 1/2 (* 1/2 k))) (- 1/2 (* 1/2 k)) (- 1/2 (* 1/2 k)) (- 1/2 (* 1/2 k)) (sqrt (* (* PI 2) n)) (pow (* (* PI 2) n) (* 1/2 k)) (pow (* (* PI 2) n) (* (cbrt (- 1/2 (* 1/2 k))) (cbrt (- 1/2 (* 1/2 k))))) (pow (* (* PI 2) n) (sqrt (- 1/2 (* 1/2 k)))) (* (* PI 2) n) (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (* 1/2 k)))) (pow (* (* PI 2) n) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (* (* PI 2) n) (pow (* (* PI 2) n) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* -1/2 k))) (pow (* (* PI 2) n) (fma (* 1/2 k) -1 (* 1/2 k))) (pow (* (* PI 2) n) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* -1/2 k))) (pow (* (* PI 2) n) (fma (* 1/2 k) -1 (* 1/2 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2) n) (* (* (* PI 2) n) (* (* PI 2) n))) (sqrt (* (* PI 2) n)) (sqrt (* (* PI 2) n)) (* n 2) (* (cbrt n) (* PI 2)) (* (sqrt n) (* PI 2)) (* (* PI 2) n) (real->posit16 (* (* PI 2) n)) (expm1 (* (* PI 2) n)) (log1p (* (* PI 2) n)) (* (* PI 2) n) (* (* PI 2) n) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (log (* (* PI 2) n)) (* (exp (* n PI)) (exp (* n PI))) (* n (* (* n n) (* (* 8 (* PI PI)) PI))) (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n))) (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n))) (cbrt (* (* PI 2) n)) (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n))) (sqrt (* (* PI 2) n)) (sqrt (* (* PI 2) n)) (* n 2) (* (cbrt n) (* PI 2)) (* (sqrt n) (* PI 2)) (* (* PI 2) n) (real->posit16 (* (* PI 2) n)) (- (fma (* 1/4 (log (* PI 2))) (* (* (exp (* 1/2 (log (* (* PI 2) n)))) (* (log n) k)) k) (fma 1/8 (* (exp (* 1/2 (log (* (* PI 2) n)))) (* (* (log n) k) (* (log n) k))) (fma (* (* (* (* (log (* PI 2)) (log (* PI 2))) (exp (* 1/2 (log (* (* PI 2) n))))) k) k) 1/8 (exp (* 1/2 (log (* (* PI 2) n))))))) (* 1/2 (* k (+ (* (log n) (exp (* 1/2 (log (* (* PI 2) n))))) (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))))))) (exp (* (log (* (* PI 2) n)) (- 1/2 (* 1/2 k)))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (- (fma (* 1/4 (log (* PI 2))) (* (* (exp (* 1/2 (log (* (* PI 2) n)))) (* (log n) k)) k) (fma 1/8 (* (exp (* 1/2 (log (* (* PI 2) n)))) (* (* (log n) k) (* (log n) k))) (fma (* (* (* (* (log (* PI 2)) (log (* PI 2))) (exp (* 1/2 (log (* (* PI 2) n))))) k) k) 1/8 (exp (* 1/2 (log (* (* PI 2) n))))))) (* 1/2 (* k (+ (* (log n) (exp (* 1/2 (log (* (* PI 2) n))))) (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))))))) (exp (* (log (* (* PI 2) n)) (- 1/2 (* 1/2 k)))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) (* (* PI 2) n) 134.122 * * * [progress]: adding candidates to table 137.417 * [progress]: [Phase 3 of 3] Extracting. 137.417 * * [regime]: Finding splitpoints for: (# # # # # # #) 137.419 * * * [regime-changes]: Trying 2 branch expressions: (n k) 137.419 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 137.464 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 137.539 * * * [regime]: Found split indices: #