51.111 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.107 * * * [progress]: [2/2] Setting up program. 0.116 * [progress]: [Phase 2 of 3] Improving. 0.116 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.116 * * [simplify]: iteration 0: 13 enodes 0.122 * * [simplify]: iteration 1: 29 enodes 0.131 * * [simplify]: iteration 2: 59 enodes 0.149 * * [simplify]: iteration 3: 120 enodes 0.230 * * [simplify]: iteration 4: 328 enodes 0.463 * * [simplify]: iteration 5: 1541 enodes 1.013 * * [simplify]: iteration complete: 5000 enodes 1.013 * * [simplify]: Extracting #0: cost 1 inf + 0 1.014 * * [simplify]: Extracting #1: cost 169 inf + 0 1.019 * * [simplify]: Extracting #2: cost 1666 inf + 1 1.029 * * [simplify]: Extracting #3: cost 2154 inf + 127 1.048 * * [simplify]: Extracting #4: cost 2277 inf + 3690 1.076 * * [simplify]: Extracting #5: cost 1696 inf + 217499 1.264 * * [simplify]: Extracting #6: cost 193 inf + 1045012 1.452 * * [simplify]: Extracting #7: cost 0 inf + 1202666 1.642 * * [simplify]: Extracting #8: cost 0 inf + 1202415 1.834 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) 1.835 * * [progress]: iteration 1 / 4 1.835 * * * [progress]: picking best candidate 1.843 * * * * [pick]: Picked # 1.843 * * * [progress]: localizing error 1.884 * * * [progress]: generating rewritten candidates 1.884 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 1.917 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 1.932 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 1.954 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 1.997 * * * [progress]: generating series expansions 1.997 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 1.998 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 1.998 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.998 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.998 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.998 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.998 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.998 * [taylor]: Taking taylor expansion of 0.5 in k 1.998 * [backup-simplify]: Simplify 0.5 into 0.5 1.998 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.998 * [taylor]: Taking taylor expansion of 1.0 in k 1.998 * [backup-simplify]: Simplify 1.0 into 1.0 1.998 * [taylor]: Taking taylor expansion of k in k 1.998 * [backup-simplify]: Simplify 0 into 0 1.998 * [backup-simplify]: Simplify 1 into 1 1.998 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.998 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.998 * [taylor]: Taking taylor expansion of 2.0 in k 1.998 * [backup-simplify]: Simplify 2.0 into 2.0 1.998 * [taylor]: Taking taylor expansion of (* n PI) in k 1.998 * [taylor]: Taking taylor expansion of n in k 1.998 * [backup-simplify]: Simplify n into n 1.998 * [taylor]: Taking taylor expansion of PI in k 1.998 * [backup-simplify]: Simplify PI into PI 1.998 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.999 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.999 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.999 * [backup-simplify]: Simplify (- 0) into 0 1.999 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.000 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.000 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.000 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.000 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.000 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.000 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.000 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.000 * [taylor]: Taking taylor expansion of 0.5 in n 2.000 * [backup-simplify]: Simplify 0.5 into 0.5 2.000 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.000 * [taylor]: Taking taylor expansion of 1.0 in n 2.000 * [backup-simplify]: Simplify 1.0 into 1.0 2.000 * [taylor]: Taking taylor expansion of k in n 2.000 * [backup-simplify]: Simplify k into k 2.000 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.000 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.000 * [taylor]: Taking taylor expansion of 2.0 in n 2.000 * [backup-simplify]: Simplify 2.0 into 2.0 2.000 * [taylor]: Taking taylor expansion of (* n PI) in n 2.000 * [taylor]: Taking taylor expansion of n in n 2.000 * [backup-simplify]: Simplify 0 into 0 2.000 * [backup-simplify]: Simplify 1 into 1 2.000 * [taylor]: Taking taylor expansion of PI in n 2.000 * [backup-simplify]: Simplify PI into PI 2.000 * [backup-simplify]: Simplify (* 0 PI) into 0 2.001 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.002 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.003 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.003 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.003 * [backup-simplify]: Simplify (- k) into (- k) 2.003 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.004 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.005 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.005 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.006 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.006 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.006 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.006 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.006 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.006 * [taylor]: Taking taylor expansion of 0.5 in n 2.006 * [backup-simplify]: Simplify 0.5 into 0.5 2.006 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.006 * [taylor]: Taking taylor expansion of 1.0 in n 2.006 * [backup-simplify]: Simplify 1.0 into 1.0 2.006 * [taylor]: Taking taylor expansion of k in n 2.006 * [backup-simplify]: Simplify k into k 2.006 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.006 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.006 * [taylor]: Taking taylor expansion of 2.0 in n 2.006 * [backup-simplify]: Simplify 2.0 into 2.0 2.006 * [taylor]: Taking taylor expansion of (* n PI) in n 2.006 * [taylor]: Taking taylor expansion of n in n 2.006 * [backup-simplify]: Simplify 0 into 0 2.006 * [backup-simplify]: Simplify 1 into 1 2.006 * [taylor]: Taking taylor expansion of PI in n 2.006 * [backup-simplify]: Simplify PI into PI 2.007 * [backup-simplify]: Simplify (* 0 PI) into 0 2.007 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.008 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.009 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.010 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.010 * [backup-simplify]: Simplify (- k) into (- k) 2.010 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.010 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.011 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.011 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.012 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.012 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.012 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.012 * [taylor]: Taking taylor expansion of 0.5 in k 2.012 * [backup-simplify]: Simplify 0.5 into 0.5 2.012 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.012 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.012 * [taylor]: Taking taylor expansion of 1.0 in k 2.012 * [backup-simplify]: Simplify 1.0 into 1.0 2.012 * [taylor]: Taking taylor expansion of k in k 2.012 * [backup-simplify]: Simplify 0 into 0 2.012 * [backup-simplify]: Simplify 1 into 1 2.012 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.012 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.012 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.012 * [taylor]: Taking taylor expansion of 2.0 in k 2.012 * [backup-simplify]: Simplify 2.0 into 2.0 2.012 * [taylor]: Taking taylor expansion of PI in k 2.013 * [backup-simplify]: Simplify PI into PI 2.013 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.013 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.014 * [taylor]: Taking taylor expansion of (log n) in k 2.014 * [taylor]: Taking taylor expansion of n in k 2.014 * [backup-simplify]: Simplify n into n 2.014 * [backup-simplify]: Simplify (log n) into (log n) 2.014 * [backup-simplify]: Simplify (- 0) into 0 2.014 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.015 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.015 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.019 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 2.020 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.021 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.021 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.022 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.023 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.023 * [backup-simplify]: Simplify (- 0) into 0 2.024 * [backup-simplify]: Simplify (+ 0 0) into 0 2.024 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 2.025 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.026 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.028 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.028 * [taylor]: Taking taylor expansion of 0 in k 2.028 * [backup-simplify]: Simplify 0 into 0 2.028 * [backup-simplify]: Simplify 0 into 0 2.029 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.030 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.031 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.032 * [backup-simplify]: Simplify (+ 0 0) into 0 2.032 * [backup-simplify]: Simplify (- 1) into -1 2.033 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.034 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.037 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2.040 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 2.043 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 2.045 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.046 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.050 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.050 * [backup-simplify]: Simplify (- 0) into 0 2.051 * [backup-simplify]: Simplify (+ 0 0) into 0 2.052 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.053 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.055 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.057 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.057 * [taylor]: Taking taylor expansion of 0 in k 2.057 * [backup-simplify]: Simplify 0 into 0 2.057 * [backup-simplify]: Simplify 0 into 0 2.057 * [backup-simplify]: Simplify 0 into 0 2.059 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.062 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.064 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.064 * [backup-simplify]: Simplify (+ 0 0) into 0 2.065 * [backup-simplify]: Simplify (- 0) into 0 2.065 * [backup-simplify]: Simplify (+ 0 0) into 0 2.067 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.070 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.075 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 2.080 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 2.091 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) 2.092 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 2.092 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.092 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.092 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.092 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.092 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.092 * [taylor]: Taking taylor expansion of 0.5 in k 2.092 * [backup-simplify]: Simplify 0.5 into 0.5 2.092 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.092 * [taylor]: Taking taylor expansion of 1.0 in k 2.092 * [backup-simplify]: Simplify 1.0 into 1.0 2.092 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.092 * [taylor]: Taking taylor expansion of k in k 2.092 * [backup-simplify]: Simplify 0 into 0 2.092 * [backup-simplify]: Simplify 1 into 1 2.093 * [backup-simplify]: Simplify (/ 1 1) into 1 2.093 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.093 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.093 * [taylor]: Taking taylor expansion of 2.0 in k 2.093 * [backup-simplify]: Simplify 2.0 into 2.0 2.093 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.093 * [taylor]: Taking taylor expansion of PI in k 2.093 * [backup-simplify]: Simplify PI into PI 2.093 * [taylor]: Taking taylor expansion of n in k 2.093 * [backup-simplify]: Simplify n into n 2.093 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.093 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.093 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.094 * [backup-simplify]: Simplify (- 1) into -1 2.094 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.095 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.095 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.095 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 2.095 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.095 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.095 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.095 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.095 * [taylor]: Taking taylor expansion of 0.5 in n 2.095 * [backup-simplify]: Simplify 0.5 into 0.5 2.095 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.095 * [taylor]: Taking taylor expansion of 1.0 in n 2.095 * [backup-simplify]: Simplify 1.0 into 1.0 2.095 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.095 * [taylor]: Taking taylor expansion of k in n 2.095 * [backup-simplify]: Simplify k into k 2.095 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.095 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.095 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.095 * [taylor]: Taking taylor expansion of 2.0 in n 2.096 * [backup-simplify]: Simplify 2.0 into 2.0 2.096 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.096 * [taylor]: Taking taylor expansion of PI in n 2.096 * [backup-simplify]: Simplify PI into PI 2.096 * [taylor]: Taking taylor expansion of n in n 2.096 * [backup-simplify]: Simplify 0 into 0 2.096 * [backup-simplify]: Simplify 1 into 1 2.096 * [backup-simplify]: Simplify (/ PI 1) into PI 2.097 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.098 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.098 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.098 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.098 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.100 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.101 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 2.102 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 2.102 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.102 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.102 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.102 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.102 * [taylor]: Taking taylor expansion of 0.5 in n 2.103 * [backup-simplify]: Simplify 0.5 into 0.5 2.103 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.103 * [taylor]: Taking taylor expansion of 1.0 in n 2.103 * [backup-simplify]: Simplify 1.0 into 1.0 2.103 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.103 * [taylor]: Taking taylor expansion of k in n 2.103 * [backup-simplify]: Simplify k into k 2.103 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.103 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.103 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.103 * [taylor]: Taking taylor expansion of 2.0 in n 2.103 * [backup-simplify]: Simplify 2.0 into 2.0 2.103 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.103 * [taylor]: Taking taylor expansion of PI in n 2.103 * [backup-simplify]: Simplify PI into PI 2.103 * [taylor]: Taking taylor expansion of n in n 2.103 * [backup-simplify]: Simplify 0 into 0 2.103 * [backup-simplify]: Simplify 1 into 1 2.104 * [backup-simplify]: Simplify (/ PI 1) into PI 2.104 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.105 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.105 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.105 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.105 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.107 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.108 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 2.109 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 2.110 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 2.110 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 2.110 * [taylor]: Taking taylor expansion of 0.5 in k 2.110 * [backup-simplify]: Simplify 0.5 into 0.5 2.110 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 2.110 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.110 * [taylor]: Taking taylor expansion of 1.0 in k 2.110 * [backup-simplify]: Simplify 1.0 into 1.0 2.110 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.110 * [taylor]: Taking taylor expansion of k in k 2.110 * [backup-simplify]: Simplify 0 into 0 2.110 * [backup-simplify]: Simplify 1 into 1 2.110 * [backup-simplify]: Simplify (/ 1 1) into 1 2.110 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.110 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.110 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.110 * [taylor]: Taking taylor expansion of 2.0 in k 2.110 * [backup-simplify]: Simplify 2.0 into 2.0 2.110 * [taylor]: Taking taylor expansion of PI in k 2.110 * [backup-simplify]: Simplify PI into PI 2.111 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.112 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.112 * [taylor]: Taking taylor expansion of (log n) in k 2.112 * [taylor]: Taking taylor expansion of n in k 2.112 * [backup-simplify]: Simplify n into n 2.112 * [backup-simplify]: Simplify (log n) into (log n) 2.113 * [backup-simplify]: Simplify (- 1) into -1 2.113 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.113 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.114 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.115 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.117 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 2.118 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 2.119 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 2.121 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.121 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.122 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.123 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.123 * [backup-simplify]: Simplify (- 0) into 0 2.123 * [backup-simplify]: Simplify (+ 0 0) into 0 2.123 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.124 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.125 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.127 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.127 * [taylor]: Taking taylor expansion of 0 in k 2.127 * [backup-simplify]: Simplify 0 into 0 2.127 * [backup-simplify]: Simplify 0 into 0 2.127 * [backup-simplify]: Simplify 0 into 0 2.127 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.128 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.130 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.130 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.130 * [backup-simplify]: Simplify (- 0) into 0 2.131 * [backup-simplify]: Simplify (+ 0 0) into 0 2.131 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.132 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.133 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.135 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.135 * [taylor]: Taking taylor expansion of 0 in k 2.135 * [backup-simplify]: Simplify 0 into 0 2.135 * [backup-simplify]: Simplify 0 into 0 2.135 * [backup-simplify]: Simplify 0 into 0 2.135 * [backup-simplify]: Simplify 0 into 0 2.135 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.136 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.139 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 2.139 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.140 * [backup-simplify]: Simplify (- 0) into 0 2.140 * [backup-simplify]: Simplify (+ 0 0) into 0 2.141 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.142 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.143 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.145 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.145 * [taylor]: Taking taylor expansion of 0 in k 2.145 * [backup-simplify]: Simplify 0 into 0 2.145 * [backup-simplify]: Simplify 0 into 0 2.146 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) 2.150 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 2.150 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 2.150 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.151 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.151 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.151 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.151 * [taylor]: Taking taylor expansion of 0.5 in k 2.151 * [backup-simplify]: Simplify 0.5 into 0.5 2.151 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.151 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.151 * [taylor]: Taking taylor expansion of k in k 2.151 * [backup-simplify]: Simplify 0 into 0 2.151 * [backup-simplify]: Simplify 1 into 1 2.151 * [backup-simplify]: Simplify (/ 1 1) into 1 2.151 * [taylor]: Taking taylor expansion of 1.0 in k 2.151 * [backup-simplify]: Simplify 1.0 into 1.0 2.151 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.151 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.151 * [taylor]: Taking taylor expansion of -2.0 in k 2.151 * [backup-simplify]: Simplify -2.0 into -2.0 2.151 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.151 * [taylor]: Taking taylor expansion of PI in k 2.151 * [backup-simplify]: Simplify PI into PI 2.151 * [taylor]: Taking taylor expansion of n in k 2.151 * [backup-simplify]: Simplify n into n 2.151 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.151 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.151 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.152 * [backup-simplify]: Simplify (+ 1 0) into 1 2.152 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.152 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.152 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 2.152 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.152 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.152 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.152 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.152 * [taylor]: Taking taylor expansion of 0.5 in n 2.152 * [backup-simplify]: Simplify 0.5 into 0.5 2.152 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.152 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.152 * [taylor]: Taking taylor expansion of k in n 2.153 * [backup-simplify]: Simplify k into k 2.153 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.153 * [taylor]: Taking taylor expansion of 1.0 in n 2.153 * [backup-simplify]: Simplify 1.0 into 1.0 2.153 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.153 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.153 * [taylor]: Taking taylor expansion of -2.0 in n 2.153 * [backup-simplify]: Simplify -2.0 into -2.0 2.153 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.153 * [taylor]: Taking taylor expansion of PI in n 2.153 * [backup-simplify]: Simplify PI into PI 2.153 * [taylor]: Taking taylor expansion of n in n 2.153 * [backup-simplify]: Simplify 0 into 0 2.153 * [backup-simplify]: Simplify 1 into 1 2.153 * [backup-simplify]: Simplify (/ PI 1) into PI 2.153 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.154 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.155 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.155 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.156 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.158 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 2.159 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 2.159 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.159 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.159 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.159 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.159 * [taylor]: Taking taylor expansion of 0.5 in n 2.159 * [backup-simplify]: Simplify 0.5 into 0.5 2.159 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.159 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.159 * [taylor]: Taking taylor expansion of k in n 2.159 * [backup-simplify]: Simplify k into k 2.159 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.159 * [taylor]: Taking taylor expansion of 1.0 in n 2.159 * [backup-simplify]: Simplify 1.0 into 1.0 2.159 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.159 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.159 * [taylor]: Taking taylor expansion of -2.0 in n 2.159 * [backup-simplify]: Simplify -2.0 into -2.0 2.159 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.160 * [taylor]: Taking taylor expansion of PI in n 2.160 * [backup-simplify]: Simplify PI into PI 2.160 * [taylor]: Taking taylor expansion of n in n 2.160 * [backup-simplify]: Simplify 0 into 0 2.160 * [backup-simplify]: Simplify 1 into 1 2.160 * [backup-simplify]: Simplify (/ PI 1) into PI 2.161 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.162 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.162 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.162 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.163 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.165 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 2.166 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 2.166 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 2.166 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 2.166 * [taylor]: Taking taylor expansion of 0.5 in k 2.166 * [backup-simplify]: Simplify 0.5 into 0.5 2.166 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 2.166 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.166 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.166 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.166 * [taylor]: Taking taylor expansion of -2.0 in k 2.166 * [backup-simplify]: Simplify -2.0 into -2.0 2.166 * [taylor]: Taking taylor expansion of PI in k 2.166 * [backup-simplify]: Simplify PI into PI 2.167 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.168 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.168 * [taylor]: Taking taylor expansion of (log n) in k 2.168 * [taylor]: Taking taylor expansion of n in k 2.168 * [backup-simplify]: Simplify n into n 2.168 * [backup-simplify]: Simplify (log n) into (log n) 2.168 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.168 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.168 * [taylor]: Taking taylor expansion of k in k 2.168 * [backup-simplify]: Simplify 0 into 0 2.168 * [backup-simplify]: Simplify 1 into 1 2.169 * [backup-simplify]: Simplify (/ 1 1) into 1 2.169 * [taylor]: Taking taylor expansion of 1.0 in k 2.169 * [backup-simplify]: Simplify 1.0 into 1.0 2.169 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.170 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.171 * [backup-simplify]: Simplify (+ 1 0) into 1 2.172 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 2.173 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 2.174 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 2.176 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 2.177 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.178 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.179 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.180 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.180 * [backup-simplify]: Simplify (+ 0 0) into 0 2.181 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.182 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.184 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.186 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.186 * [taylor]: Taking taylor expansion of 0 in k 2.186 * [backup-simplify]: Simplify 0 into 0 2.186 * [backup-simplify]: Simplify 0 into 0 2.186 * [backup-simplify]: Simplify 0 into 0 2.187 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.187 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.189 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 2.189 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.189 * [backup-simplify]: Simplify (+ 0 0) into 0 2.190 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.191 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.192 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.193 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.193 * [taylor]: Taking taylor expansion of 0 in k 2.194 * [backup-simplify]: Simplify 0 into 0 2.194 * [backup-simplify]: Simplify 0 into 0 2.194 * [backup-simplify]: Simplify 0 into 0 2.194 * [backup-simplify]: Simplify 0 into 0 2.194 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.195 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.198 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 2.198 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.199 * [backup-simplify]: Simplify (+ 0 0) into 0 2.200 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.200 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.202 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.203 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.203 * [taylor]: Taking taylor expansion of 0 in k 2.203 * [backup-simplify]: Simplify 0 into 0 2.203 * [backup-simplify]: Simplify 0 into 0 2.204 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2.204 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 2.204 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 2.204 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 2.204 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.204 * [taylor]: Taking taylor expansion of 1.0 in k 2.204 * [backup-simplify]: Simplify 1.0 into 1.0 2.204 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.205 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.205 * [taylor]: Taking taylor expansion of k in k 2.205 * [backup-simplify]: Simplify 0 into 0 2.205 * [backup-simplify]: Simplify 1 into 1 2.205 * [backup-simplify]: Simplify (/ 1 1) into 1 2.205 * [backup-simplify]: Simplify (sqrt 0) into 0 2.206 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.206 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.206 * [taylor]: Taking taylor expansion of 1.0 in k 2.206 * [backup-simplify]: Simplify 1.0 into 1.0 2.206 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.206 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.206 * [taylor]: Taking taylor expansion of k in k 2.206 * [backup-simplify]: Simplify 0 into 0 2.206 * [backup-simplify]: Simplify 1 into 1 2.207 * [backup-simplify]: Simplify (/ 1 1) into 1 2.207 * [backup-simplify]: Simplify (sqrt 0) into 0 2.208 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.208 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.208 * [backup-simplify]: Simplify 0 into 0 2.209 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.209 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.210 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.212 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.213 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.213 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.214 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.216 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.217 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.218 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.219 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 2.219 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 2.219 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 2.219 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.219 * [taylor]: Taking taylor expansion of 1.0 in k 2.219 * [backup-simplify]: Simplify 1.0 into 1.0 2.219 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.220 * [taylor]: Taking taylor expansion of k in k 2.220 * [backup-simplify]: Simplify 0 into 0 2.220 * [backup-simplify]: Simplify 1 into 1 2.220 * [backup-simplify]: Simplify (sqrt 0) into 0 2.221 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.221 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.221 * [taylor]: Taking taylor expansion of 1.0 in k 2.221 * [backup-simplify]: Simplify 1.0 into 1.0 2.221 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.221 * [taylor]: Taking taylor expansion of k in k 2.222 * [backup-simplify]: Simplify 0 into 0 2.222 * [backup-simplify]: Simplify 1 into 1 2.222 * [backup-simplify]: Simplify (sqrt 0) into 0 2.223 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.224 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.224 * [backup-simplify]: Simplify 0 into 0 2.225 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.226 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.229 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.230 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.231 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.233 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.235 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.235 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.236 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 2.236 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 2.236 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 2.236 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.236 * [taylor]: Taking taylor expansion of 1.0 in k 2.236 * [backup-simplify]: Simplify 1.0 into 1.0 2.236 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.236 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.236 * [taylor]: Taking taylor expansion of -1 in k 2.236 * [backup-simplify]: Simplify -1 into -1 2.236 * [taylor]: Taking taylor expansion of k in k 2.236 * [backup-simplify]: Simplify 0 into 0 2.236 * [backup-simplify]: Simplify 1 into 1 2.236 * [backup-simplify]: Simplify (/ -1 1) into -1 2.237 * [backup-simplify]: Simplify (sqrt 0) into 0 2.237 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.238 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.238 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.238 * [taylor]: Taking taylor expansion of 1.0 in k 2.238 * [backup-simplify]: Simplify 1.0 into 1.0 2.238 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.238 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.238 * [taylor]: Taking taylor expansion of -1 in k 2.238 * [backup-simplify]: Simplify -1 into -1 2.238 * [taylor]: Taking taylor expansion of k in k 2.238 * [backup-simplify]: Simplify 0 into 0 2.238 * [backup-simplify]: Simplify 1 into 1 2.238 * [backup-simplify]: Simplify (/ -1 1) into -1 2.238 * [backup-simplify]: Simplify (sqrt 0) into 0 2.239 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.240 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.240 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.240 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.242 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.244 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 2.244 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.244 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.247 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.250 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 2.250 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.251 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 2.251 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 2.251 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.251 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.251 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.251 * [taylor]: Taking taylor expansion of 2.0 in n 2.251 * [backup-simplify]: Simplify 2.0 into 2.0 2.251 * [taylor]: Taking taylor expansion of (* n PI) in n 2.251 * [taylor]: Taking taylor expansion of n in n 2.251 * [backup-simplify]: Simplify 0 into 0 2.251 * [backup-simplify]: Simplify 1 into 1 2.251 * [taylor]: Taking taylor expansion of PI in n 2.251 * [backup-simplify]: Simplify PI into PI 2.251 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.251 * [taylor]: Taking taylor expansion of 2.0 in n 2.251 * [backup-simplify]: Simplify 2.0 into 2.0 2.251 * [taylor]: Taking taylor expansion of (* n PI) in n 2.251 * [taylor]: Taking taylor expansion of n in n 2.251 * [backup-simplify]: Simplify 0 into 0 2.251 * [backup-simplify]: Simplify 1 into 1 2.252 * [taylor]: Taking taylor expansion of PI in n 2.252 * [backup-simplify]: Simplify PI into PI 2.252 * [backup-simplify]: Simplify (* 0 PI) into 0 2.252 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.252 * [backup-simplify]: Simplify 0 into 0 2.253 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.254 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.254 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.255 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.256 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.256 * [backup-simplify]: Simplify 0 into 0 2.256 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.261 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.261 * [backup-simplify]: Simplify 0 into 0 2.262 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.263 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.263 * [backup-simplify]: Simplify 0 into 0 2.264 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.265 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.265 * [backup-simplify]: Simplify 0 into 0 2.266 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.267 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.267 * [backup-simplify]: Simplify 0 into 0 2.268 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.269 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.270 * [backup-simplify]: Simplify 0 into 0 2.270 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.270 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 2.270 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.270 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.270 * [taylor]: Taking taylor expansion of 2.0 in n 2.270 * [backup-simplify]: Simplify 2.0 into 2.0 2.270 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.270 * [taylor]: Taking taylor expansion of PI in n 2.270 * [backup-simplify]: Simplify PI into PI 2.270 * [taylor]: Taking taylor expansion of n in n 2.270 * [backup-simplify]: Simplify 0 into 0 2.270 * [backup-simplify]: Simplify 1 into 1 2.271 * [backup-simplify]: Simplify (/ PI 1) into PI 2.271 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.271 * [taylor]: Taking taylor expansion of 2.0 in n 2.271 * [backup-simplify]: Simplify 2.0 into 2.0 2.271 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.271 * [taylor]: Taking taylor expansion of PI in n 2.271 * [backup-simplify]: Simplify PI into PI 2.271 * [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 * [backup-simplify]: Simplify (/ PI 1) into PI 2.272 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.272 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.273 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.273 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.273 * [backup-simplify]: Simplify 0 into 0 2.274 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.274 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.274 * [backup-simplify]: Simplify 0 into 0 2.275 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.276 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.276 * [backup-simplify]: Simplify 0 into 0 2.277 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.277 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.277 * [backup-simplify]: Simplify 0 into 0 2.278 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.279 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.279 * [backup-simplify]: Simplify 0 into 0 2.280 * [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 2.281 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.281 * [backup-simplify]: Simplify 0 into 0 2.281 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 2.282 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 2.282 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.282 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.282 * [taylor]: Taking taylor expansion of -2.0 in n 2.282 * [backup-simplify]: Simplify -2.0 into -2.0 2.282 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.282 * [taylor]: Taking taylor expansion of PI in n 2.282 * [backup-simplify]: Simplify PI into PI 2.282 * [taylor]: Taking taylor expansion of n in n 2.282 * [backup-simplify]: Simplify 0 into 0 2.282 * [backup-simplify]: Simplify 1 into 1 2.282 * [backup-simplify]: Simplify (/ PI 1) into PI 2.282 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.282 * [taylor]: Taking taylor expansion of -2.0 in n 2.282 * [backup-simplify]: Simplify -2.0 into -2.0 2.282 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.282 * [taylor]: Taking taylor expansion of PI in n 2.282 * [backup-simplify]: Simplify PI into PI 2.282 * [taylor]: Taking taylor expansion of n in n 2.282 * [backup-simplify]: Simplify 0 into 0 2.282 * [backup-simplify]: Simplify 1 into 1 2.283 * [backup-simplify]: Simplify (/ PI 1) into PI 2.283 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.283 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.284 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.284 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.284 * [backup-simplify]: Simplify 0 into 0 2.285 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.286 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.286 * [backup-simplify]: Simplify 0 into 0 2.287 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.288 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.288 * [backup-simplify]: Simplify 0 into 0 2.289 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.290 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.290 * [backup-simplify]: Simplify 0 into 0 2.292 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.293 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.293 * [backup-simplify]: Simplify 0 into 0 2.294 * [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 2.296 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.296 * [backup-simplify]: Simplify 0 into 0 2.297 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 2.297 * * * * [progress]: [ 4 / 4 ] generating series at (2) 2.297 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) 2.298 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (k n) around 0 2.298 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 2.298 * [taylor]: Taking taylor expansion of 1.0 in n 2.298 * [backup-simplify]: Simplify 1.0 into 1.0 2.298 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 2.298 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.298 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.298 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.298 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.298 * [taylor]: Taking taylor expansion of 0.5 in n 2.298 * [backup-simplify]: Simplify 0.5 into 0.5 2.298 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.298 * [taylor]: Taking taylor expansion of 1.0 in n 2.298 * [backup-simplify]: Simplify 1.0 into 1.0 2.298 * [taylor]: Taking taylor expansion of k in n 2.298 * [backup-simplify]: Simplify k into k 2.298 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.298 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.298 * [taylor]: Taking taylor expansion of 2.0 in n 2.298 * [backup-simplify]: Simplify 2.0 into 2.0 2.298 * [taylor]: Taking taylor expansion of (* n PI) in n 2.298 * [taylor]: Taking taylor expansion of n in n 2.298 * [backup-simplify]: Simplify 0 into 0 2.298 * [backup-simplify]: Simplify 1 into 1 2.298 * [taylor]: Taking taylor expansion of PI in n 2.298 * [backup-simplify]: Simplify PI into PI 2.298 * [backup-simplify]: Simplify (* 0 PI) into 0 2.299 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.300 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.301 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.301 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.301 * [backup-simplify]: Simplify (- k) into (- k) 2.301 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.301 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.302 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.303 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.304 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.304 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.304 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.304 * [taylor]: Taking taylor expansion of k in n 2.304 * [backup-simplify]: Simplify k into k 2.304 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.304 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.304 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.304 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.304 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 2.304 * [taylor]: Taking taylor expansion of 1.0 in k 2.304 * [backup-simplify]: Simplify 1.0 into 1.0 2.304 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 2.304 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.304 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.304 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.304 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.304 * [taylor]: Taking taylor expansion of 0.5 in k 2.304 * [backup-simplify]: Simplify 0.5 into 0.5 2.304 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.304 * [taylor]: Taking taylor expansion of 1.0 in k 2.304 * [backup-simplify]: Simplify 1.0 into 1.0 2.304 * [taylor]: Taking taylor expansion of k in k 2.304 * [backup-simplify]: Simplify 0 into 0 2.304 * [backup-simplify]: Simplify 1 into 1 2.304 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.305 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.305 * [taylor]: Taking taylor expansion of 2.0 in k 2.305 * [backup-simplify]: Simplify 2.0 into 2.0 2.305 * [taylor]: Taking taylor expansion of (* n PI) in k 2.305 * [taylor]: Taking taylor expansion of n in k 2.305 * [backup-simplify]: Simplify n into n 2.305 * [taylor]: Taking taylor expansion of PI in k 2.305 * [backup-simplify]: Simplify PI into PI 2.305 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.305 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.305 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.305 * [backup-simplify]: Simplify (- 0) into 0 2.305 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.306 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.306 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.306 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.306 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.306 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.306 * [taylor]: Taking taylor expansion of k in k 2.306 * [backup-simplify]: Simplify 0 into 0 2.306 * [backup-simplify]: Simplify 1 into 1 2.306 * [backup-simplify]: Simplify (/ 1 1) into 1 2.307 * [backup-simplify]: Simplify (sqrt 0) into 0 2.308 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.308 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 2.308 * [taylor]: Taking taylor expansion of 1.0 in k 2.308 * [backup-simplify]: Simplify 1.0 into 1.0 2.308 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 2.308 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.308 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.308 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.308 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.308 * [taylor]: Taking taylor expansion of 0.5 in k 2.308 * [backup-simplify]: Simplify 0.5 into 0.5 2.308 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.308 * [taylor]: Taking taylor expansion of 1.0 in k 2.308 * [backup-simplify]: Simplify 1.0 into 1.0 2.308 * [taylor]: Taking taylor expansion of k in k 2.308 * [backup-simplify]: Simplify 0 into 0 2.308 * [backup-simplify]: Simplify 1 into 1 2.308 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.308 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.308 * [taylor]: Taking taylor expansion of 2.0 in k 2.308 * [backup-simplify]: Simplify 2.0 into 2.0 2.308 * [taylor]: Taking taylor expansion of (* n PI) in k 2.308 * [taylor]: Taking taylor expansion of n in k 2.308 * [backup-simplify]: Simplify n into n 2.308 * [taylor]: Taking taylor expansion of PI in k 2.308 * [backup-simplify]: Simplify PI into PI 2.308 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.308 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.308 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.308 * [backup-simplify]: Simplify (- 0) into 0 2.309 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.309 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.309 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.309 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.309 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.309 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.309 * [taylor]: Taking taylor expansion of k in k 2.309 * [backup-simplify]: Simplify 0 into 0 2.309 * [backup-simplify]: Simplify 1 into 1 2.309 * [backup-simplify]: Simplify (/ 1 1) into 1 2.310 * [backup-simplify]: Simplify (sqrt 0) into 0 2.310 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.311 * [backup-simplify]: Simplify (* (pow (* 2.0 (* n PI)) 0.5) 0) into 0 2.311 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.311 * [taylor]: Taking taylor expansion of 0 in n 2.311 * [backup-simplify]: Simplify 0 into 0 2.311 * [backup-simplify]: Simplify 0 into 0 2.311 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 2.312 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 2.312 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 2.312 * [backup-simplify]: Simplify (- 1) into -1 2.313 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.314 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 2.314 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 2.315 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) 2.316 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) 0)) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 2.317 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.317 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 2.317 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 2.317 * [taylor]: Taking taylor expansion of +nan.0 in n 2.317 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.317 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.317 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.317 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.317 * [taylor]: Taking taylor expansion of 0.5 in n 2.317 * [backup-simplify]: Simplify 0.5 into 0.5 2.317 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.317 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.317 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.317 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.317 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.317 * [taylor]: Taking taylor expansion of 1.0 in n 2.317 * [backup-simplify]: Simplify 1.0 into 1.0 2.317 * [taylor]: Taking taylor expansion of (log PI) in n 2.317 * [taylor]: Taking taylor expansion of PI in n 2.317 * [backup-simplify]: Simplify PI into PI 2.317 * [backup-simplify]: Simplify (log PI) into (log PI) 2.318 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.319 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.319 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.319 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.319 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.319 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.319 * [taylor]: Taking taylor expansion of 1.0 in n 2.319 * [backup-simplify]: Simplify 1.0 into 1.0 2.319 * [taylor]: Taking taylor expansion of (log n) in n 2.319 * [taylor]: Taking taylor expansion of n in n 2.319 * [backup-simplify]: Simplify 0 into 0 2.319 * [backup-simplify]: Simplify 1 into 1 2.320 * [backup-simplify]: Simplify (log 1) into 0 2.320 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.320 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.320 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.320 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.320 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.320 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.320 * [taylor]: Taking taylor expansion of 1.0 in n 2.320 * [backup-simplify]: Simplify 1.0 into 1.0 2.320 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.320 * [taylor]: Taking taylor expansion of 2.0 in n 2.320 * [backup-simplify]: Simplify 2.0 into 2.0 2.320 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.321 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.322 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.322 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 2.323 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 2.324 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 2.325 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 2.326 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.326 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 2.327 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 2.328 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.328 * [backup-simplify]: Simplify 0 into 0 2.329 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.331 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.332 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 2.333 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 2.335 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0 2.335 * [backup-simplify]: Simplify (- 0) into 0 2.336 * [backup-simplify]: Simplify (+ 0 0) into 0 2.337 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 2.338 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 2.339 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) 2.343 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) +nan.0) (* (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))) 2.348 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) 2.348 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) in n 2.348 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) in n 2.348 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 2.348 * [taylor]: Taking taylor expansion of +nan.0 in n 2.348 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.348 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 2.348 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.348 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.348 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.348 * [taylor]: Taking taylor expansion of 0.5 in n 2.348 * [backup-simplify]: Simplify 0.5 into 0.5 2.348 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.348 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.348 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.348 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.348 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.349 * [taylor]: Taking taylor expansion of 1.0 in n 2.349 * [backup-simplify]: Simplify 1.0 into 1.0 2.349 * [taylor]: Taking taylor expansion of (log PI) in n 2.349 * [taylor]: Taking taylor expansion of PI in n 2.349 * [backup-simplify]: Simplify PI into PI 2.349 * [backup-simplify]: Simplify (log PI) into (log PI) 2.350 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.352 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.352 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.352 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.352 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.352 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.352 * [taylor]: Taking taylor expansion of 1.0 in n 2.352 * [backup-simplify]: Simplify 1.0 into 1.0 2.352 * [taylor]: Taking taylor expansion of (log n) in n 2.352 * [taylor]: Taking taylor expansion of n in n 2.352 * [backup-simplify]: Simplify 0 into 0 2.352 * [backup-simplify]: Simplify 1 into 1 2.353 * [backup-simplify]: Simplify (log 1) into 0 2.353 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.353 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.353 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.353 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.353 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.353 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.353 * [taylor]: Taking taylor expansion of 1.0 in n 2.353 * [backup-simplify]: Simplify 1.0 into 1.0 2.353 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.353 * [taylor]: Taking taylor expansion of 2.0 in n 2.353 * [backup-simplify]: Simplify 2.0 into 2.0 2.354 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.355 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.356 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.357 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 2.358 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 2.360 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 2.361 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 2.362 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.362 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.362 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.362 * [taylor]: Taking taylor expansion of 2.0 in n 2.362 * [backup-simplify]: Simplify 2.0 into 2.0 2.362 * [taylor]: Taking taylor expansion of (* n PI) in n 2.362 * [taylor]: Taking taylor expansion of n in n 2.362 * [backup-simplify]: Simplify 0 into 0 2.362 * [backup-simplify]: Simplify 1 into 1 2.362 * [taylor]: Taking taylor expansion of PI in n 2.362 * [backup-simplify]: Simplify PI into PI 2.362 * [backup-simplify]: Simplify (* 0 PI) into 0 2.363 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.364 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.365 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.366 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.366 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 2.366 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 2.366 * [taylor]: Taking taylor expansion of +nan.0 in n 2.366 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.366 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.366 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.366 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.366 * [taylor]: Taking taylor expansion of 0.5 in n 2.366 * [backup-simplify]: Simplify 0.5 into 0.5 2.366 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.366 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.366 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.366 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.366 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.366 * [taylor]: Taking taylor expansion of 1.0 in n 2.366 * [backup-simplify]: Simplify 1.0 into 1.0 2.366 * [taylor]: Taking taylor expansion of (log PI) in n 2.366 * [taylor]: Taking taylor expansion of PI in n 2.366 * [backup-simplify]: Simplify PI into PI 2.366 * [backup-simplify]: Simplify (log PI) into (log PI) 2.367 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.368 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.368 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.368 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.368 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.368 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.368 * [taylor]: Taking taylor expansion of 1.0 in n 2.368 * [backup-simplify]: Simplify 1.0 into 1.0 2.368 * [taylor]: Taking taylor expansion of (log n) in n 2.368 * [taylor]: Taking taylor expansion of n in n 2.368 * [backup-simplify]: Simplify 0 into 0 2.368 * [backup-simplify]: Simplify 1 into 1 2.368 * [backup-simplify]: Simplify (log 1) into 0 2.369 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.369 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.369 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.369 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.369 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.369 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.369 * [taylor]: Taking taylor expansion of 1.0 in n 2.369 * [backup-simplify]: Simplify 1.0 into 1.0 2.369 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.369 * [taylor]: Taking taylor expansion of 2.0 in n 2.369 * [backup-simplify]: Simplify 2.0 into 2.0 2.369 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.370 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.375 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.376 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 2.377 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 2.377 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 2.378 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 2.379 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.380 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.382 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n))) 2.383 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) 2.384 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 2.385 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 2.389 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) 2.395 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI))))))))) 2.402 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) 2.403 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 2.404 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 2.406 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 2.407 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.408 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.408 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 2.409 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.410 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 2.412 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 2.413 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 2.414 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 2.416 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 2.418 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0 2.420 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0 2.422 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.424 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0 2.424 * [backup-simplify]: Simplify (- 0) into 0 2.424 * [backup-simplify]: Simplify 0 into 0 2.424 * [backup-simplify]: Simplify 0 into 0 2.425 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.429 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.430 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.432 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 2.435 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0 2.435 * [backup-simplify]: Simplify (- 0) into 0 2.436 * [backup-simplify]: Simplify (+ 0 0) into 0 2.437 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 2.439 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 2.441 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 3))) 2.446 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) +nan.0) (+ (* (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) +nan.0) (* (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 2.454 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 2.454 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n 2.454 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n 2.454 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 2.454 * [taylor]: Taking taylor expansion of +nan.0 in n 2.454 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.454 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 2.454 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.454 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.454 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.454 * [taylor]: Taking taylor expansion of 0.5 in n 2.454 * [backup-simplify]: Simplify 0.5 into 0.5 2.454 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.454 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.454 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.454 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.454 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.455 * [taylor]: Taking taylor expansion of 1.0 in n 2.455 * [backup-simplify]: Simplify 1.0 into 1.0 2.455 * [taylor]: Taking taylor expansion of (log PI) in n 2.455 * [taylor]: Taking taylor expansion of PI in n 2.455 * [backup-simplify]: Simplify PI into PI 2.455 * [backup-simplify]: Simplify (log PI) into (log PI) 2.455 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.456 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.457 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.457 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.457 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.457 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.457 * [taylor]: Taking taylor expansion of 1.0 in n 2.457 * [backup-simplify]: Simplify 1.0 into 1.0 2.457 * [taylor]: Taking taylor expansion of (log n) in n 2.457 * [taylor]: Taking taylor expansion of n in n 2.457 * [backup-simplify]: Simplify 0 into 0 2.457 * [backup-simplify]: Simplify 1 into 1 2.457 * [backup-simplify]: Simplify (log 1) into 0 2.457 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.457 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.457 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.457 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.457 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.457 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.457 * [taylor]: Taking taylor expansion of 1.0 in n 2.457 * [backup-simplify]: Simplify 1.0 into 1.0 2.457 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.457 * [taylor]: Taking taylor expansion of 2.0 in n 2.457 * [backup-simplify]: Simplify 2.0 into 2.0 2.458 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.458 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.459 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.460 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 2.460 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 2.461 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 2.462 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 2.463 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.463 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.463 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.463 * [taylor]: Taking taylor expansion of 2.0 in n 2.463 * [backup-simplify]: Simplify 2.0 into 2.0 2.463 * [taylor]: Taking taylor expansion of (* n PI) in n 2.463 * [taylor]: Taking taylor expansion of n in n 2.463 * [backup-simplify]: Simplify 0 into 0 2.463 * [backup-simplify]: Simplify 1 into 1 2.463 * [taylor]: Taking taylor expansion of PI in n 2.463 * [backup-simplify]: Simplify PI into PI 2.463 * [backup-simplify]: Simplify (* 0 PI) into 0 2.464 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.465 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.466 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.466 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.466 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n 2.466 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n 2.466 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 2.466 * [taylor]: Taking taylor expansion of +nan.0 in n 2.466 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.466 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 2.466 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 2.466 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 2.466 * [taylor]: Taking taylor expansion of 0.5 in n 2.466 * [backup-simplify]: Simplify 0.5 into 0.5 2.467 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 2.467 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 2.467 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.467 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.467 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.467 * [taylor]: Taking taylor expansion of 1.0 in n 2.467 * [backup-simplify]: Simplify 1.0 into 1.0 2.467 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.467 * [taylor]: Taking taylor expansion of 2.0 in n 2.467 * [backup-simplify]: Simplify 2.0 into 2.0 2.467 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.467 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.468 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.468 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 2.468 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.468 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.468 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.468 * [taylor]: Taking taylor expansion of 1.0 in n 2.469 * [backup-simplify]: Simplify 1.0 into 1.0 2.469 * [taylor]: Taking taylor expansion of (log n) in n 2.469 * [taylor]: Taking taylor expansion of n in n 2.469 * [backup-simplify]: Simplify 0 into 0 2.469 * [backup-simplify]: Simplify 1 into 1 2.469 * [backup-simplify]: Simplify (log 1) into 0 2.469 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.469 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.469 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.469 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.469 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.469 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.469 * [taylor]: Taking taylor expansion of 1.0 in n 2.469 * [backup-simplify]: Simplify 1.0 into 1.0 2.469 * [taylor]: Taking taylor expansion of (log PI) in n 2.469 * [taylor]: Taking taylor expansion of PI in n 2.469 * [backup-simplify]: Simplify PI into PI 2.470 * [backup-simplify]: Simplify (log PI) into (log PI) 2.470 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.471 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.472 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.473 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 2.474 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 2.475 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 2.476 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.476 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n 2.476 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n 2.476 * [taylor]: Taking taylor expansion of +nan.0 in n 2.476 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.476 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 2.476 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.476 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.476 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.476 * [taylor]: Taking taylor expansion of 0.5 in n 2.476 * [backup-simplify]: Simplify 0.5 into 0.5 2.476 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.476 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.476 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.476 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.476 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.476 * [taylor]: Taking taylor expansion of 1.0 in n 2.476 * [backup-simplify]: Simplify 1.0 into 1.0 2.476 * [taylor]: Taking taylor expansion of (log PI) in n 2.476 * [taylor]: Taking taylor expansion of PI in n 2.476 * [backup-simplify]: Simplify PI into PI 2.477 * [backup-simplify]: Simplify (log PI) into (log PI) 2.477 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.479 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.479 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.479 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.479 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.479 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.479 * [taylor]: Taking taylor expansion of 1.0 in n 2.479 * [backup-simplify]: Simplify 1.0 into 1.0 2.479 * [taylor]: Taking taylor expansion of (log n) in n 2.479 * [taylor]: Taking taylor expansion of n in n 2.479 * [backup-simplify]: Simplify 0 into 0 2.479 * [backup-simplify]: Simplify 1 into 1 2.480 * [backup-simplify]: Simplify (log 1) into 0 2.480 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.480 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.480 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.480 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.480 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.480 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.480 * [taylor]: Taking taylor expansion of 1.0 in n 2.480 * [backup-simplify]: Simplify 1.0 into 1.0 2.480 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.480 * [taylor]: Taking taylor expansion of 2.0 in n 2.481 * [backup-simplify]: Simplify 2.0 into 2.0 2.481 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.482 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.484 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.484 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 2.486 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 2.487 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 2.488 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 2.490 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.490 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 2.490 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.490 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.490 * [taylor]: Taking taylor expansion of 2.0 in n 2.490 * [backup-simplify]: Simplify 2.0 into 2.0 2.490 * [taylor]: Taking taylor expansion of (* n PI) in n 2.490 * [taylor]: Taking taylor expansion of n in n 2.490 * [backup-simplify]: Simplify 0 into 0 2.490 * [backup-simplify]: Simplify 1 into 1 2.490 * [taylor]: Taking taylor expansion of PI in n 2.490 * [backup-simplify]: Simplify PI into PI 2.491 * [backup-simplify]: Simplify (* 0 PI) into 0 2.491 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.493 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.494 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.495 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.497 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.499 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.502 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n))) 2.510 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) 2.512 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 2.513 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.515 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.517 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 2.520 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) 2.523 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2))) 2.526 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2)))))))) 2.536 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) 2.543 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2)))))))))) 2.551 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) 2.561 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) 2.575 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n))))))))))))))) 2.600 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n))))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow k 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log n) 2) (pow k 2))))))))))))))))))))))) 2.600 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) 2.600 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (k n) around 0 2.601 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 2.601 * [taylor]: Taking taylor expansion of 1.0 in n 2.601 * [backup-simplify]: Simplify 1.0 into 1.0 2.601 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 2.601 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.601 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.601 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.601 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.601 * [taylor]: Taking taylor expansion of 0.5 in n 2.601 * [backup-simplify]: Simplify 0.5 into 0.5 2.601 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.601 * [taylor]: Taking taylor expansion of 1.0 in n 2.601 * [backup-simplify]: Simplify 1.0 into 1.0 2.601 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.601 * [taylor]: Taking taylor expansion of k in n 2.601 * [backup-simplify]: Simplify k into k 2.601 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.601 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.601 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.601 * [taylor]: Taking taylor expansion of 2.0 in n 2.601 * [backup-simplify]: Simplify 2.0 into 2.0 2.601 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.601 * [taylor]: Taking taylor expansion of PI in n 2.601 * [backup-simplify]: Simplify PI into PI 2.601 * [taylor]: Taking taylor expansion of n in n 2.601 * [backup-simplify]: Simplify 0 into 0 2.601 * [backup-simplify]: Simplify 1 into 1 2.601 * [backup-simplify]: Simplify (/ PI 1) into PI 2.602 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.602 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.602 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.602 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.603 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.603 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.604 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 2.605 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 2.605 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.605 * [taylor]: Taking taylor expansion of k in n 2.605 * [backup-simplify]: Simplify k into k 2.605 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.605 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.605 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 2.605 * [taylor]: Taking taylor expansion of 1.0 in k 2.605 * [backup-simplify]: Simplify 1.0 into 1.0 2.605 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 2.605 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.605 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.605 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.605 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.605 * [taylor]: Taking taylor expansion of 0.5 in k 2.605 * [backup-simplify]: Simplify 0.5 into 0.5 2.605 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.605 * [taylor]: Taking taylor expansion of 1.0 in k 2.605 * [backup-simplify]: Simplify 1.0 into 1.0 2.605 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.605 * [taylor]: Taking taylor expansion of k in k 2.605 * [backup-simplify]: Simplify 0 into 0 2.605 * [backup-simplify]: Simplify 1 into 1 2.606 * [backup-simplify]: Simplify (/ 1 1) into 1 2.606 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.606 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.606 * [taylor]: Taking taylor expansion of 2.0 in k 2.606 * [backup-simplify]: Simplify 2.0 into 2.0 2.606 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.606 * [taylor]: Taking taylor expansion of PI in k 2.606 * [backup-simplify]: Simplify PI into PI 2.606 * [taylor]: Taking taylor expansion of n in k 2.606 * [backup-simplify]: Simplify n into n 2.606 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.606 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.606 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.606 * [backup-simplify]: Simplify (- 1) into -1 2.606 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.607 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.607 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.607 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 2.607 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.607 * [taylor]: Taking taylor expansion of k in k 2.607 * [backup-simplify]: Simplify 0 into 0 2.607 * [backup-simplify]: Simplify 1 into 1 2.607 * [backup-simplify]: Simplify (sqrt 0) into 0 2.608 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.609 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 2.609 * [taylor]: Taking taylor expansion of 1.0 in k 2.609 * [backup-simplify]: Simplify 1.0 into 1.0 2.609 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 2.609 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.609 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.609 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.609 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.609 * [taylor]: Taking taylor expansion of 0.5 in k 2.609 * [backup-simplify]: Simplify 0.5 into 0.5 2.609 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.609 * [taylor]: Taking taylor expansion of 1.0 in k 2.609 * [backup-simplify]: Simplify 1.0 into 1.0 2.609 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.609 * [taylor]: Taking taylor expansion of k in k 2.609 * [backup-simplify]: Simplify 0 into 0 2.609 * [backup-simplify]: Simplify 1 into 1 2.609 * [backup-simplify]: Simplify (/ 1 1) into 1 2.609 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.609 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.609 * [taylor]: Taking taylor expansion of 2.0 in k 2.609 * [backup-simplify]: Simplify 2.0 into 2.0 2.609 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.609 * [taylor]: Taking taylor expansion of PI in k 2.609 * [backup-simplify]: Simplify PI into PI 2.609 * [taylor]: Taking taylor expansion of n in k 2.609 * [backup-simplify]: Simplify n into n 2.609 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.609 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.609 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.610 * [backup-simplify]: Simplify (- 1) into -1 2.610 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.610 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.610 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.610 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 2.610 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.610 * [taylor]: Taking taylor expansion of k in k 2.610 * [backup-simplify]: Simplify 0 into 0 2.610 * [backup-simplify]: Simplify 1 into 1 2.611 * [backup-simplify]: Simplify (sqrt 0) into 0 2.611 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.612 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 0) into 0 2.612 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.612 * [taylor]: Taking taylor expansion of 0 in n 2.612 * [backup-simplify]: Simplify 0 into 0 2.612 * [backup-simplify]: Simplify 0 into 0 2.612 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 2.613 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 2.613 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 2.613 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 2.613 * [taylor]: Taking taylor expansion of +nan.0 in n 2.613 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.613 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 2.613 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 2.613 * [taylor]: Taking taylor expansion of 0.5 in n 2.613 * [backup-simplify]: Simplify 0.5 into 0.5 2.613 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 2.613 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.613 * [taylor]: Taking taylor expansion of 1.0 in n 2.613 * [backup-simplify]: Simplify 1.0 into 1.0 2.613 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.613 * [taylor]: Taking taylor expansion of k in n 2.613 * [backup-simplify]: Simplify k into k 2.613 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.613 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.613 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.613 * [taylor]: Taking taylor expansion of 2.0 in n 2.613 * [backup-simplify]: Simplify 2.0 into 2.0 2.613 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.613 * [taylor]: Taking taylor expansion of PI in n 2.613 * [backup-simplify]: Simplify PI into PI 2.613 * [taylor]: Taking taylor expansion of n in n 2.613 * [backup-simplify]: Simplify 0 into 0 2.613 * [backup-simplify]: Simplify 1 into 1 2.614 * [backup-simplify]: Simplify (/ PI 1) into PI 2.614 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.615 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.615 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.615 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.616 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.616 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 2.617 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 2.618 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 2.619 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 2.620 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 2.620 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 2.620 * [backup-simplify]: Simplify 0 into 0 2.622 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.627 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 2.628 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 2.628 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 2.628 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 2.628 * [taylor]: Taking taylor expansion of +nan.0 in n 2.628 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.628 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 2.628 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 2.628 * [taylor]: Taking taylor expansion of 0.5 in n 2.628 * [backup-simplify]: Simplify 0.5 into 0.5 2.628 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 2.628 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.628 * [taylor]: Taking taylor expansion of 1.0 in n 2.628 * [backup-simplify]: Simplify 1.0 into 1.0 2.628 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.628 * [taylor]: Taking taylor expansion of k in n 2.628 * [backup-simplify]: Simplify k into k 2.628 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.628 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.628 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.628 * [taylor]: Taking taylor expansion of 2.0 in n 2.629 * [backup-simplify]: Simplify 2.0 into 2.0 2.629 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.629 * [taylor]: Taking taylor expansion of PI in n 2.629 * [backup-simplify]: Simplify PI into PI 2.629 * [taylor]: Taking taylor expansion of n in n 2.629 * [backup-simplify]: Simplify 0 into 0 2.629 * [backup-simplify]: Simplify 1 into 1 2.629 * [backup-simplify]: Simplify (/ PI 1) into PI 2.630 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.631 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.631 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.631 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.633 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.634 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 2.635 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 2.636 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 2.637 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 2.639 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 2.640 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 2.641 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.642 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.644 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.644 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.644 * [backup-simplify]: Simplify (- 0) into 0 2.645 * [backup-simplify]: Simplify (+ 0 0) into 0 2.646 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.648 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.649 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into 0 2.651 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.653 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0 2.654 * [backup-simplify]: Simplify (- 0) into 0 2.654 * [backup-simplify]: Simplify 0 into 0 2.654 * [backup-simplify]: Simplify 0 into 0 2.658 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.659 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 2.660 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 2.660 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 2.660 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 2.660 * [taylor]: Taking taylor expansion of +nan.0 in n 2.660 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.660 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 2.660 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 2.660 * [taylor]: Taking taylor expansion of 0.5 in n 2.661 * [backup-simplify]: Simplify 0.5 into 0.5 2.661 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 2.661 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.661 * [taylor]: Taking taylor expansion of 1.0 in n 2.661 * [backup-simplify]: Simplify 1.0 into 1.0 2.661 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.661 * [taylor]: Taking taylor expansion of k in n 2.661 * [backup-simplify]: Simplify k into k 2.661 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.661 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.661 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.661 * [taylor]: Taking taylor expansion of 2.0 in n 2.661 * [backup-simplify]: Simplify 2.0 into 2.0 2.661 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.661 * [taylor]: Taking taylor expansion of PI in n 2.661 * [backup-simplify]: Simplify PI into PI 2.661 * [taylor]: Taking taylor expansion of n in n 2.661 * [backup-simplify]: Simplify 0 into 0 2.661 * [backup-simplify]: Simplify 1 into 1 2.662 * [backup-simplify]: Simplify (/ PI 1) into PI 2.662 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.663 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.663 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.663 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.665 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.666 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 2.667 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 2.668 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 2.670 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 2.671 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 2.672 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 2.677 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 2.678 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 2.679 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0 2.679 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 2.679 * [taylor]: Taking taylor expansion of 1.0 in n 2.679 * [backup-simplify]: Simplify 1.0 into 1.0 2.679 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 2.679 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.679 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.679 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.679 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.679 * [taylor]: Taking taylor expansion of 0.5 in n 2.679 * [backup-simplify]: Simplify 0.5 into 0.5 2.679 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.679 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.679 * [taylor]: Taking taylor expansion of k in n 2.679 * [backup-simplify]: Simplify k into k 2.679 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.679 * [taylor]: Taking taylor expansion of 1.0 in n 2.679 * [backup-simplify]: Simplify 1.0 into 1.0 2.679 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.679 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.679 * [taylor]: Taking taylor expansion of -2.0 in n 2.679 * [backup-simplify]: Simplify -2.0 into -2.0 2.679 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.679 * [taylor]: Taking taylor expansion of PI in n 2.679 * [backup-simplify]: Simplify PI into PI 2.679 * [taylor]: Taking taylor expansion of n in n 2.679 * [backup-simplify]: Simplify 0 into 0 2.679 * [backup-simplify]: Simplify 1 into 1 2.680 * [backup-simplify]: Simplify (/ PI 1) into PI 2.680 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.681 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.682 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.682 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.683 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.684 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 2.686 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 2.686 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.686 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.686 * [taylor]: Taking taylor expansion of -1 in n 2.686 * [backup-simplify]: Simplify -1 into -1 2.686 * [taylor]: Taking taylor expansion of k in n 2.686 * [backup-simplify]: Simplify k into k 2.686 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.686 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.686 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.686 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.688 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) 2.688 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.688 * [taylor]: Taking taylor expansion of 1.0 in k 2.688 * [backup-simplify]: Simplify 1.0 into 1.0 2.688 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.688 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.688 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.688 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.688 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.688 * [taylor]: Taking taylor expansion of 0.5 in k 2.688 * [backup-simplify]: Simplify 0.5 into 0.5 2.688 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.688 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.688 * [taylor]: Taking taylor expansion of k in k 2.688 * [backup-simplify]: Simplify 0 into 0 2.688 * [backup-simplify]: Simplify 1 into 1 2.688 * [backup-simplify]: Simplify (/ 1 1) into 1 2.688 * [taylor]: Taking taylor expansion of 1.0 in k 2.688 * [backup-simplify]: Simplify 1.0 into 1.0 2.689 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.689 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.689 * [taylor]: Taking taylor expansion of -2.0 in k 2.689 * [backup-simplify]: Simplify -2.0 into -2.0 2.689 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.689 * [taylor]: Taking taylor expansion of PI in k 2.689 * [backup-simplify]: Simplify PI into PI 2.689 * [taylor]: Taking taylor expansion of n in k 2.689 * [backup-simplify]: Simplify n into n 2.689 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.689 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.689 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.689 * [backup-simplify]: Simplify (+ 1 0) into 1 2.690 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.690 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.690 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 2.690 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.690 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.690 * [taylor]: Taking taylor expansion of -1 in k 2.690 * [backup-simplify]: Simplify -1 into -1 2.690 * [taylor]: Taking taylor expansion of k in k 2.691 * [backup-simplify]: Simplify 0 into 0 2.691 * [backup-simplify]: Simplify 1 into 1 2.691 * [backup-simplify]: Simplify (/ -1 1) into -1 2.691 * [backup-simplify]: Simplify (sqrt 0) into 0 2.693 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.693 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 2.693 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.693 * [taylor]: Taking taylor expansion of 1.0 in k 2.693 * [backup-simplify]: Simplify 1.0 into 1.0 2.693 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.693 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.693 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.693 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.693 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.693 * [taylor]: Taking taylor expansion of 0.5 in k 2.693 * [backup-simplify]: Simplify 0.5 into 0.5 2.693 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.693 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.693 * [taylor]: Taking taylor expansion of k in k 2.693 * [backup-simplify]: Simplify 0 into 0 2.693 * [backup-simplify]: Simplify 1 into 1 2.694 * [backup-simplify]: Simplify (/ 1 1) into 1 2.694 * [taylor]: Taking taylor expansion of 1.0 in k 2.694 * [backup-simplify]: Simplify 1.0 into 1.0 2.694 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.694 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.694 * [taylor]: Taking taylor expansion of -2.0 in k 2.694 * [backup-simplify]: Simplify -2.0 into -2.0 2.694 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.694 * [taylor]: Taking taylor expansion of PI in k 2.694 * [backup-simplify]: Simplify PI into PI 2.694 * [taylor]: Taking taylor expansion of n in k 2.694 * [backup-simplify]: Simplify n into n 2.694 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.694 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.694 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.695 * [backup-simplify]: Simplify (+ 1 0) into 1 2.695 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.696 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.696 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 2.696 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.696 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.696 * [taylor]: Taking taylor expansion of -1 in k 2.696 * [backup-simplify]: Simplify -1 into -1 2.696 * [taylor]: Taking taylor expansion of k in k 2.696 * [backup-simplify]: Simplify 0 into 0 2.696 * [backup-simplify]: Simplify 1 into 1 2.696 * [backup-simplify]: Simplify (/ -1 1) into -1 2.697 * [backup-simplify]: Simplify (sqrt 0) into 0 2.698 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.698 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 2.699 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 2.699 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 2.699 * [taylor]: Taking taylor expansion of +nan.0 in n 2.699 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.699 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 2.699 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 2.699 * [taylor]: Taking taylor expansion of 0.5 in n 2.699 * [backup-simplify]: Simplify 0.5 into 0.5 2.699 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 2.699 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.699 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.699 * [taylor]: Taking taylor expansion of -2.0 in n 2.699 * [backup-simplify]: Simplify -2.0 into -2.0 2.699 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.699 * [taylor]: Taking taylor expansion of PI in n 2.699 * [backup-simplify]: Simplify PI into PI 2.699 * [taylor]: Taking taylor expansion of n in n 2.699 * [backup-simplify]: Simplify 0 into 0 2.699 * [backup-simplify]: Simplify 1 into 1 2.700 * [backup-simplify]: Simplify (/ PI 1) into PI 2.700 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.701 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.701 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.701 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.701 * [taylor]: Taking taylor expansion of k in n 2.701 * [backup-simplify]: Simplify k into k 2.701 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.701 * [taylor]: Taking taylor expansion of 1.0 in n 2.701 * [backup-simplify]: Simplify 1.0 into 1.0 2.703 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.703 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.704 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 2.705 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 2.707 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 2.708 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 2.709 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 2.710 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.714 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.715 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 2.715 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 2.716 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 2.716 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 2.716 * [taylor]: Taking taylor expansion of +nan.0 in n 2.716 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.716 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 2.716 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 2.716 * [taylor]: Taking taylor expansion of 0.5 in n 2.716 * [backup-simplify]: Simplify 0.5 into 0.5 2.716 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 2.716 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.716 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.716 * [taylor]: Taking taylor expansion of -2.0 in n 2.716 * [backup-simplify]: Simplify -2.0 into -2.0 2.716 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.716 * [taylor]: Taking taylor expansion of PI in n 2.716 * [backup-simplify]: Simplify PI into PI 2.716 * [taylor]: Taking taylor expansion of n in n 2.716 * [backup-simplify]: Simplify 0 into 0 2.716 * [backup-simplify]: Simplify 1 into 1 2.717 * [backup-simplify]: Simplify (/ PI 1) into PI 2.717 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.718 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.718 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.718 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.718 * [taylor]: Taking taylor expansion of k in n 2.718 * [backup-simplify]: Simplify k into k 2.718 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.718 * [taylor]: Taking taylor expansion of 1.0 in n 2.718 * [backup-simplify]: Simplify 1.0 into 1.0 2.720 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.720 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.721 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 2.722 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 2.724 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 2.725 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 2.726 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 2.728 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 2.729 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.729 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.730 * [backup-simplify]: Simplify (+ 0 0) into 0 2.731 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.731 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.733 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.734 * [backup-simplify]: Simplify (+ (* (- (log (* -2.0 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.735 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into 0 2.736 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.737 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0 2.737 * [backup-simplify]: Simplify 0 into 0 2.738 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.741 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.742 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 2.742 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 2.742 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 2.742 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 2.742 * [taylor]: Taking taylor expansion of +nan.0 in n 2.742 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.742 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 2.742 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 2.742 * [taylor]: Taking taylor expansion of 0.5 in n 2.742 * [backup-simplify]: Simplify 0.5 into 0.5 2.743 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 2.743 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.743 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.743 * [taylor]: Taking taylor expansion of -2.0 in n 2.743 * [backup-simplify]: Simplify -2.0 into -2.0 2.743 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.743 * [taylor]: Taking taylor expansion of PI in n 2.743 * [backup-simplify]: Simplify PI into PI 2.743 * [taylor]: Taking taylor expansion of n in n 2.743 * [backup-simplify]: Simplify 0 into 0 2.743 * [backup-simplify]: Simplify 1 into 1 2.743 * [backup-simplify]: Simplify (/ PI 1) into PI 2.743 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.744 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.744 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.744 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.744 * [taylor]: Taking taylor expansion of k in n 2.744 * [backup-simplify]: Simplify k into k 2.744 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.744 * [taylor]: Taking taylor expansion of 1.0 in n 2.744 * [backup-simplify]: Simplify 1.0 into 1.0 2.745 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.745 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.746 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 2.747 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 2.747 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 2.748 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 2.749 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 2.750 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 2.753 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)))))))) 2.753 * * * [progress]: simplifying candidates 2.755 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 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(- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3)))))))) (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)))))))) 2.758 * * [simplify]: iteration 0: 353 enodes 2.838 * * [simplify]: iteration 1: 986 enodes 3.469 * * [simplify]: iteration 2: 4715 enodes 4.628 * * [simplify]: iteration complete: 5000 enodes 4.628 * * [simplify]: Extracting #0: cost 120 inf + 0 4.631 * * [simplify]: Extracting #1: cost 754 inf + 2 4.639 * * [simplify]: Extracting #2: cost 1261 inf + 6610 4.651 * * [simplify]: Extracting #3: cost 1154 inf + 54970 4.680 * * [simplify]: Extracting #4: cost 697 inf + 207170 4.758 * * [simplify]: Extracting #5: cost 353 inf + 383174 4.885 * * [simplify]: Extracting #6: cost 363 inf + 426599 4.977 * * [simplify]: Extracting #7: cost 320 inf + 465999 5.124 * * [simplify]: Extracting #8: cost 88 inf + 686627 5.257 * * [simplify]: Extracting #9: cost 5 inf + 783573 5.443 * * [simplify]: Extracting #10: cost 0 inf + 785898 5.596 * * [simplify]: Extracting #11: cost 0 inf + 785578 5.770 * [simplify]: Simplified to: (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* (* 2.0 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(sqrt k)))) (+ (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (log (/ 1.0 (sqrt k)))) (+ (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (log (/ 1.0 (sqrt k)))) (+ (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))) (log (/ 1.0 (sqrt k)))) (exp (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (* (/ (/ (* 1.0 (* 1.0 1.0)) (sqrt k)) k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (* (cbrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (cbrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (cbrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ 1.0 (sqrt k)))) (/ 1.0 (/ (sqrt k) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ 1.0 (sqrt k)) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (/ 1.0 (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (/ 1.0 (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (cbrt (sqrt k)))) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (cbrt k))) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (sqrt k))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (sqrt k))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (cbrt (sqrt k)))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (* (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (/ 1.0 (sqrt k))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (+ (+ (* (* (* k k) (* (log n) (exp (* (log (* (* 2.0 PI) n)) 0.5)))) (* 0.25 (log (* 2.0 PI)))) (* (* 0.125 (exp (* (log (* (* 2.0 PI) n)) 0.5))) (* (* (log n) k) (* (log n) k)))) (- (+ (exp (* (log (* (* 2.0 PI) n)) 0.5)) (* (* 0.125 (* (log (* 2.0 PI)) (* (log (* 2.0 PI)) (exp (* (log (* (* 2.0 PI) n)) 0.5))))) (* k k))) (* (* k (+ (* (exp (* (log (* (* 2.0 PI) n)) 0.5)) (log n)) (* (log (* 2.0 PI)) (exp (* (log (* (* 2.0 PI) n)) 0.5))))) 0.5))) (exp (* (log (* (* 2.0 PI) n)) (* (- 1.0 k) 0.5))) (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5))) (- (- (* (* +nan.0 k) k) (- +nan.0 (* +nan.0 k)))) (+ (- (/ +nan.0 k) (/ +nan.0 (* (* k k) k))) (/ (- +nan.0) (* k k))) (- (- (/ +nan.0 (* k k)) (- (/ +nan.0 k) +nan.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (* (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (- k)) (- (* (* k k) (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5))) (+ (- (* (* (log n) (* k k)) (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) +nan.0)) (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5))) (+ (- (* (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) (* (* (log (* 2.0 PI)) k) (* (log (* 2.0 PI)) k))) +nan.0) (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) (* (* (log n) (* (* k k) (log (* 2.0 PI)))) +nan.0))) (- (* (* +nan.0 (* (log (* 2.0 PI)) k)) (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (+ (- (* (* (* k (log n)) (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) +nan.0) (* (* +nan.0 (* (* k k) (log (* 2.0 PI)))) (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5))) (* (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (* (* (log n) k) (* (log n) k))))))))) (+ (/ (- (* +nan.0 (exp (* (log (* (* 2.0 PI) n)) (* (- 1.0 k) 0.5))))) (* k k)) (* +nan.0 (- (/ (exp (* (log (* (* 2.0 PI) n)) (* (- 1.0 k) 0.5))) k) (/ (exp (* (log (* (* 2.0 PI) n)) (* (- 1.0 k) 0.5))) (* (* k k) k))))) (+ (* (- +nan.0) (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5)))) (* +nan.0 (- (/ (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5))) k) (/ (/ (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5))) k) k)))) 5.793 * * * [progress]: adding candidates to table 6.642 * * [progress]: iteration 2 / 4 6.642 * * * [progress]: picking best candidate 6.690 * * * * [pick]: Picked # 6.690 * * * [progress]: localizing error 6.731 * * * [progress]: generating rewritten candidates 6.731 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 6.747 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 1) 6.751 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 6.759 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2 1) 6.799 * * * [progress]: generating series expansions 6.800 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 6.801 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 6.801 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 6.801 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 6.801 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.801 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.801 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 6.801 * [taylor]: Taking taylor expansion of 0.5 in k 6.801 * [backup-simplify]: Simplify 0.5 into 0.5 6.802 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.802 * [taylor]: Taking taylor expansion of 1.0 in k 6.802 * [backup-simplify]: Simplify 1.0 into 1.0 6.802 * [taylor]: Taking taylor expansion of k in k 6.802 * [backup-simplify]: Simplify 0 into 0 6.802 * [backup-simplify]: Simplify 1 into 1 6.802 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.802 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.802 * [taylor]: Taking taylor expansion of 2.0 in k 6.802 * [backup-simplify]: Simplify 2.0 into 2.0 6.802 * [taylor]: Taking taylor expansion of (* n PI) in k 6.802 * [taylor]: Taking taylor expansion of n in k 6.802 * [backup-simplify]: Simplify n into n 6.802 * [taylor]: Taking taylor expansion of PI in k 6.802 * [backup-simplify]: Simplify PI into PI 6.802 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.802 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.802 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.802 * [backup-simplify]: Simplify (- 0) into 0 6.803 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.803 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 6.803 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 6.803 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 6.803 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 6.803 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.803 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.803 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 6.803 * [taylor]: Taking taylor expansion of 0.5 in n 6.803 * [backup-simplify]: Simplify 0.5 into 0.5 6.803 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.803 * [taylor]: Taking taylor expansion of 1.0 in n 6.803 * [backup-simplify]: Simplify 1.0 into 1.0 6.803 * [taylor]: Taking taylor expansion of k in n 6.803 * [backup-simplify]: Simplify k into k 6.803 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.803 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.803 * [taylor]: Taking taylor expansion of 2.0 in n 6.803 * [backup-simplify]: Simplify 2.0 into 2.0 6.803 * [taylor]: Taking taylor expansion of (* n PI) in n 6.803 * [taylor]: Taking taylor expansion of n in n 6.803 * [backup-simplify]: Simplify 0 into 0 6.803 * [backup-simplify]: Simplify 1 into 1 6.803 * [taylor]: Taking taylor expansion of PI in n 6.803 * [backup-simplify]: Simplify PI into PI 6.804 * [backup-simplify]: Simplify (* 0 PI) into 0 6.804 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.805 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.806 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.807 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.807 * [backup-simplify]: Simplify (- k) into (- k) 6.807 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.807 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 6.808 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.809 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 6.809 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 6.809 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 6.809 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.809 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.809 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 6.809 * [taylor]: Taking taylor expansion of 0.5 in n 6.809 * [backup-simplify]: Simplify 0.5 into 0.5 6.809 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.809 * [taylor]: Taking taylor expansion of 1.0 in n 6.809 * [backup-simplify]: Simplify 1.0 into 1.0 6.810 * [taylor]: Taking taylor expansion of k in n 6.810 * [backup-simplify]: Simplify k into k 6.810 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.810 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.810 * [taylor]: Taking taylor expansion of 2.0 in n 6.810 * [backup-simplify]: Simplify 2.0 into 2.0 6.810 * [taylor]: Taking taylor expansion of (* n PI) in n 6.810 * [taylor]: Taking taylor expansion of n in n 6.810 * [backup-simplify]: Simplify 0 into 0 6.810 * [backup-simplify]: Simplify 1 into 1 6.810 * [taylor]: Taking taylor expansion of PI in n 6.810 * [backup-simplify]: Simplify PI into PI 6.810 * [backup-simplify]: Simplify (* 0 PI) into 0 6.810 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.811 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.812 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.813 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.813 * [backup-simplify]: Simplify (- k) into (- k) 6.813 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.813 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 6.814 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.815 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 6.815 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 6.815 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 6.815 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 6.815 * [taylor]: Taking taylor expansion of 0.5 in k 6.815 * [backup-simplify]: Simplify 0.5 into 0.5 6.815 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 6.816 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.816 * [taylor]: Taking taylor expansion of 1.0 in k 6.816 * [backup-simplify]: Simplify 1.0 into 1.0 6.816 * [taylor]: Taking taylor expansion of k in k 6.816 * [backup-simplify]: Simplify 0 into 0 6.816 * [backup-simplify]: Simplify 1 into 1 6.816 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 6.816 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.816 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.816 * [taylor]: Taking taylor expansion of 2.0 in k 6.816 * [backup-simplify]: Simplify 2.0 into 2.0 6.816 * [taylor]: Taking taylor expansion of PI in k 6.816 * [backup-simplify]: Simplify PI into PI 6.816 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.817 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.817 * [taylor]: Taking taylor expansion of (log n) in k 6.817 * [taylor]: Taking taylor expansion of n in k 6.817 * [backup-simplify]: Simplify n into n 6.817 * [backup-simplify]: Simplify (log n) into (log n) 6.817 * [backup-simplify]: Simplify (- 0) into 0 6.817 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.818 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.819 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.819 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 6.820 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 6.821 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 6.822 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.822 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.823 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.824 * [backup-simplify]: Simplify (- 0) into 0 6.824 * [backup-simplify]: Simplify (+ 0 0) into 0 6.824 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 6.825 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.826 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.827 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.827 * [taylor]: Taking taylor expansion of 0 in k 6.827 * [backup-simplify]: Simplify 0 into 0 6.827 * [backup-simplify]: Simplify 0 into 0 6.828 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.829 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.829 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.829 * [backup-simplify]: Simplify (+ 0 0) into 0 6.830 * [backup-simplify]: Simplify (- 1) into -1 6.830 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.831 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.832 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 6.834 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 6.836 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 6.837 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.838 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.842 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 6.842 * [backup-simplify]: Simplify (- 0) into 0 6.843 * [backup-simplify]: Simplify (+ 0 0) into 0 6.843 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.845 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.846 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.848 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.848 * [taylor]: Taking taylor expansion of 0 in k 6.848 * [backup-simplify]: Simplify 0 into 0 6.848 * [backup-simplify]: Simplify 0 into 0 6.848 * [backup-simplify]: Simplify 0 into 0 6.849 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.850 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 6.852 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.852 * [backup-simplify]: Simplify (+ 0 0) into 0 6.852 * [backup-simplify]: Simplify (- 0) into 0 6.852 * [backup-simplify]: Simplify (+ 0 0) into 0 6.854 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.855 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.858 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 6.861 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 6.867 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) 6.868 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 6.868 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 6.868 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 6.868 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.868 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.868 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 6.868 * [taylor]: Taking taylor expansion of 0.5 in k 6.868 * [backup-simplify]: Simplify 0.5 into 0.5 6.868 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.868 * [taylor]: Taking taylor expansion of 1.0 in k 6.868 * [backup-simplify]: Simplify 1.0 into 1.0 6.868 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.868 * [taylor]: Taking taylor expansion of k in k 6.868 * [backup-simplify]: Simplify 0 into 0 6.868 * [backup-simplify]: Simplify 1 into 1 6.868 * [backup-simplify]: Simplify (/ 1 1) into 1 6.868 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.868 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.868 * [taylor]: Taking taylor expansion of 2.0 in k 6.868 * [backup-simplify]: Simplify 2.0 into 2.0 6.868 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.868 * [taylor]: Taking taylor expansion of PI in k 6.868 * [backup-simplify]: Simplify PI into PI 6.868 * [taylor]: Taking taylor expansion of n in k 6.868 * [backup-simplify]: Simplify n into n 6.869 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.869 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.869 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.869 * [backup-simplify]: Simplify (- 1) into -1 6.869 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.869 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 6.870 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 6.870 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 6.870 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.870 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.870 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.870 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.870 * [taylor]: Taking taylor expansion of 0.5 in n 6.870 * [backup-simplify]: Simplify 0.5 into 0.5 6.870 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.870 * [taylor]: Taking taylor expansion of 1.0 in n 6.870 * [backup-simplify]: Simplify 1.0 into 1.0 6.870 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.870 * [taylor]: Taking taylor expansion of k in n 6.870 * [backup-simplify]: Simplify k into k 6.870 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.870 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.870 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.870 * [taylor]: Taking taylor expansion of 2.0 in n 6.870 * [backup-simplify]: Simplify 2.0 into 2.0 6.870 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.870 * [taylor]: Taking taylor expansion of PI in n 6.870 * [backup-simplify]: Simplify PI into PI 6.870 * [taylor]: Taking taylor expansion of n in n 6.870 * [backup-simplify]: Simplify 0 into 0 6.870 * [backup-simplify]: Simplify 1 into 1 6.871 * [backup-simplify]: Simplify (/ PI 1) into PI 6.871 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.873 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.873 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.873 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.873 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.874 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.875 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 6.877 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 6.877 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.877 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.877 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.877 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.877 * [taylor]: Taking taylor expansion of 0.5 in n 6.877 * [backup-simplify]: Simplify 0.5 into 0.5 6.877 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.877 * [taylor]: Taking taylor expansion of 1.0 in n 6.877 * [backup-simplify]: Simplify 1.0 into 1.0 6.877 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.877 * [taylor]: Taking taylor expansion of k in n 6.877 * [backup-simplify]: Simplify k into k 6.877 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.877 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.877 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.877 * [taylor]: Taking taylor expansion of 2.0 in n 6.877 * [backup-simplify]: Simplify 2.0 into 2.0 6.877 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.877 * [taylor]: Taking taylor expansion of PI in n 6.878 * [backup-simplify]: Simplify PI into PI 6.878 * [taylor]: Taking taylor expansion of n in n 6.878 * [backup-simplify]: Simplify 0 into 0 6.878 * [backup-simplify]: Simplify 1 into 1 6.878 * [backup-simplify]: Simplify (/ PI 1) into PI 6.879 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.880 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.880 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.880 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.880 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.882 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.883 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 6.884 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 6.884 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 6.884 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 6.884 * [taylor]: Taking taylor expansion of 0.5 in k 6.884 * [backup-simplify]: Simplify 0.5 into 0.5 6.884 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 6.884 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.884 * [taylor]: Taking taylor expansion of 1.0 in k 6.884 * [backup-simplify]: Simplify 1.0 into 1.0 6.884 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.884 * [taylor]: Taking taylor expansion of k in k 6.884 * [backup-simplify]: Simplify 0 into 0 6.884 * [backup-simplify]: Simplify 1 into 1 6.885 * [backup-simplify]: Simplify (/ 1 1) into 1 6.885 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.885 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.885 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.885 * [taylor]: Taking taylor expansion of 2.0 in k 6.885 * [backup-simplify]: Simplify 2.0 into 2.0 6.885 * [taylor]: Taking taylor expansion of PI in k 6.885 * [backup-simplify]: Simplify PI into PI 6.885 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.886 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.887 * [taylor]: Taking taylor expansion of (log n) in k 6.887 * [taylor]: Taking taylor expansion of n in k 6.887 * [backup-simplify]: Simplify n into n 6.887 * [backup-simplify]: Simplify (log n) into (log n) 6.894 * [backup-simplify]: Simplify (- 1) into -1 6.895 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.895 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.897 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.898 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.899 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 6.900 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 6.902 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 6.903 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.904 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.905 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.906 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.906 * [backup-simplify]: Simplify (- 0) into 0 6.906 * [backup-simplify]: Simplify (+ 0 0) into 0 6.907 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.908 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.910 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.912 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.912 * [taylor]: Taking taylor expansion of 0 in k 6.912 * [backup-simplify]: Simplify 0 into 0 6.912 * [backup-simplify]: Simplify 0 into 0 6.912 * [backup-simplify]: Simplify 0 into 0 6.913 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.914 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.916 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 6.916 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.916 * [backup-simplify]: Simplify (- 0) into 0 6.916 * [backup-simplify]: Simplify (+ 0 0) into 0 6.917 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.918 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.919 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.920 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.920 * [taylor]: Taking taylor expansion of 0 in k 6.920 * [backup-simplify]: Simplify 0 into 0 6.920 * [backup-simplify]: Simplify 0 into 0 6.920 * [backup-simplify]: Simplify 0 into 0 6.920 * [backup-simplify]: Simplify 0 into 0 6.921 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.922 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.925 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 6.925 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.926 * [backup-simplify]: Simplify (- 0) into 0 6.926 * [backup-simplify]: Simplify (+ 0 0) into 0 6.927 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.928 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.929 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 6.930 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.930 * [taylor]: Taking taylor expansion of 0 in k 6.930 * [backup-simplify]: Simplify 0 into 0 6.930 * [backup-simplify]: Simplify 0 into 0 6.931 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) 6.932 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 6.932 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 6.932 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 6.932 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.932 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.932 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 6.932 * [taylor]: Taking taylor expansion of 0.5 in k 6.932 * [backup-simplify]: Simplify 0.5 into 0.5 6.932 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.932 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.932 * [taylor]: Taking taylor expansion of k in k 6.932 * [backup-simplify]: Simplify 0 into 0 6.932 * [backup-simplify]: Simplify 1 into 1 6.932 * [backup-simplify]: Simplify (/ 1 1) into 1 6.932 * [taylor]: Taking taylor expansion of 1.0 in k 6.932 * [backup-simplify]: Simplify 1.0 into 1.0 6.932 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.932 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.932 * [taylor]: Taking taylor expansion of -2.0 in k 6.932 * [backup-simplify]: Simplify -2.0 into -2.0 6.932 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.932 * [taylor]: Taking taylor expansion of PI in k 6.932 * [backup-simplify]: Simplify PI into PI 6.932 * [taylor]: Taking taylor expansion of n in k 6.932 * [backup-simplify]: Simplify n into n 6.932 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.933 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.933 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.933 * [backup-simplify]: Simplify (+ 1 0) into 1 6.933 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 6.933 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 6.933 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 6.933 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 6.933 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.933 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.933 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 6.934 * [taylor]: Taking taylor expansion of 0.5 in n 6.934 * [backup-simplify]: Simplify 0.5 into 0.5 6.934 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.934 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.934 * [taylor]: Taking taylor expansion of k in n 6.934 * [backup-simplify]: Simplify k into k 6.934 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.934 * [taylor]: Taking taylor expansion of 1.0 in n 6.934 * [backup-simplify]: Simplify 1.0 into 1.0 6.934 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.934 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.934 * [taylor]: Taking taylor expansion of -2.0 in n 6.934 * [backup-simplify]: Simplify -2.0 into -2.0 6.934 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.934 * [taylor]: Taking taylor expansion of PI in n 6.934 * [backup-simplify]: Simplify PI into PI 6.934 * [taylor]: Taking taylor expansion of n in n 6.934 * [backup-simplify]: Simplify 0 into 0 6.934 * [backup-simplify]: Simplify 1 into 1 6.934 * [backup-simplify]: Simplify (/ PI 1) into PI 6.934 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.935 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.935 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.935 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 6.936 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.937 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 6.938 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 6.938 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 6.938 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.938 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.938 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 6.938 * [taylor]: Taking taylor expansion of 0.5 in n 6.938 * [backup-simplify]: Simplify 0.5 into 0.5 6.938 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.938 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.938 * [taylor]: Taking taylor expansion of k in n 6.938 * [backup-simplify]: Simplify k into k 6.938 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.938 * [taylor]: Taking taylor expansion of 1.0 in n 6.938 * [backup-simplify]: Simplify 1.0 into 1.0 6.938 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.938 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.938 * [taylor]: Taking taylor expansion of -2.0 in n 6.938 * [backup-simplify]: Simplify -2.0 into -2.0 6.938 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.938 * [taylor]: Taking taylor expansion of PI in n 6.938 * [backup-simplify]: Simplify PI into PI 6.938 * [taylor]: Taking taylor expansion of n in n 6.938 * [backup-simplify]: Simplify 0 into 0 6.938 * [backup-simplify]: Simplify 1 into 1 6.938 * [backup-simplify]: Simplify (/ PI 1) into PI 6.939 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.939 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.939 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.940 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 6.940 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.941 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 6.942 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 6.942 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 6.942 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 6.942 * [taylor]: Taking taylor expansion of 0.5 in k 6.942 * [backup-simplify]: Simplify 0.5 into 0.5 6.942 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 6.942 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.942 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.942 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.942 * [taylor]: Taking taylor expansion of -2.0 in k 6.942 * [backup-simplify]: Simplify -2.0 into -2.0 6.942 * [taylor]: Taking taylor expansion of PI in k 6.942 * [backup-simplify]: Simplify PI into PI 6.943 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.943 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.943 * [taylor]: Taking taylor expansion of (log n) in k 6.943 * [taylor]: Taking taylor expansion of n in k 6.943 * [backup-simplify]: Simplify n into n 6.943 * [backup-simplify]: Simplify (log n) into (log n) 6.943 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.943 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.943 * [taylor]: Taking taylor expansion of k in k 6.943 * [backup-simplify]: Simplify 0 into 0 6.943 * [backup-simplify]: Simplify 1 into 1 6.944 * [backup-simplify]: Simplify (/ 1 1) into 1 6.944 * [taylor]: Taking taylor expansion of 1.0 in k 6.944 * [backup-simplify]: Simplify 1.0 into 1.0 6.944 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.944 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 6.945 * [backup-simplify]: Simplify (+ 1 0) into 1 6.945 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 6.946 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 6.948 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 6.949 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 6.950 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.951 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.953 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.953 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.953 * [backup-simplify]: Simplify (+ 0 0) into 0 6.954 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 6.955 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.957 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.959 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 6.959 * [taylor]: Taking taylor expansion of 0 in k 6.959 * [backup-simplify]: Simplify 0 into 0 6.959 * [backup-simplify]: Simplify 0 into 0 6.959 * [backup-simplify]: Simplify 0 into 0 6.960 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.961 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.964 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 6.965 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.965 * [backup-simplify]: Simplify (+ 0 0) into 0 6.966 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 6.968 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.969 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 6.972 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.972 * [taylor]: Taking taylor expansion of 0 in k 6.972 * [backup-simplify]: Simplify 0 into 0 6.972 * [backup-simplify]: Simplify 0 into 0 6.972 * [backup-simplify]: Simplify 0 into 0 6.972 * [backup-simplify]: Simplify 0 into 0 6.973 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.974 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.980 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 6.981 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.981 * [backup-simplify]: Simplify (+ 0 0) into 0 6.983 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 6.985 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.987 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 6.990 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.990 * [taylor]: Taking taylor expansion of 0 in k 6.990 * [backup-simplify]: Simplify 0 into 0 6.990 * [backup-simplify]: Simplify 0 into 0 6.991 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 6.991 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 1) 6.992 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 6.992 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 6.992 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 6.992 * [taylor]: Taking taylor expansion of 1.0 in k 6.992 * [backup-simplify]: Simplify 1.0 into 1.0 6.992 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.992 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.992 * [taylor]: Taking taylor expansion of k in k 6.992 * [backup-simplify]: Simplify 0 into 0 6.992 * [backup-simplify]: Simplify 1 into 1 6.992 * [backup-simplify]: Simplify (/ 1 1) into 1 6.993 * [backup-simplify]: Simplify (sqrt 0) into 0 6.994 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.994 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 6.994 * [taylor]: Taking taylor expansion of 1.0 in k 6.994 * [backup-simplify]: Simplify 1.0 into 1.0 6.994 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.994 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.994 * [taylor]: Taking taylor expansion of k in k 6.994 * [backup-simplify]: Simplify 0 into 0 6.994 * [backup-simplify]: Simplify 1 into 1 6.995 * [backup-simplify]: Simplify (/ 1 1) into 1 6.995 * [backup-simplify]: Simplify (sqrt 0) into 0 6.997 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.997 * [backup-simplify]: Simplify (* 1.0 0) into 0 6.997 * [backup-simplify]: Simplify 0 into 0 6.999 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 6.999 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 7.000 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 7.003 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 7.006 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 7.007 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 7.008 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.012 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 7.014 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 7.015 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 7.016 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 7.016 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 7.016 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 7.017 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 7.017 * [taylor]: Taking taylor expansion of 1.0 in k 7.017 * [backup-simplify]: Simplify 1.0 into 1.0 7.017 * [taylor]: Taking taylor expansion of (sqrt k) in k 7.017 * [taylor]: Taking taylor expansion of k in k 7.017 * [backup-simplify]: Simplify 0 into 0 7.017 * [backup-simplify]: Simplify 1 into 1 7.017 * [backup-simplify]: Simplify (sqrt 0) into 0 7.018 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 7.019 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 7.019 * [taylor]: Taking taylor expansion of 1.0 in k 7.019 * [backup-simplify]: Simplify 1.0 into 1.0 7.019 * [taylor]: Taking taylor expansion of (sqrt k) in k 7.019 * [taylor]: Taking taylor expansion of k in k 7.019 * [backup-simplify]: Simplify 0 into 0 7.019 * [backup-simplify]: Simplify 1 into 1 7.019 * [backup-simplify]: Simplify (sqrt 0) into 0 7.020 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 7.021 * [backup-simplify]: Simplify (* 1.0 0) into 0 7.021 * [backup-simplify]: Simplify 0 into 0 7.028 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 7.029 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 7.032 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 7.034 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 7.034 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 7.039 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 7.041 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 7.041 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 7.043 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 7.043 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 7.043 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 7.043 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 7.044 * [taylor]: Taking taylor expansion of 1.0 in k 7.044 * [backup-simplify]: Simplify 1.0 into 1.0 7.044 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 7.044 * [taylor]: Taking taylor expansion of (/ -1 k) in k 7.044 * [taylor]: Taking taylor expansion of -1 in k 7.044 * [backup-simplify]: Simplify -1 into -1 7.044 * [taylor]: Taking taylor expansion of k in k 7.044 * [backup-simplify]: Simplify 0 into 0 7.044 * [backup-simplify]: Simplify 1 into 1 7.044 * [backup-simplify]: Simplify (/ -1 1) into -1 7.045 * [backup-simplify]: Simplify (sqrt 0) into 0 7.046 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 7.047 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 7.047 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 7.047 * [taylor]: Taking taylor expansion of 1.0 in k 7.047 * [backup-simplify]: Simplify 1.0 into 1.0 7.047 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 7.047 * [taylor]: Taking taylor expansion of (/ -1 k) in k 7.047 * [taylor]: Taking taylor expansion of -1 in k 7.047 * [backup-simplify]: Simplify -1 into -1 7.047 * [taylor]: Taking taylor expansion of k in k 7.047 * [backup-simplify]: Simplify 0 into 0 7.047 * [backup-simplify]: Simplify 1 into 1 7.047 * [backup-simplify]: Simplify (/ -1 1) into -1 7.048 * [backup-simplify]: Simplify (sqrt 0) into 0 7.049 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 7.050 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 7.050 * [backup-simplify]: Simplify +nan.0 into +nan.0 7.051 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 7.054 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 7.057 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 7.057 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 7.058 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.063 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 7.068 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 7.068 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 7.069 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 7.069 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 7.069 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 7.070 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 7.070 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 7.070 * [taylor]: Taking taylor expansion of 1.0 in k 7.070 * [backup-simplify]: Simplify 1.0 into 1.0 7.070 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 7.070 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.070 * [taylor]: Taking taylor expansion of k in k 7.070 * [backup-simplify]: Simplify 0 into 0 7.070 * [backup-simplify]: Simplify 1 into 1 7.070 * [backup-simplify]: Simplify (/ 1 1) into 1 7.071 * [backup-simplify]: Simplify (sqrt 0) into 0 7.072 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 7.072 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 7.072 * [taylor]: Taking taylor expansion of 1.0 in k 7.072 * [backup-simplify]: Simplify 1.0 into 1.0 7.072 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 7.072 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.072 * [taylor]: Taking taylor expansion of k in k 7.072 * [backup-simplify]: Simplify 0 into 0 7.072 * [backup-simplify]: Simplify 1 into 1 7.072 * [backup-simplify]: Simplify (/ 1 1) into 1 7.073 * [backup-simplify]: Simplify (sqrt 0) into 0 7.074 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 7.074 * [backup-simplify]: Simplify (* 1.0 0) into 0 7.075 * [backup-simplify]: Simplify 0 into 0 7.076 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 7.076 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 7.077 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 7.079 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 7.080 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 7.081 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 7.081 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.083 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 7.085 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 7.085 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 7.086 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 7.086 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 7.086 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 7.086 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 7.086 * [taylor]: Taking taylor expansion of 1.0 in k 7.086 * [backup-simplify]: Simplify 1.0 into 1.0 7.086 * [taylor]: Taking taylor expansion of (sqrt k) in k 7.086 * [taylor]: Taking taylor expansion of k in k 7.086 * [backup-simplify]: Simplify 0 into 0 7.086 * [backup-simplify]: Simplify 1 into 1 7.086 * [backup-simplify]: Simplify (sqrt 0) into 0 7.087 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 7.087 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 7.087 * [taylor]: Taking taylor expansion of 1.0 in k 7.087 * [backup-simplify]: Simplify 1.0 into 1.0 7.087 * [taylor]: Taking taylor expansion of (sqrt k) in k 7.087 * [taylor]: Taking taylor expansion of k in k 7.087 * [backup-simplify]: Simplify 0 into 0 7.087 * [backup-simplify]: Simplify 1 into 1 7.087 * [backup-simplify]: Simplify (sqrt 0) into 0 7.088 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 7.089 * [backup-simplify]: Simplify (* 1.0 0) into 0 7.089 * [backup-simplify]: Simplify 0 into 0 7.089 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 7.090 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 7.092 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 7.093 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 7.093 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 7.095 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 7.097 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 7.097 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 7.098 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 7.098 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 7.098 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 7.098 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 7.098 * [taylor]: Taking taylor expansion of 1.0 in k 7.098 * [backup-simplify]: Simplify 1.0 into 1.0 7.098 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 7.098 * [taylor]: Taking taylor expansion of (/ -1 k) in k 7.098 * [taylor]: Taking taylor expansion of -1 in k 7.098 * [backup-simplify]: Simplify -1 into -1 7.098 * [taylor]: Taking taylor expansion of k in k 7.098 * [backup-simplify]: Simplify 0 into 0 7.098 * [backup-simplify]: Simplify 1 into 1 7.098 * [backup-simplify]: Simplify (/ -1 1) into -1 7.099 * [backup-simplify]: Simplify (sqrt 0) into 0 7.099 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 7.100 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 7.100 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 7.100 * [taylor]: Taking taylor expansion of 1.0 in k 7.100 * [backup-simplify]: Simplify 1.0 into 1.0 7.100 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 7.100 * [taylor]: Taking taylor expansion of (/ -1 k) in k 7.100 * [taylor]: Taking taylor expansion of -1 in k 7.100 * [backup-simplify]: Simplify -1 into -1 7.100 * [taylor]: Taking taylor expansion of k in k 7.100 * [backup-simplify]: Simplify 0 into 0 7.100 * [backup-simplify]: Simplify 1 into 1 7.100 * [backup-simplify]: Simplify (/ -1 1) into -1 7.100 * [backup-simplify]: Simplify (sqrt 0) into 0 7.101 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 7.101 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 7.102 * [backup-simplify]: Simplify +nan.0 into +nan.0 7.102 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 7.104 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 7.105 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 7.106 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 7.106 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.109 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 7.112 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 7.113 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 7.114 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 7.114 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2 1) 7.115 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 7.115 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 7.115 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 7.115 * [taylor]: Taking taylor expansion of 2.0 in n 7.115 * [backup-simplify]: Simplify 2.0 into 2.0 7.115 * [taylor]: Taking taylor expansion of (* n PI) in n 7.115 * [taylor]: Taking taylor expansion of n in n 7.115 * [backup-simplify]: Simplify 0 into 0 7.115 * [backup-simplify]: Simplify 1 into 1 7.115 * [taylor]: Taking taylor expansion of PI in n 7.115 * [backup-simplify]: Simplify PI into PI 7.115 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 7.115 * [taylor]: Taking taylor expansion of 2.0 in n 7.115 * [backup-simplify]: Simplify 2.0 into 2.0 7.115 * [taylor]: Taking taylor expansion of (* n PI) in n 7.115 * [taylor]: Taking taylor expansion of n in n 7.115 * [backup-simplify]: Simplify 0 into 0 7.115 * [backup-simplify]: Simplify 1 into 1 7.115 * [taylor]: Taking taylor expansion of PI in n 7.115 * [backup-simplify]: Simplify PI into PI 7.117 * [backup-simplify]: Simplify (* 0 PI) into 0 7.117 * [backup-simplify]: Simplify (* 2.0 0) into 0 7.117 * [backup-simplify]: Simplify 0 into 0 7.119 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.121 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 7.121 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 7.122 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 7.123 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 7.123 * [backup-simplify]: Simplify 0 into 0 7.125 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 7.126 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 7.126 * [backup-simplify]: Simplify 0 into 0 7.127 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 7.129 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 7.129 * [backup-simplify]: Simplify 0 into 0 7.131 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 7.132 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 7.132 * [backup-simplify]: Simplify 0 into 0 7.134 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 7.136 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 7.136 * [backup-simplify]: Simplify 0 into 0 7.138 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 7.140 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 7.140 * [backup-simplify]: Simplify 0 into 0 7.140 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 7.141 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 7.141 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 7.141 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 7.141 * [taylor]: Taking taylor expansion of 2.0 in n 7.141 * [backup-simplify]: Simplify 2.0 into 2.0 7.141 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.141 * [taylor]: Taking taylor expansion of PI in n 7.141 * [backup-simplify]: Simplify PI into PI 7.141 * [taylor]: Taking taylor expansion of n in n 7.141 * [backup-simplify]: Simplify 0 into 0 7.141 * [backup-simplify]: Simplify 1 into 1 7.142 * [backup-simplify]: Simplify (/ PI 1) into PI 7.142 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 7.142 * [taylor]: Taking taylor expansion of 2.0 in n 7.142 * [backup-simplify]: Simplify 2.0 into 2.0 7.142 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.142 * [taylor]: Taking taylor expansion of PI in n 7.142 * [backup-simplify]: Simplify PI into PI 7.142 * [taylor]: Taking taylor expansion of n in n 7.142 * [backup-simplify]: Simplify 0 into 0 7.142 * [backup-simplify]: Simplify 1 into 1 7.143 * [backup-simplify]: Simplify (/ PI 1) into PI 7.143 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 7.144 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 7.145 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.145 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 7.145 * [backup-simplify]: Simplify 0 into 0 7.147 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.148 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 7.148 * [backup-simplify]: Simplify 0 into 0 7.149 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.150 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 7.150 * [backup-simplify]: Simplify 0 into 0 7.151 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.159 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 7.160 * [backup-simplify]: Simplify 0 into 0 7.161 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.163 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 7.163 * [backup-simplify]: Simplify 0 into 0 7.164 * [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 7.166 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 7.166 * [backup-simplify]: Simplify 0 into 0 7.166 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 7.167 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 7.167 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 7.167 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 7.167 * [taylor]: Taking taylor expansion of -2.0 in n 7.167 * [backup-simplify]: Simplify -2.0 into -2.0 7.167 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.167 * [taylor]: Taking taylor expansion of PI in n 7.167 * [backup-simplify]: Simplify PI into PI 7.167 * [taylor]: Taking taylor expansion of n in n 7.167 * [backup-simplify]: Simplify 0 into 0 7.167 * [backup-simplify]: Simplify 1 into 1 7.168 * [backup-simplify]: Simplify (/ PI 1) into PI 7.168 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 7.168 * [taylor]: Taking taylor expansion of -2.0 in n 7.168 * [backup-simplify]: Simplify -2.0 into -2.0 7.168 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.168 * [taylor]: Taking taylor expansion of PI in n 7.168 * [backup-simplify]: Simplify PI into PI 7.168 * [taylor]: Taking taylor expansion of n in n 7.168 * [backup-simplify]: Simplify 0 into 0 7.168 * [backup-simplify]: Simplify 1 into 1 7.169 * [backup-simplify]: Simplify (/ PI 1) into PI 7.169 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 7.170 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 7.171 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.172 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 7.172 * [backup-simplify]: Simplify 0 into 0 7.173 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.174 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 7.174 * [backup-simplify]: Simplify 0 into 0 7.175 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.176 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 7.176 * [backup-simplify]: Simplify 0 into 0 7.177 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.179 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 7.179 * [backup-simplify]: Simplify 0 into 0 7.180 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.181 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 7.182 * [backup-simplify]: Simplify 0 into 0 7.183 * [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 7.184 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 7.185 * [backup-simplify]: Simplify 0 into 0 7.185 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 7.185 * * * [progress]: simplifying candidates 7.187 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 7.189 * * [simplify]: iteration 0: 236 enodes 7.251 * * [simplify]: iteration 1: 605 enodes 7.589 * * [simplify]: iteration 2: 2695 enodes 8.473 * * [simplify]: iteration complete: 5000 enodes 8.473 * * [simplify]: Extracting #0: cost 83 inf + 0 8.474 * * [simplify]: Extracting #1: cost 627 inf + 2 8.483 * * [simplify]: Extracting #2: cost 1559 inf + 2274 8.509 * * [simplify]: Extracting #3: cost 1159 inf + 76195 8.551 * * [simplify]: Extracting #4: cost 547 inf + 220951 8.644 * * [simplify]: Extracting #5: cost 248 inf + 330983 8.733 * * [simplify]: Extracting #6: cost 94 inf + 394524 8.817 * * [simplify]: Extracting #7: cost 34 inf + 413656 8.893 * * [simplify]: Extracting #8: cost 10 inf + 421827 8.978 * * [simplify]: Extracting #9: cost 1 inf + 425420 9.101 * * [simplify]: Extracting #10: cost 0 inf + 426088 9.212 * [simplify]: Simplified to: (* (/ (- 1.0 k) 2.0) (log (* (* n 2.0) PI))) (* (/ (- 1.0 k) 2.0) (log (* (* n 2.0) PI))) (* (/ (- 1.0 k) 2.0) (log (* (* n 2.0) PI))) (* (/ (- 1.0 k) 2.0) (log (* (* n 2.0) PI))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* n 2.0) PI) (/ 1.0 2.0)) (pow (* (* n 2.0) PI) (/ k 2.0)) (pow (* (* n 2.0) PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* n 2.0) PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* n 2.0) PI) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* (* n 2.0) PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* n 2.0) PI) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* n 2.0) PI) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* n 2.0) PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* n 2.0) PI) (sqrt (- 1.0 k))) (pow (* (* n 2.0) PI) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* (* n 2.0) PI) (/ 1 (sqrt 2.0))) (* (* n 2.0) PI) (pow (* (* n 2.0) PI) (/ (+ (sqrt k) (sqrt 1.0)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* n 2.0) PI) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0))) (pow (* (* n 2.0) PI) (+ (sqrt k) (sqrt 1.0))) (pow (* (* n 2.0) PI) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* (* n 2.0) PI) (/ 1 (sqrt 2.0))) (* (* n 2.0) PI) (* (* n 2.0) PI) (exp (* (- 1.0 k) (log (* (* n 2.0) PI)))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (/ (- 1.0 k) 2.0) (log (* (* n 2.0) PI))) (exp (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (* (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (* (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))) (sqrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (pow (* (* n 2.0) PI) (/ (/ (- 1.0 k) 2) 2.0)) (pow (* (* n 2.0) PI) (/ (/ (- 1.0 k) 2) 2.0)) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (* (/ 1.0 (sqrt k)) (/ (* 1.0 1.0) k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (/ (fabs (cbrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (* (/ 1.0 (sqrt k)) (/ (* 1.0 1.0) k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (/ (fabs (cbrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (* (* n 2.0) PI) (* (* n 2.0) PI) (log (* (* n 2.0) PI)) (log (* (* n 2.0) PI)) (log (* (* n 2.0) PI)) (exp (* (* n 2.0) PI)) (* (* (* 2.0 (* (* 2.0 PI) (* 2.0 PI))) (* PI (* n n))) n) (* (* (* (* n 2.0) PI) (sqrt (* (* n 2.0) PI))) (* (* (* n 2.0) PI) (sqrt (* (* n 2.0) PI)))) (* (cbrt (* (* n 2.0) PI)) (cbrt (* (* n 2.0) PI))) (cbrt (* (* n 2.0) PI)) (* (* (* (* n 2.0) PI) (sqrt (* (* n 2.0) PI))) (* (* (* n 2.0) PI) (sqrt (* (* n 2.0) PI)))) (sqrt (* (* n 2.0) PI)) (sqrt (* (* n 2.0) PI)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* (sqrt n) PI) 2.0) (* 2.0 PI) (* PI n) (+ (+ (* 0.125 (* (exp (* (log (* (* n 2.0) PI)) 0.5)) (* (* (* k k) (log n)) (log n)))) (* (* (* 0.25 (log (* 2.0 PI))) (* (* k k) (log n))) (exp (* (log (* (* n 2.0) PI)) 0.5)))) (- (+ (* (* 0.125 (* (exp (* (log (* (* n 2.0) PI)) 0.5)) (* k k))) (* (log (* 2.0 PI)) (log (* 2.0 PI)))) (exp (* (log (* (* n 2.0) PI)) 0.5))) (* 0.5 (* k (+ (* (log n) (exp (* (log (* (* n 2.0) PI)) 0.5))) (* (exp (* (log (* (* n 2.0) PI)) 0.5)) (log (* 2.0 PI)))))))) (exp (* (- 1.0 k) (* (log (* (* n 2.0) PI)) 0.5))) (exp (* (* 0.5 (- 1.0 k)) (- (log (* -2.0 PI)) (log (/ -1 n))))) (- (- (* k (* k +nan.0)) (- +nan.0 (* k +nan.0)))) (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ (/ +nan.0 (* k k)) k))) (+ (- (/ +nan.0 k) +nan.0) (/ (- +nan.0) (* k k))) (- (- (* k (* k +nan.0)) (- +nan.0 (* k +nan.0)))) (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ (/ +nan.0 (* k k)) k))) (+ (- (/ +nan.0 k) +nan.0) (/ (- +nan.0) (* k k))) (* (* n 2.0) PI) (* (* n 2.0) PI) (* (* n 2.0) PI) 9.234 * * * [progress]: adding candidates to table 10.131 * * [progress]: iteration 3 / 4 10.131 * * * [progress]: picking best candidate 10.187 * * * * [pick]: Picked # 10.188 * * * [progress]: localizing error 10.278 * * * [progress]: generating rewritten candidates 10.278 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 10.309 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 1) 10.343 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1 1) 10.351 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 10.398 * * * [progress]: generating series expansions 10.398 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 10.399 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 10.399 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 10.399 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 10.399 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 10.399 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 10.399 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 10.399 * [taylor]: Taking taylor expansion of 0.5 in k 10.399 * [backup-simplify]: Simplify 0.5 into 0.5 10.399 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 10.400 * [taylor]: Taking taylor expansion of 1.0 in k 10.400 * [backup-simplify]: Simplify 1.0 into 1.0 10.400 * [taylor]: Taking taylor expansion of k in k 10.400 * [backup-simplify]: Simplify 0 into 0 10.400 * [backup-simplify]: Simplify 1 into 1 10.400 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 10.400 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 10.400 * [taylor]: Taking taylor expansion of 2.0 in k 10.400 * [backup-simplify]: Simplify 2.0 into 2.0 10.400 * [taylor]: Taking taylor expansion of (* n PI) in k 10.400 * [taylor]: Taking taylor expansion of n in k 10.400 * [backup-simplify]: Simplify n into n 10.400 * [taylor]: Taking taylor expansion of PI in k 10.400 * [backup-simplify]: Simplify PI into PI 10.400 * [backup-simplify]: Simplify (* n PI) into (* n PI) 10.400 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 10.400 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 10.401 * [backup-simplify]: Simplify (- 0) into 0 10.401 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 10.402 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 10.402 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 10.402 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 10.402 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 10.402 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 10.402 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 10.402 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 10.402 * [taylor]: Taking taylor expansion of 0.5 in n 10.402 * [backup-simplify]: Simplify 0.5 into 0.5 10.402 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 10.402 * [taylor]: Taking taylor expansion of 1.0 in n 10.402 * [backup-simplify]: Simplify 1.0 into 1.0 10.402 * [taylor]: Taking taylor expansion of k in n 10.402 * [backup-simplify]: Simplify k into k 10.402 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 10.402 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.402 * [taylor]: Taking taylor expansion of 2.0 in n 10.402 * [backup-simplify]: Simplify 2.0 into 2.0 10.402 * [taylor]: Taking taylor expansion of (* n PI) in n 10.402 * [taylor]: Taking taylor expansion of n in n 10.402 * [backup-simplify]: Simplify 0 into 0 10.402 * [backup-simplify]: Simplify 1 into 1 10.403 * [taylor]: Taking taylor expansion of PI in n 10.403 * [backup-simplify]: Simplify PI into PI 10.403 * [backup-simplify]: Simplify (* 0 PI) into 0 10.404 * [backup-simplify]: Simplify (* 2.0 0) into 0 10.405 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.407 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 10.408 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.408 * [backup-simplify]: Simplify (- k) into (- k) 10.409 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 10.409 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 10.410 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.411 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 10.413 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 10.413 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 10.413 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 10.413 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 10.413 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 10.413 * [taylor]: Taking taylor expansion of 0.5 in n 10.413 * [backup-simplify]: Simplify 0.5 into 0.5 10.413 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 10.413 * [taylor]: Taking taylor expansion of 1.0 in n 10.413 * [backup-simplify]: Simplify 1.0 into 1.0 10.413 * [taylor]: Taking taylor expansion of k in n 10.413 * [backup-simplify]: Simplify k into k 10.413 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 10.413 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.413 * [taylor]: Taking taylor expansion of 2.0 in n 10.413 * [backup-simplify]: Simplify 2.0 into 2.0 10.413 * [taylor]: Taking taylor expansion of (* n PI) in n 10.413 * [taylor]: Taking taylor expansion of n in n 10.413 * [backup-simplify]: Simplify 0 into 0 10.413 * [backup-simplify]: Simplify 1 into 1 10.413 * [taylor]: Taking taylor expansion of PI in n 10.413 * [backup-simplify]: Simplify PI into PI 10.414 * [backup-simplify]: Simplify (* 0 PI) into 0 10.414 * [backup-simplify]: Simplify (* 2.0 0) into 0 10.416 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.418 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 10.419 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.419 * [backup-simplify]: Simplify (- k) into (- k) 10.419 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 10.419 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 10.421 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.422 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 10.423 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 10.424 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 10.424 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 10.424 * [taylor]: Taking taylor expansion of 0.5 in k 10.424 * [backup-simplify]: Simplify 0.5 into 0.5 10.424 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 10.424 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 10.424 * [taylor]: Taking taylor expansion of 1.0 in k 10.424 * [backup-simplify]: Simplify 1.0 into 1.0 10.424 * [taylor]: Taking taylor expansion of k in k 10.424 * [backup-simplify]: Simplify 0 into 0 10.424 * [backup-simplify]: Simplify 1 into 1 10.424 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 10.424 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 10.424 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 10.424 * [taylor]: Taking taylor expansion of 2.0 in k 10.424 * [backup-simplify]: Simplify 2.0 into 2.0 10.424 * [taylor]: Taking taylor expansion of PI in k 10.424 * [backup-simplify]: Simplify PI into PI 10.425 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.426 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.426 * [taylor]: Taking taylor expansion of (log n) in k 10.426 * [taylor]: Taking taylor expansion of n in k 10.426 * [backup-simplify]: Simplify n into n 10.426 * [backup-simplify]: Simplify (log n) into (log n) 10.426 * [backup-simplify]: Simplify (- 0) into 0 10.427 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 10.428 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 10.429 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 10.430 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 10.431 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 10.433 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 10.434 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 10.435 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 10.437 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.437 * [backup-simplify]: Simplify (- 0) into 0 10.438 * [backup-simplify]: Simplify (+ 0 0) into 0 10.438 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 10.440 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.441 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 10.443 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.443 * [taylor]: Taking taylor expansion of 0 in k 10.443 * [backup-simplify]: Simplify 0 into 0 10.443 * [backup-simplify]: Simplify 0 into 0 10.444 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 10.446 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.447 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 10.447 * [backup-simplify]: Simplify (+ 0 0) into 0 10.448 * [backup-simplify]: Simplify (- 1) into -1 10.448 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.450 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 10.452 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 10.456 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 10.459 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 10.461 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 10.462 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 10.476 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 10.477 * [backup-simplify]: Simplify (- 0) into 0 10.477 * [backup-simplify]: Simplify (+ 0 0) into 0 10.478 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 10.480 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.481 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 10.484 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.484 * [taylor]: Taking taylor expansion of 0 in k 10.484 * [backup-simplify]: Simplify 0 into 0 10.484 * [backup-simplify]: Simplify 0 into 0 10.484 * [backup-simplify]: Simplify 0 into 0 10.485 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.489 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 10.491 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 10.491 * [backup-simplify]: Simplify (+ 0 0) into 0 10.491 * [backup-simplify]: Simplify (- 0) into 0 10.492 * [backup-simplify]: Simplify (+ 0 0) into 0 10.494 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 10.495 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 10.498 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 10.501 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 10.507 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) 10.508 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 10.508 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 10.508 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 10.508 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 10.508 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 10.508 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 10.508 * [taylor]: Taking taylor expansion of 0.5 in k 10.508 * [backup-simplify]: Simplify 0.5 into 0.5 10.508 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 10.508 * [taylor]: Taking taylor expansion of 1.0 in k 10.508 * [backup-simplify]: Simplify 1.0 into 1.0 10.508 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.508 * [taylor]: Taking taylor expansion of k in k 10.508 * [backup-simplify]: Simplify 0 into 0 10.508 * [backup-simplify]: Simplify 1 into 1 10.509 * [backup-simplify]: Simplify (/ 1 1) into 1 10.509 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 10.509 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 10.509 * [taylor]: Taking taylor expansion of 2.0 in k 10.509 * [backup-simplify]: Simplify 2.0 into 2.0 10.509 * [taylor]: Taking taylor expansion of (/ PI n) in k 10.509 * [taylor]: Taking taylor expansion of PI in k 10.509 * [backup-simplify]: Simplify PI into PI 10.509 * [taylor]: Taking taylor expansion of n in k 10.509 * [backup-simplify]: Simplify n into n 10.509 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 10.509 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 10.509 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 10.509 * [backup-simplify]: Simplify (- 1) into -1 10.509 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.510 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 10.510 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 10.510 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 10.510 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 10.510 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 10.510 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 10.510 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 10.510 * [taylor]: Taking taylor expansion of 0.5 in n 10.510 * [backup-simplify]: Simplify 0.5 into 0.5 10.510 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 10.510 * [taylor]: Taking taylor expansion of 1.0 in n 10.510 * [backup-simplify]: Simplify 1.0 into 1.0 10.510 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.510 * [taylor]: Taking taylor expansion of k in n 10.510 * [backup-simplify]: Simplify k into k 10.510 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.510 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 10.510 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.510 * [taylor]: Taking taylor expansion of 2.0 in n 10.510 * [backup-simplify]: Simplify 2.0 into 2.0 10.510 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.510 * [taylor]: Taking taylor expansion of PI in n 10.510 * [backup-simplify]: Simplify PI into PI 10.510 * [taylor]: Taking taylor expansion of n in n 10.510 * [backup-simplify]: Simplify 0 into 0 10.510 * [backup-simplify]: Simplify 1 into 1 10.511 * [backup-simplify]: Simplify (/ PI 1) into PI 10.511 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.512 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.512 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 10.512 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 10.512 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 10.513 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.513 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 10.514 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 10.514 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 10.514 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 10.514 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 10.514 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 10.514 * [taylor]: Taking taylor expansion of 0.5 in n 10.514 * [backup-simplify]: Simplify 0.5 into 0.5 10.514 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 10.514 * [taylor]: Taking taylor expansion of 1.0 in n 10.514 * [backup-simplify]: Simplify 1.0 into 1.0 10.514 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.514 * [taylor]: Taking taylor expansion of k in n 10.514 * [backup-simplify]: Simplify k into k 10.514 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.514 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 10.514 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.515 * [taylor]: Taking taylor expansion of 2.0 in n 10.515 * [backup-simplify]: Simplify 2.0 into 2.0 10.515 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.515 * [taylor]: Taking taylor expansion of PI in n 10.515 * [backup-simplify]: Simplify PI into PI 10.515 * [taylor]: Taking taylor expansion of n in n 10.515 * [backup-simplify]: Simplify 0 into 0 10.515 * [backup-simplify]: Simplify 1 into 1 10.515 * [backup-simplify]: Simplify (/ PI 1) into PI 10.515 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.516 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.516 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 10.516 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 10.516 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 10.517 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.518 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 10.519 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 10.519 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 10.519 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 10.519 * [taylor]: Taking taylor expansion of 0.5 in k 10.519 * [backup-simplify]: Simplify 0.5 into 0.5 10.519 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 10.519 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 10.519 * [taylor]: Taking taylor expansion of 1.0 in k 10.519 * [backup-simplify]: Simplify 1.0 into 1.0 10.519 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.519 * [taylor]: Taking taylor expansion of k in k 10.519 * [backup-simplify]: Simplify 0 into 0 10.519 * [backup-simplify]: Simplify 1 into 1 10.519 * [backup-simplify]: Simplify (/ 1 1) into 1 10.519 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 10.519 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 10.519 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 10.519 * [taylor]: Taking taylor expansion of 2.0 in k 10.519 * [backup-simplify]: Simplify 2.0 into 2.0 10.519 * [taylor]: Taking taylor expansion of PI in k 10.519 * [backup-simplify]: Simplify PI into PI 10.520 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.520 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.520 * [taylor]: Taking taylor expansion of (log n) in k 10.520 * [taylor]: Taking taylor expansion of n in k 10.520 * [backup-simplify]: Simplify n into n 10.520 * [backup-simplify]: Simplify (log n) into (log n) 10.521 * [backup-simplify]: Simplify (- 1) into -1 10.521 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.521 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 10.522 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 10.522 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 10.523 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 10.524 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 10.524 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 10.525 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.526 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 10.527 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.528 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 10.528 * [backup-simplify]: Simplify (- 0) into 0 10.528 * [backup-simplify]: Simplify (+ 0 0) into 0 10.529 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 10.530 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.531 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 10.533 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.533 * [taylor]: Taking taylor expansion of 0 in k 10.534 * [backup-simplify]: Simplify 0 into 0 10.534 * [backup-simplify]: Simplify 0 into 0 10.534 * [backup-simplify]: Simplify 0 into 0 10.534 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.535 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.537 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 10.537 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.537 * [backup-simplify]: Simplify (- 0) into 0 10.537 * [backup-simplify]: Simplify (+ 0 0) into 0 10.538 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 10.539 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.540 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 10.541 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.541 * [taylor]: Taking taylor expansion of 0 in k 10.541 * [backup-simplify]: Simplify 0 into 0 10.541 * [backup-simplify]: Simplify 0 into 0 10.541 * [backup-simplify]: Simplify 0 into 0 10.541 * [backup-simplify]: Simplify 0 into 0 10.542 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.543 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.546 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 10.546 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.546 * [backup-simplify]: Simplify (- 0) into 0 10.547 * [backup-simplify]: Simplify (+ 0 0) into 0 10.547 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 10.548 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.549 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 10.551 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 10.551 * [taylor]: Taking taylor expansion of 0 in k 10.551 * [backup-simplify]: Simplify 0 into 0 10.551 * [backup-simplify]: Simplify 0 into 0 10.552 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) 10.552 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 10.552 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 10.552 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 10.552 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 10.552 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 10.553 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 10.553 * [taylor]: Taking taylor expansion of 0.5 in k 10.553 * [backup-simplify]: Simplify 0.5 into 0.5 10.553 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 10.553 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.553 * [taylor]: Taking taylor expansion of k in k 10.553 * [backup-simplify]: Simplify 0 into 0 10.553 * [backup-simplify]: Simplify 1 into 1 10.553 * [backup-simplify]: Simplify (/ 1 1) into 1 10.553 * [taylor]: Taking taylor expansion of 1.0 in k 10.553 * [backup-simplify]: Simplify 1.0 into 1.0 10.553 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 10.553 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 10.553 * [taylor]: Taking taylor expansion of -2.0 in k 10.553 * [backup-simplify]: Simplify -2.0 into -2.0 10.553 * [taylor]: Taking taylor expansion of (/ PI n) in k 10.553 * [taylor]: Taking taylor expansion of PI in k 10.553 * [backup-simplify]: Simplify PI into PI 10.553 * [taylor]: Taking taylor expansion of n in k 10.553 * [backup-simplify]: Simplify n into n 10.553 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 10.553 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 10.553 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 10.553 * [backup-simplify]: Simplify (+ 1 0) into 1 10.554 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 10.554 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 10.554 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 10.554 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 10.554 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 10.554 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 10.554 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 10.554 * [taylor]: Taking taylor expansion of 0.5 in n 10.554 * [backup-simplify]: Simplify 0.5 into 0.5 10.554 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 10.554 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.554 * [taylor]: Taking taylor expansion of k in n 10.554 * [backup-simplify]: Simplify k into k 10.554 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.554 * [taylor]: Taking taylor expansion of 1.0 in n 10.554 * [backup-simplify]: Simplify 1.0 into 1.0 10.554 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 10.554 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.554 * [taylor]: Taking taylor expansion of -2.0 in n 10.554 * [backup-simplify]: Simplify -2.0 into -2.0 10.554 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.554 * [taylor]: Taking taylor expansion of PI in n 10.554 * [backup-simplify]: Simplify PI into PI 10.554 * [taylor]: Taking taylor expansion of n in n 10.554 * [backup-simplify]: Simplify 0 into 0 10.554 * [backup-simplify]: Simplify 1 into 1 10.555 * [backup-simplify]: Simplify (/ PI 1) into PI 10.555 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.556 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.556 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 10.556 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 10.557 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.557 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 10.558 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 10.558 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 10.558 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 10.558 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 10.558 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 10.558 * [taylor]: Taking taylor expansion of 0.5 in n 10.558 * [backup-simplify]: Simplify 0.5 into 0.5 10.558 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 10.558 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.558 * [taylor]: Taking taylor expansion of k in n 10.558 * [backup-simplify]: Simplify k into k 10.558 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.558 * [taylor]: Taking taylor expansion of 1.0 in n 10.559 * [backup-simplify]: Simplify 1.0 into 1.0 10.559 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 10.559 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.559 * [taylor]: Taking taylor expansion of -2.0 in n 10.559 * [backup-simplify]: Simplify -2.0 into -2.0 10.559 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.559 * [taylor]: Taking taylor expansion of PI in n 10.559 * [backup-simplify]: Simplify PI into PI 10.559 * [taylor]: Taking taylor expansion of n in n 10.559 * [backup-simplify]: Simplify 0 into 0 10.559 * [backup-simplify]: Simplify 1 into 1 10.559 * [backup-simplify]: Simplify (/ PI 1) into PI 10.559 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.560 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.560 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 10.560 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 10.561 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.562 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 10.563 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 10.563 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 10.563 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 10.563 * [taylor]: Taking taylor expansion of 0.5 in k 10.563 * [backup-simplify]: Simplify 0.5 into 0.5 10.563 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 10.563 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 10.563 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 10.563 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 10.564 * [taylor]: Taking taylor expansion of -2.0 in k 10.564 * [backup-simplify]: Simplify -2.0 into -2.0 10.564 * [taylor]: Taking taylor expansion of PI in k 10.564 * [backup-simplify]: Simplify PI into PI 10.564 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.565 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.565 * [taylor]: Taking taylor expansion of (log n) in k 10.565 * [taylor]: Taking taylor expansion of n in k 10.565 * [backup-simplify]: Simplify n into n 10.565 * [backup-simplify]: Simplify (log n) into (log n) 10.565 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 10.565 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.565 * [taylor]: Taking taylor expansion of k in k 10.565 * [backup-simplify]: Simplify 0 into 0 10.566 * [backup-simplify]: Simplify 1 into 1 10.566 * [backup-simplify]: Simplify (/ 1 1) into 1 10.566 * [taylor]: Taking taylor expansion of 1.0 in k 10.566 * [backup-simplify]: Simplify 1.0 into 1.0 10.566 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 10.567 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 10.568 * [backup-simplify]: Simplify (+ 1 0) into 1 10.569 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 10.570 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 10.571 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 10.573 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 10.574 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.575 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 10.576 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 10.576 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 10.577 * [backup-simplify]: Simplify (+ 0 0) into 0 10.577 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 10.579 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.580 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 10.582 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 10.582 * [taylor]: Taking taylor expansion of 0 in k 10.582 * [backup-simplify]: Simplify 0 into 0 10.582 * [backup-simplify]: Simplify 0 into 0 10.582 * [backup-simplify]: Simplify 0 into 0 10.590 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.591 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.595 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 10.595 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.596 * [backup-simplify]: Simplify (+ 0 0) into 0 10.597 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 10.598 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.600 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 10.603 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.603 * [taylor]: Taking taylor expansion of 0 in k 10.603 * [backup-simplify]: Simplify 0 into 0 10.603 * [backup-simplify]: Simplify 0 into 0 10.603 * [backup-simplify]: Simplify 0 into 0 10.603 * [backup-simplify]: Simplify 0 into 0 10.604 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.605 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.612 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 10.612 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.612 * [backup-simplify]: Simplify (+ 0 0) into 0 10.614 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 10.615 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.617 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 10.620 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 10.620 * [taylor]: Taking taylor expansion of 0 in k 10.620 * [backup-simplify]: Simplify 0 into 0 10.620 * [backup-simplify]: Simplify 0 into 0 10.622 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 10.622 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 1) 10.622 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) into (* 1.0 (sqrt (/ 1 k))) 10.622 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 10.622 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 10.622 * [taylor]: Taking taylor expansion of 1.0 in k 10.622 * [backup-simplify]: Simplify 1.0 into 1.0 10.622 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 10.622 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.622 * [taylor]: Taking taylor expansion of k in k 10.622 * [backup-simplify]: Simplify 0 into 0 10.622 * [backup-simplify]: Simplify 1 into 1 10.623 * [backup-simplify]: Simplify (/ 1 1) into 1 10.623 * [backup-simplify]: Simplify (sqrt 0) into 0 10.625 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.625 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 10.625 * [taylor]: Taking taylor expansion of 1.0 in k 10.625 * [backup-simplify]: Simplify 1.0 into 1.0 10.625 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 10.625 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.625 * [taylor]: Taking taylor expansion of k in k 10.625 * [backup-simplify]: Simplify 0 into 0 10.625 * [backup-simplify]: Simplify 1 into 1 10.625 * [backup-simplify]: Simplify (/ 1 1) into 1 10.626 * [backup-simplify]: Simplify (sqrt 0) into 0 10.627 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.627 * [backup-simplify]: Simplify (* 1.0 0) into 0 10.627 * [backup-simplify]: Simplify 0 into 0 10.629 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 10.629 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.630 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 10.633 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 10.635 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 10.635 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.636 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.640 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 10.642 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 10.643 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.644 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 10.644 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) into (* 1.0 (sqrt k)) 10.644 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 10.644 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 10.644 * [taylor]: Taking taylor expansion of 1.0 in k 10.644 * [backup-simplify]: Simplify 1.0 into 1.0 10.644 * [taylor]: Taking taylor expansion of (sqrt k) in k 10.644 * [taylor]: Taking taylor expansion of k in k 10.644 * [backup-simplify]: Simplify 0 into 0 10.644 * [backup-simplify]: Simplify 1 into 1 10.645 * [backup-simplify]: Simplify (sqrt 0) into 0 10.646 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.646 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 10.646 * [taylor]: Taking taylor expansion of 1.0 in k 10.646 * [backup-simplify]: Simplify 1.0 into 1.0 10.646 * [taylor]: Taking taylor expansion of (sqrt k) in k 10.646 * [taylor]: Taking taylor expansion of k in k 10.646 * [backup-simplify]: Simplify 0 into 0 10.646 * [backup-simplify]: Simplify 1 into 1 10.647 * [backup-simplify]: Simplify (sqrt 0) into 0 10.648 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.648 * [backup-simplify]: Simplify (* 1.0 0) into 0 10.648 * [backup-simplify]: Simplify 0 into 0 10.650 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 10.650 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.653 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 10.655 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 10.655 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.657 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 10.658 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 10.659 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.660 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 10.660 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) into (/ 1.0 (sqrt (/ -1 k))) 10.660 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 10.660 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 10.660 * [taylor]: Taking taylor expansion of 1.0 in k 10.660 * [backup-simplify]: Simplify 1.0 into 1.0 10.660 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 10.660 * [taylor]: Taking taylor expansion of (/ -1 k) in k 10.660 * [taylor]: Taking taylor expansion of -1 in k 10.660 * [backup-simplify]: Simplify -1 into -1 10.660 * [taylor]: Taking taylor expansion of k in k 10.660 * [backup-simplify]: Simplify 0 into 0 10.660 * [backup-simplify]: Simplify 1 into 1 10.660 * [backup-simplify]: Simplify (/ -1 1) into -1 10.661 * [backup-simplify]: Simplify (sqrt 0) into 0 10.661 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 10.662 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 10.662 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 10.662 * [taylor]: Taking taylor expansion of 1.0 in k 10.662 * [backup-simplify]: Simplify 1.0 into 1.0 10.662 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 10.662 * [taylor]: Taking taylor expansion of (/ -1 k) in k 10.662 * [taylor]: Taking taylor expansion of -1 in k 10.662 * [backup-simplify]: Simplify -1 into -1 10.662 * [taylor]: Taking taylor expansion of k in k 10.662 * [backup-simplify]: Simplify 0 into 0 10.662 * [backup-simplify]: Simplify 1 into 1 10.662 * [backup-simplify]: Simplify (/ -1 1) into -1 10.662 * [backup-simplify]: Simplify (sqrt 0) into 0 10.663 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 10.663 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 10.663 * [backup-simplify]: Simplify +nan.0 into +nan.0 10.664 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 10.666 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 10.667 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 10.668 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.668 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.670 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 10.673 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 10.673 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.674 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 10.674 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1 1) 10.674 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt k))) into (* 1.0 (pow (/ 1 k) 1/4)) 10.674 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0 10.674 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 10.674 * [taylor]: Taking taylor expansion of 1.0 in k 10.674 * [backup-simplify]: Simplify 1.0 into 1.0 10.674 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 10.674 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 10.674 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 10.674 * [taylor]: Taking taylor expansion of 1/4 in k 10.674 * [backup-simplify]: Simplify 1/4 into 1/4 10.674 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 10.674 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.674 * [taylor]: Taking taylor expansion of k in k 10.674 * [backup-simplify]: Simplify 0 into 0 10.674 * [backup-simplify]: Simplify 1 into 1 10.675 * [backup-simplify]: Simplify (/ 1 1) into 1 10.675 * [backup-simplify]: Simplify (log 1) into 0 10.675 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 10.675 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 10.675 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 10.675 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 10.675 * [taylor]: Taking taylor expansion of 1.0 in k 10.675 * [backup-simplify]: Simplify 1.0 into 1.0 10.675 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 10.675 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 10.675 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 10.675 * [taylor]: Taking taylor expansion of 1/4 in k 10.675 * [backup-simplify]: Simplify 1/4 into 1/4 10.675 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 10.675 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.675 * [taylor]: Taking taylor expansion of k in k 10.675 * [backup-simplify]: Simplify 0 into 0 10.675 * [backup-simplify]: Simplify 1 into 1 10.676 * [backup-simplify]: Simplify (/ 1 1) into 1 10.676 * [backup-simplify]: Simplify (log 1) into 0 10.676 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 10.676 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 10.676 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 10.676 * [backup-simplify]: Simplify (* 1.0 (pow k -1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 10.677 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 10.677 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 10.678 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 10.678 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 10.678 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 10.679 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 10.680 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k -1/4))) into 0 10.680 * [backup-simplify]: Simplify 0 into 0 10.680 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.682 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 10.682 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 10.683 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 10.684 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.684 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k -1/4)))) into 0 10.684 * [backup-simplify]: Simplify 0 into 0 10.685 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.689 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 10.690 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 10.691 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 10.693 * [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 10.694 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))) into 0 10.694 * [backup-simplify]: Simplify 0 into 0 10.695 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.706 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 10.706 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 10.708 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 10.711 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.713 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))) into 0 10.713 * [backup-simplify]: Simplify 0 into 0 10.714 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.739 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 10.740 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 10.742 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 10.746 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 10.748 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))))) into 0 10.748 * [backup-simplify]: Simplify 0 into 0 10.749 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.776 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 10.776 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 10.778 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 10.781 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.782 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))))) into 0 10.783 * [backup-simplify]: Simplify 0 into 0 10.783 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 10.783 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 k)))) into (* 1.0 (pow k 1/4)) 10.783 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0 10.783 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 10.783 * [taylor]: Taking taylor expansion of 1.0 in k 10.783 * [backup-simplify]: Simplify 1.0 into 1.0 10.783 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 10.783 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 10.783 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 10.783 * [taylor]: Taking taylor expansion of 1/4 in k 10.783 * [backup-simplify]: Simplify 1/4 into 1/4 10.783 * [taylor]: Taking taylor expansion of (log k) in k 10.783 * [taylor]: Taking taylor expansion of k in k 10.783 * [backup-simplify]: Simplify 0 into 0 10.783 * [backup-simplify]: Simplify 1 into 1 10.783 * [backup-simplify]: Simplify (log 1) into 0 10.784 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 10.784 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 10.784 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 10.784 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 10.784 * [taylor]: Taking taylor expansion of 1.0 in k 10.784 * [backup-simplify]: Simplify 1.0 into 1.0 10.784 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 10.784 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 10.784 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 10.784 * [taylor]: Taking taylor expansion of 1/4 in k 10.784 * [backup-simplify]: Simplify 1/4 into 1/4 10.784 * [taylor]: Taking taylor expansion of (log k) in k 10.784 * [taylor]: Taking taylor expansion of k in k 10.784 * [backup-simplify]: Simplify 0 into 0 10.784 * [backup-simplify]: Simplify 1 into 1 10.784 * [backup-simplify]: Simplify (log 1) into 0 10.784 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 10.784 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 10.784 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 10.785 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4)) 10.785 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4)) 10.785 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 10.786 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 10.786 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 10.787 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 10.787 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k 1/4))) into 0 10.787 * [backup-simplify]: Simplify 0 into 0 10.789 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 10.789 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 10.790 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 10.790 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.791 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0 10.791 * [backup-simplify]: Simplify 0 into 0 10.794 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 10.794 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 10.795 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 10.796 * [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 10.797 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))) into 0 10.797 * [backup-simplify]: Simplify 0 into 0 10.802 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 10.803 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 10.804 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0 10.805 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.806 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))) into 0 10.806 * [backup-simplify]: Simplify 0 into 0 10.815 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 10.816 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 10.817 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0 10.819 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 10.820 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))))) into 0 10.820 * [backup-simplify]: Simplify 0 into 0 10.842 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 10.843 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 10.845 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0 10.851 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.854 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))))) into 0 10.854 * [backup-simplify]: Simplify 0 into 0 10.854 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 10.854 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) into (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) 10.854 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0 10.854 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 10.854 * [taylor]: Taking taylor expansion of 1.0 in k 10.854 * [backup-simplify]: Simplify 1.0 into 1.0 10.854 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 10.854 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 10.854 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 10.854 * [taylor]: Taking taylor expansion of (/ -1 k) in k 10.854 * [taylor]: Taking taylor expansion of -1 in k 10.854 * [backup-simplify]: Simplify -1 into -1 10.854 * [taylor]: Taking taylor expansion of k in k 10.854 * [backup-simplify]: Simplify 0 into 0 10.854 * [backup-simplify]: Simplify 1 into 1 10.855 * [backup-simplify]: Simplify (/ -1 1) into -1 10.855 * [backup-simplify]: Simplify (sqrt 0) into 0 10.857 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 10.857 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 10.858 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 10.859 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 10.862 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 10.864 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 10.866 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 10.866 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 10.866 * [taylor]: Taking taylor expansion of 1.0 in k 10.866 * [backup-simplify]: Simplify 1.0 into 1.0 10.866 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 10.866 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 10.866 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 10.866 * [taylor]: Taking taylor expansion of (/ -1 k) in k 10.866 * [taylor]: Taking taylor expansion of -1 in k 10.866 * [backup-simplify]: Simplify -1 into -1 10.866 * [taylor]: Taking taylor expansion of k in k 10.866 * [backup-simplify]: Simplify 0 into 0 10.866 * [backup-simplify]: Simplify 1 into 1 10.867 * [backup-simplify]: Simplify (/ -1 1) into -1 10.867 * [backup-simplify]: Simplify (sqrt 0) into 0 10.868 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 10.869 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 10.869 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 10.870 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 10.873 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 10.875 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 10.877 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 10.878 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0)) 10.879 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0)) 10.882 * [backup-simplify]: Simplify (+ (* 1.0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0))) into (- (* +nan.0 (/ 1 (sqrt +nan.0)))) 10.885 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (sqrt +nan.0)))) into (- (* +nan.0 (/ 1 (sqrt +nan.0)))) 10.886 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.890 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 10.893 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 10.899 * [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))) 10.912 * [backup-simplify]: Simplify (+ (* 1.0 (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))) (+ (* 0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0)))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (sqrt +nan.0)))))) 10.920 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (sqrt +nan.0)))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (sqrt +nan.0)))))) 10.931 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (sqrt +nan.0)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ 1 (sqrt +nan.0)))) (/ 1 (- k))) (* 1.0 (sqrt +nan.0)))) into (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2))))))))) 10.931 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 10.932 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 10.932 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 10.932 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 10.932 * [taylor]: Taking taylor expansion of 1.0 in k 10.932 * [backup-simplify]: Simplify 1.0 into 1.0 10.932 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 10.932 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.932 * [taylor]: Taking taylor expansion of k in k 10.932 * [backup-simplify]: Simplify 0 into 0 10.932 * [backup-simplify]: Simplify 1 into 1 10.932 * [backup-simplify]: Simplify (/ 1 1) into 1 10.933 * [backup-simplify]: Simplify (sqrt 0) into 0 10.934 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.934 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 10.934 * [taylor]: Taking taylor expansion of 1.0 in k 10.934 * [backup-simplify]: Simplify 1.0 into 1.0 10.934 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 10.934 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.934 * [taylor]: Taking taylor expansion of k in k 10.935 * [backup-simplify]: Simplify 0 into 0 10.935 * [backup-simplify]: Simplify 1 into 1 10.935 * [backup-simplify]: Simplify (/ 1 1) into 1 10.935 * [backup-simplify]: Simplify (sqrt 0) into 0 10.937 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.937 * [backup-simplify]: Simplify (* 1.0 0) into 0 10.937 * [backup-simplify]: Simplify 0 into 0 10.939 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 10.939 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.940 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 10.943 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 10.945 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 10.946 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.947 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.951 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 10.954 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 10.954 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.956 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 10.956 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 10.956 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 10.956 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 10.956 * [taylor]: Taking taylor expansion of 1.0 in k 10.956 * [backup-simplify]: Simplify 1.0 into 1.0 10.956 * [taylor]: Taking taylor expansion of (sqrt k) in k 10.956 * [taylor]: Taking taylor expansion of k in k 10.956 * [backup-simplify]: Simplify 0 into 0 10.956 * [backup-simplify]: Simplify 1 into 1 10.956 * [backup-simplify]: Simplify (sqrt 0) into 0 10.958 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.958 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 10.958 * [taylor]: Taking taylor expansion of 1.0 in k 10.958 * [backup-simplify]: Simplify 1.0 into 1.0 10.958 * [taylor]: Taking taylor expansion of (sqrt k) in k 10.958 * [taylor]: Taking taylor expansion of k in k 10.958 * [backup-simplify]: Simplify 0 into 0 10.958 * [backup-simplify]: Simplify 1 into 1 10.958 * [backup-simplify]: Simplify (sqrt 0) into 0 10.960 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 10.960 * [backup-simplify]: Simplify (* 1.0 0) into 0 10.960 * [backup-simplify]: Simplify 0 into 0 10.962 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 10.962 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.965 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 10.967 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 10.968 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.972 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 10.974 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 10.975 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.984 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 10.984 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 10.985 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 10.985 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 10.985 * [taylor]: Taking taylor expansion of 1.0 in k 10.985 * [backup-simplify]: Simplify 1.0 into 1.0 10.985 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 10.985 * [taylor]: Taking taylor expansion of (/ -1 k) in k 10.985 * [taylor]: Taking taylor expansion of -1 in k 10.985 * [backup-simplify]: Simplify -1 into -1 10.985 * [taylor]: Taking taylor expansion of k in k 10.985 * [backup-simplify]: Simplify 0 into 0 10.985 * [backup-simplify]: Simplify 1 into 1 10.985 * [backup-simplify]: Simplify (/ -1 1) into -1 10.986 * [backup-simplify]: Simplify (sqrt 0) into 0 10.987 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 10.988 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 10.988 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 10.988 * [taylor]: Taking taylor expansion of 1.0 in k 10.988 * [backup-simplify]: Simplify 1.0 into 1.0 10.988 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 10.988 * [taylor]: Taking taylor expansion of (/ -1 k) in k 10.988 * [taylor]: Taking taylor expansion of -1 in k 10.988 * [backup-simplify]: Simplify -1 into -1 10.988 * [taylor]: Taking taylor expansion of k in k 10.988 * [backup-simplify]: Simplify 0 into 0 10.988 * [backup-simplify]: Simplify 1 into 1 10.988 * [backup-simplify]: Simplify (/ -1 1) into -1 10.989 * [backup-simplify]: Simplify (sqrt 0) into 0 10.990 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 10.990 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 10.991 * [backup-simplify]: Simplify +nan.0 into +nan.0 10.992 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 10.995 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 10.998 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 10.998 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 10.999 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.003 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.007 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 11.008 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.009 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 11.009 * * * [progress]: simplifying candidates 11.025 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt 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(sqrt (sqrt k))))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (- (/ 1.0 (sqrt (sqrt k)))) (- (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) 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(sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 1.0 (pow (/ 1 k) 1/4)) (* 1.0 (pow (/ 1 k) 1/4)) (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2))))))))) (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 11.035 * * [simplify]: iteration 0: 569 enodes 11.290 * * [simplify]: iteration 1: 1415 enodes 11.635 * * [simplify]: iteration complete: 5000 enodes 11.635 * * [simplify]: Extracting #0: cost 264 inf + 0 11.638 * * [simplify]: Extracting #1: cost 1524 inf + 84 11.646 * * [simplify]: Extracting #2: cost 1833 inf + 23942 11.691 * * [simplify]: Extracting #3: cost 1313 inf + 167978 11.769 * * [simplify]: Extracting #4: cost 598 inf + 356978 11.845 * * [simplify]: Extracting #5: cost 190 inf + 492064 11.963 * * [simplify]: Extracting #6: cost 21 inf + 562220 12.059 * * [simplify]: Extracting #7: cost 4 inf + 566516 12.181 * * [simplify]: Extracting #8: cost 0 inf + 567608 12.307 * [simplify]: Simplified to: (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0)) (pow (* 2.0 (* PI n)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 (* PI n)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* PI n)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* 2.0 (* PI n)) (/ (cbrt (- 1.0 k)) (/ (sqrt 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(* (/ 1.0 (sqrt k)) (/ (* 1.0 1.0) (sqrt (sqrt k)))) (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (cbrt (/ 1.0 (sqrt (sqrt k)))) (* (/ 1.0 (sqrt (sqrt k))) (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))) (- 1.0) (- (sqrt (sqrt k))) (* (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (/ (fabs (cbrt (sqrt k))) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (/ (cbrt 1.0) (/ (sqrt (fabs (cbrt k))) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (sqrt (sqrt (sqrt 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(sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) 1 (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) 1.0) (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ 1.0 (fabs (cbrt (sqrt k)))) (/ 1.0 (sqrt (fabs (cbrt k)))) (/ 1.0 (sqrt (sqrt (sqrt k)))) 1.0 (/ 1.0 (sqrt (sqrt (sqrt k)))) 1.0 (/ 1.0 (sqrt (sqrt (sqrt k)))) 1.0 (/ (sqrt (sqrt k)) (cbrt 1.0)) (/ (sqrt (sqrt k)) (sqrt 1.0)) (/ (sqrt (sqrt k)) 1.0) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ 1.0 (/ (/ (* (sqrt k) k) 1.0) 1.0)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (/ (fabs (cbrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) 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(sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (+ (* (log (* 2.0 PI)) (* (* (* k k) (* (log n) (exp (* 0.5 (log (* 2.0 (* PI n))))))) 0.25)) (+ (* (* 0.125 (exp (* 0.5 (log (* 2.0 (* PI n)))))) (* (* (log n) k) (* (log n) k))) (- (+ (exp (* 0.5 (log (* 2.0 (* PI n))))) (* (* (exp (* 0.5 (log (* 2.0 (* PI n))))) (* k k)) (* (* (log (* 2.0 PI)) (log (* 2.0 PI))) 0.125))) (* 0.5 (* k (+ (* (exp (* 0.5 (log (* 2.0 (* PI n))))) (log n)) (* (log (* 2.0 PI)) (exp (* 0.5 (log (* 2.0 (* PI n)))))))))))) (exp (* (- 1.0 k) (* (log (* 2.0 (* PI n))) 0.5))) (exp (* (* (- (log (* PI -2.0)) (log (/ -1 n))) (- 1.0 k)) 0.5)) (+ (* (- (* k k)) +nan.0) (- +nan.0 (* +nan.0 k))) (- (- (/ +nan.0 (* k k)) (- (/ +nan.0 k) (/ +nan.0 (* (* k k) k))))) (- (- (/ +nan.0 (* k k)) (- (/ +nan.0 k) +nan.0))) (* 1.0 (pow (/ 1 k) 1/4)) (* 1.0 (pow (/ 1 k) 1/4)) (+ (- (* (sqrt +nan.0) 1.0) (/ (/ +nan.0 (sqrt +nan.0)) k)) (- (/ +nan.0 (* (* (* k k) +nan.0) (sqrt +nan.0))) (/ (/ +nan.0 (sqrt +nan.0)) (* k k)))) (+ (* (- (* k k)) +nan.0) (- +nan.0 (* +nan.0 k))) (- (- (/ +nan.0 (* k k)) (- (/ +nan.0 k) (/ +nan.0 (* (* k k) k))))) (- (- (/ +nan.0 (* k k)) (- (/ +nan.0 k) +nan.0))) 12.430 * * * [progress]: adding candidates to table 14.879 * * [progress]: iteration 4 / 4 14.879 * * * [progress]: picking best candidate 14.938 * * * * [pick]: Picked # 14.939 * * * [progress]: localizing error 14.981 * * * [progress]: generating rewritten candidates 14.981 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 2) 14.990 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2) 14.996 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 15.024 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 15.034 * * * [progress]: generating series expansions 15.034 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 2) 15.035 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) 15.035 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in (k) around 0 15.035 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 15.035 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 15.035 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 15.035 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 15.035 * [taylor]: Taking taylor expansion of 0.5 in k 15.035 * [backup-simplify]: Simplify 0.5 into 0.5 15.035 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 15.035 * [taylor]: Taking taylor expansion of 1.0 in k 15.035 * [backup-simplify]: Simplify 1.0 into 1.0 15.035 * [taylor]: Taking taylor expansion of k in k 15.035 * [backup-simplify]: Simplify 0 into 0 15.035 * [backup-simplify]: Simplify 1 into 1 15.035 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 15.035 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 15.035 * [taylor]: Taking taylor expansion of 2.0 in k 15.035 * [backup-simplify]: Simplify 2.0 into 2.0 15.035 * [taylor]: Taking taylor expansion of PI in k 15.035 * [backup-simplify]: Simplify PI into PI 15.035 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.036 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.036 * [backup-simplify]: Simplify (- 0) into 0 15.037 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 15.037 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 15.038 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 15.040 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 15.040 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 15.040 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 15.040 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 15.040 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 15.040 * [taylor]: Taking taylor expansion of 0.5 in k 15.040 * [backup-simplify]: Simplify 0.5 into 0.5 15.040 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 15.040 * [taylor]: Taking taylor expansion of 1.0 in k 15.040 * [backup-simplify]: Simplify 1.0 into 1.0 15.040 * [taylor]: Taking taylor expansion of k in k 15.040 * [backup-simplify]: Simplify 0 into 0 15.040 * [backup-simplify]: Simplify 1 into 1 15.040 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 15.040 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 15.040 * [taylor]: Taking taylor expansion of 2.0 in k 15.040 * [backup-simplify]: Simplify 2.0 into 2.0 15.040 * [taylor]: Taking taylor expansion of PI in k 15.040 * [backup-simplify]: Simplify PI into PI 15.040 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.041 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.041 * [backup-simplify]: Simplify (- 0) into 0 15.042 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 15.042 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 15.043 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 15.045 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 15.045 * [backup-simplify]: Simplify (pow (* 2.0 PI) 0.5) into (pow (* 2.0 PI) 0.5) 15.046 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 15.047 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 15.047 * [backup-simplify]: Simplify (- 1) into -1 15.048 * [backup-simplify]: Simplify (+ 0 -1) into -1 15.049 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 15.051 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 PI)))) into (- (* 0.5 (log (* 2.0 PI)))) 15.059 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 1) 1)))) into (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) 15.063 * [backup-simplify]: Simplify (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) into (* -0.5 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (log (* 2.0 PI)))) 15.064 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 15.066 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 15.066 * [backup-simplify]: Simplify (- 0) into 0 15.066 * [backup-simplify]: Simplify (+ 0 0) into 0 15.067 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 15.068 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 PI))))) into 0 15.077 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) 15.083 * [backup-simplify]: Simplify (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) into (* 0.125 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) 15.093 * [backup-simplify]: Simplify (+ (* (* 0.125 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) (pow k 2)) (+ (* (* -0.5 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (log (* 2.0 PI)))) k) (pow (* 2.0 PI) 0.5))) into (- (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (pow (* 2.0 PI) 0.5)) (* 0.5 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (log (* 2.0 PI)) k)))) 15.094 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) 15.094 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in (k) around 0 15.094 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 15.094 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 15.094 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 15.094 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 15.094 * [taylor]: Taking taylor expansion of 0.5 in k 15.094 * [backup-simplify]: Simplify 0.5 into 0.5 15.094 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 15.094 * [taylor]: Taking taylor expansion of 1.0 in k 15.094 * [backup-simplify]: Simplify 1.0 into 1.0 15.094 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.094 * [taylor]: Taking taylor expansion of k in k 15.094 * [backup-simplify]: Simplify 0 into 0 15.094 * [backup-simplify]: Simplify 1 into 1 15.094 * [backup-simplify]: Simplify (/ 1 1) into 1 15.094 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 15.094 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 15.094 * [taylor]: Taking taylor expansion of 2.0 in k 15.094 * [backup-simplify]: Simplify 2.0 into 2.0 15.094 * [taylor]: Taking taylor expansion of PI in k 15.094 * [backup-simplify]: Simplify PI into PI 15.095 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.095 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.096 * [backup-simplify]: Simplify (- 1) into -1 15.096 * [backup-simplify]: Simplify (+ 0 -1) into -1 15.096 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 15.097 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 15.098 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 15.098 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 15.098 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 15.098 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 15.098 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 15.098 * [taylor]: Taking taylor expansion of 0.5 in k 15.098 * [backup-simplify]: Simplify 0.5 into 0.5 15.098 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 15.098 * [taylor]: Taking taylor expansion of 1.0 in k 15.098 * [backup-simplify]: Simplify 1.0 into 1.0 15.098 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.098 * [taylor]: Taking taylor expansion of k in k 15.098 * [backup-simplify]: Simplify 0 into 0 15.098 * [backup-simplify]: Simplify 1 into 1 15.099 * [backup-simplify]: Simplify (/ 1 1) into 1 15.099 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 15.099 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 15.099 * [taylor]: Taking taylor expansion of 2.0 in k 15.099 * [backup-simplify]: Simplify 2.0 into 2.0 15.099 * [taylor]: Taking taylor expansion of PI in k 15.099 * [backup-simplify]: Simplify PI into PI 15.099 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.100 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.100 * [backup-simplify]: Simplify (- 1) into -1 15.100 * [backup-simplify]: Simplify (+ 0 -1) into -1 15.100 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 15.479 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 15.481 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 15.482 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 15.482 * [backup-simplify]: Simplify 0 into 0 15.482 * [backup-simplify]: Simplify 0 into 0 15.482 * [backup-simplify]: Simplify 0 into 0 15.482 * [backup-simplify]: Simplify 0 into 0 15.483 * [backup-simplify]: Simplify 0 into 0 15.483 * [backup-simplify]: Simplify 0 into 0 15.484 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log (* 2.0 PI))))) into (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) 15.484 * [backup-simplify]: Simplify (pow (* 2.0 PI) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) 15.484 * [approximate]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in (k) around 0 15.484 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 15.485 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 15.485 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 15.485 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 15.485 * [taylor]: Taking taylor expansion of 0.5 in k 15.485 * [backup-simplify]: Simplify 0.5 into 0.5 15.485 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 15.485 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.485 * [taylor]: Taking taylor expansion of k in k 15.485 * [backup-simplify]: Simplify 0 into 0 15.485 * [backup-simplify]: Simplify 1 into 1 15.485 * [backup-simplify]: Simplify (/ 1 1) into 1 15.485 * [taylor]: Taking taylor expansion of 1.0 in k 15.485 * [backup-simplify]: Simplify 1.0 into 1.0 15.485 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 15.485 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 15.485 * [taylor]: Taking taylor expansion of 2.0 in k 15.485 * [backup-simplify]: Simplify 2.0 into 2.0 15.485 * [taylor]: Taking taylor expansion of PI in k 15.485 * [backup-simplify]: Simplify PI into PI 15.486 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.487 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.487 * [backup-simplify]: Simplify (+ 1 0) into 1 15.487 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 15.488 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 15.489 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 15.489 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 15.489 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 15.489 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 15.489 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 15.489 * [taylor]: Taking taylor expansion of 0.5 in k 15.489 * [backup-simplify]: Simplify 0.5 into 0.5 15.489 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 15.489 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.489 * [taylor]: Taking taylor expansion of k in k 15.489 * [backup-simplify]: Simplify 0 into 0 15.489 * [backup-simplify]: Simplify 1 into 1 15.490 * [backup-simplify]: Simplify (/ 1 1) into 1 15.490 * [taylor]: Taking taylor expansion of 1.0 in k 15.490 * [backup-simplify]: Simplify 1.0 into 1.0 15.490 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 15.490 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 15.490 * [taylor]: Taking taylor expansion of 2.0 in k 15.490 * [backup-simplify]: Simplify 2.0 into 2.0 15.490 * [taylor]: Taking taylor expansion of PI in k 15.490 * [backup-simplify]: Simplify PI into PI 15.490 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.491 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.491 * [backup-simplify]: Simplify (+ 1 0) into 1 15.491 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 15.492 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 15.493 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 15.494 * [backup-simplify]: Simplify (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 15.494 * [backup-simplify]: Simplify 0 into 0 15.494 * [backup-simplify]: Simplify 0 into 0 15.494 * [backup-simplify]: Simplify 0 into 0 15.494 * [backup-simplify]: Simplify 0 into 0 15.494 * [backup-simplify]: Simplify 0 into 0 15.494 * [backup-simplify]: Simplify 0 into 0 15.495 * [backup-simplify]: Simplify (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) 15.495 * * * * [progress]: [ 2 / 4 ] generating series at (2 2) 15.495 * [backup-simplify]: Simplify (pow n (/ (- 1.0 k) 2.0)) into (pow n (* 0.5 (- 1.0 k))) 15.495 * [approximate]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in (n k) around 0 15.495 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in k 15.495 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in k 15.495 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in k 15.495 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 15.495 * [taylor]: Taking taylor expansion of 0.5 in k 15.495 * [backup-simplify]: Simplify 0.5 into 0.5 15.495 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 15.495 * [taylor]: Taking taylor expansion of 1.0 in k 15.495 * [backup-simplify]: Simplify 1.0 into 1.0 15.495 * [taylor]: Taking taylor expansion of k in k 15.495 * [backup-simplify]: Simplify 0 into 0 15.495 * [backup-simplify]: Simplify 1 into 1 15.495 * [taylor]: Taking taylor expansion of (log n) in k 15.495 * [taylor]: Taking taylor expansion of n in k 15.495 * [backup-simplify]: Simplify n into n 15.495 * [backup-simplify]: Simplify (log n) into (log n) 15.496 * [backup-simplify]: Simplify (- 0) into 0 15.496 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 15.496 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 15.496 * [backup-simplify]: Simplify (* 0.5 (log n)) into (* 0.5 (log n)) 15.496 * [backup-simplify]: Simplify (exp (* 0.5 (log n))) into (pow n 0.5) 15.496 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in n 15.496 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in n 15.496 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in n 15.496 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 15.496 * [taylor]: Taking taylor expansion of 0.5 in n 15.496 * [backup-simplify]: Simplify 0.5 into 0.5 15.496 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 15.496 * [taylor]: Taking taylor expansion of 1.0 in n 15.496 * [backup-simplify]: Simplify 1.0 into 1.0 15.496 * [taylor]: Taking taylor expansion of k in n 15.496 * [backup-simplify]: Simplify k into k 15.496 * [taylor]: Taking taylor expansion of (log n) in n 15.496 * [taylor]: Taking taylor expansion of n in n 15.496 * [backup-simplify]: Simplify 0 into 0 15.496 * [backup-simplify]: Simplify 1 into 1 15.497 * [backup-simplify]: Simplify (log 1) into 0 15.497 * [backup-simplify]: Simplify (- k) into (- k) 15.497 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 15.497 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 15.497 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 15.497 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (log n)) into (* 0.5 (* (- 1.0 k) (log n))) 15.497 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (log n)))) into (exp (* 0.5 (* (- 1.0 k) (log n)))) 15.497 * [taylor]: Taking taylor expansion of (pow n (* 0.5 (- 1.0 k))) in n 15.497 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log n))) in n 15.497 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log n)) in n 15.497 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 15.497 * [taylor]: Taking taylor expansion of 0.5 in n 15.497 * [backup-simplify]: Simplify 0.5 into 0.5 15.497 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 15.497 * [taylor]: Taking taylor expansion of 1.0 in n 15.497 * [backup-simplify]: Simplify 1.0 into 1.0 15.497 * [taylor]: Taking taylor expansion of k in n 15.497 * [backup-simplify]: Simplify k into k 15.498 * [taylor]: Taking taylor expansion of (log n) in n 15.498 * [taylor]: Taking taylor expansion of n in n 15.498 * [backup-simplify]: Simplify 0 into 0 15.498 * [backup-simplify]: Simplify 1 into 1 15.498 * [backup-simplify]: Simplify (log 1) into 0 15.498 * [backup-simplify]: Simplify (- k) into (- k) 15.498 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 15.498 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 15.498 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 15.498 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (log n)) into (* 0.5 (* (- 1.0 k) (log n))) 15.499 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (log n)))) into (exp (* 0.5 (* (- 1.0 k) (log n)))) 15.499 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (log n)))) in k 15.499 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (log n))) in k 15.499 * [taylor]: Taking taylor expansion of 0.5 in k 15.499 * [backup-simplify]: Simplify 0.5 into 0.5 15.499 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (log n)) in k 15.499 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 15.499 * [taylor]: Taking taylor expansion of 1.0 in k 15.499 * [backup-simplify]: Simplify 1.0 into 1.0 15.499 * [taylor]: Taking taylor expansion of k in k 15.499 * [backup-simplify]: Simplify 0 into 0 15.499 * [backup-simplify]: Simplify 1 into 1 15.499 * [taylor]: Taking taylor expansion of (log n) in k 15.499 * [taylor]: Taking taylor expansion of n in k 15.499 * [backup-simplify]: Simplify n into n 15.499 * [backup-simplify]: Simplify (log n) into (log n) 15.499 * [backup-simplify]: Simplify (- 0) into 0 15.499 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 15.499 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 15.499 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (log n))) into (* 0.5 (log n)) 15.500 * [backup-simplify]: Simplify (exp (* 0.5 (log n))) into (pow n 0.5) 15.500 * [backup-simplify]: Simplify (pow n 0.5) into (pow n 0.5) 15.500 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 15.501 * [backup-simplify]: Simplify (- 0) into 0 15.501 * [backup-simplify]: Simplify (+ 0 0) into 0 15.501 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 15.501 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 15.502 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (log n))) into 0 15.502 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 15.502 * [taylor]: Taking taylor expansion of 0 in k 15.502 * [backup-simplify]: Simplify 0 into 0 15.502 * [backup-simplify]: Simplify 0 into 0 15.503 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 15.503 * [backup-simplify]: Simplify (- 1) into -1 15.503 * [backup-simplify]: Simplify (+ 0 -1) into -1 15.504 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (log n))) into (- (log n)) 15.504 * [backup-simplify]: Simplify (+ (* 0.5 (- (log n))) (* 0 (* 1.0 (log n)))) into (- (* 0.5 (log n))) 15.504 * [backup-simplify]: Simplify (* (exp (* 0.5 (log n))) (+ (* (/ (pow (- (* 0.5 (log n))) 1) 1)))) into (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) 15.504 * [backup-simplify]: Simplify (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) into (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) 15.506 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 15.506 * [backup-simplify]: Simplify (- 0) into 0 15.506 * [backup-simplify]: Simplify (+ 0 0) into 0 15.507 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 15.507 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 15.508 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 15.508 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 15.508 * [taylor]: Taking taylor expansion of 0 in k 15.508 * [backup-simplify]: Simplify 0 into 0 15.508 * [backup-simplify]: Simplify 0 into 0 15.508 * [backup-simplify]: Simplify 0 into 0 15.510 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 15.510 * [backup-simplify]: Simplify (- 0) into 0 15.510 * [backup-simplify]: Simplify (+ 0 0) into 0 15.511 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (log n)))) into 0 15.511 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (log n))) (* 0 (* 1.0 (log n))))) into 0 15.512 * [backup-simplify]: Simplify (* (exp (* 0.5 (log n))) (+ (* (/ (pow (- (* 0.5 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) 15.512 * [backup-simplify]: Simplify (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) into (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) 15.513 * [backup-simplify]: Simplify (+ (* (* 0.125 (* (pow (pow n 1.0) 0.5) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -0.5 (* (pow (pow n 1.0) 0.5) (log n))) (* k 1)) (pow n 0.5))) into (- (+ (* 0.125 (* (pow (pow n 1.0) 0.5) (* (pow (log n) 2) (pow k 2)))) (pow n 0.5)) (* 0.5 (* (pow (pow n 1.0) 0.5) (* (log n) k)))) 15.513 * [backup-simplify]: Simplify (pow (/ 1 n) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) 15.513 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 15.513 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in k 15.513 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in k 15.513 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in k 15.513 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 15.513 * [taylor]: Taking taylor expansion of 0.5 in k 15.513 * [backup-simplify]: Simplify 0.5 into 0.5 15.513 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 15.513 * [taylor]: Taking taylor expansion of 1.0 in k 15.513 * [backup-simplify]: Simplify 1.0 into 1.0 15.513 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.513 * [taylor]: Taking taylor expansion of k in k 15.513 * [backup-simplify]: Simplify 0 into 0 15.513 * [backup-simplify]: Simplify 1 into 1 15.513 * [backup-simplify]: Simplify (/ 1 1) into 1 15.513 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 15.513 * [taylor]: Taking taylor expansion of (/ 1 n) in k 15.513 * [taylor]: Taking taylor expansion of n in k 15.513 * [backup-simplify]: Simplify n into n 15.513 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 15.513 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 15.514 * [backup-simplify]: Simplify (- 1) into -1 15.514 * [backup-simplify]: Simplify (+ 0 -1) into -1 15.515 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 15.515 * [backup-simplify]: Simplify (* -0.5 (log (/ 1 n))) into (* -0.5 (log (/ 1 n))) 15.515 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ 1 n))))) 15.515 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in n 15.515 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in n 15.515 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in n 15.515 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 15.515 * [taylor]: Taking taylor expansion of 0.5 in n 15.515 * [backup-simplify]: Simplify 0.5 into 0.5 15.515 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 15.515 * [taylor]: Taking taylor expansion of 1.0 in n 15.515 * [backup-simplify]: Simplify 1.0 into 1.0 15.515 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.515 * [taylor]: Taking taylor expansion of k in n 15.515 * [backup-simplify]: Simplify k into k 15.515 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.515 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 15.515 * [taylor]: Taking taylor expansion of (/ 1 n) in n 15.515 * [taylor]: Taking taylor expansion of n in n 15.515 * [backup-simplify]: Simplify 0 into 0 15.515 * [backup-simplify]: Simplify 1 into 1 15.516 * [backup-simplify]: Simplify (/ 1 1) into 1 15.516 * [backup-simplify]: Simplify (log 1) into 0 15.516 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 15.516 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 15.516 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 15.517 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 15.517 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log n))) into (* -0.5 (* (- 1.0 (/ 1 k)) (log n))) 15.517 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) into (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) 15.517 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.5 (- 1.0 (/ 1 k)))) in n 15.517 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in n 15.517 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ 1 n))) in n 15.517 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 15.517 * [taylor]: Taking taylor expansion of 0.5 in n 15.517 * [backup-simplify]: Simplify 0.5 into 0.5 15.518 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 15.518 * [taylor]: Taking taylor expansion of 1.0 in n 15.518 * [backup-simplify]: Simplify 1.0 into 1.0 15.518 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.518 * [taylor]: Taking taylor expansion of k in n 15.518 * [backup-simplify]: Simplify k into k 15.518 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.518 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 15.518 * [taylor]: Taking taylor expansion of (/ 1 n) in n 15.518 * [taylor]: Taking taylor expansion of n in n 15.518 * [backup-simplify]: Simplify 0 into 0 15.518 * [backup-simplify]: Simplify 1 into 1 15.518 * [backup-simplify]: Simplify (/ 1 1) into 1 15.518 * [backup-simplify]: Simplify (log 1) into 0 15.518 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 15.518 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 15.518 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 15.519 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 15.519 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log n))) into (* -0.5 (* (- 1.0 (/ 1 k)) (log n))) 15.519 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) into (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) 15.519 * [taylor]: Taking taylor expansion of (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) in k 15.519 * [taylor]: Taking taylor expansion of (* -0.5 (* (- 1.0 (/ 1 k)) (log n))) in k 15.519 * [taylor]: Taking taylor expansion of -0.5 in k 15.519 * [backup-simplify]: Simplify -0.5 into -0.5 15.519 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log n)) in k 15.519 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 15.519 * [taylor]: Taking taylor expansion of 1.0 in k 15.519 * [backup-simplify]: Simplify 1.0 into 1.0 15.519 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.519 * [taylor]: Taking taylor expansion of k in k 15.519 * [backup-simplify]: Simplify 0 into 0 15.519 * [backup-simplify]: Simplify 1 into 1 15.520 * [backup-simplify]: Simplify (/ 1 1) into 1 15.520 * [taylor]: Taking taylor expansion of (log n) in k 15.520 * [taylor]: Taking taylor expansion of n in k 15.520 * [backup-simplify]: Simplify n into n 15.520 * [backup-simplify]: Simplify (log n) into (log n) 15.520 * [backup-simplify]: Simplify (- 1) into -1 15.520 * [backup-simplify]: Simplify (+ 0 -1) into -1 15.520 * [backup-simplify]: Simplify (* -1 (log n)) into (* -1 (log n)) 15.520 * [backup-simplify]: Simplify (* -0.5 (* -1 (log n))) into (* 0.5 (log n)) 15.520 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) into (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) 15.520 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) into (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) 15.521 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 15.522 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 15.522 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 15.522 * [backup-simplify]: Simplify (- 0) into 0 15.522 * [backup-simplify]: Simplify (+ 0 0) into 0 15.523 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 15.523 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 15.523 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 15.524 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 15.524 * [taylor]: Taking taylor expansion of 0 in k 15.524 * [backup-simplify]: Simplify 0 into 0 15.524 * [backup-simplify]: Simplify 0 into 0 15.524 * [backup-simplify]: Simplify 0 into 0 15.524 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.526 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 15.526 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 15.526 * [backup-simplify]: Simplify (- 0) into 0 15.526 * [backup-simplify]: Simplify (+ 0 0) into 0 15.527 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 15.527 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 15.528 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 15.529 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 15.530 * [taylor]: Taking taylor expansion of 0 in k 15.530 * [backup-simplify]: Simplify 0 into 0 15.530 * [backup-simplify]: Simplify 0 into 0 15.530 * [backup-simplify]: Simplify 0 into 0 15.530 * [backup-simplify]: Simplify 0 into 0 15.531 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.534 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 15.534 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 15.534 * [backup-simplify]: Simplify (- 0) into 0 15.535 * [backup-simplify]: Simplify (+ 0 0) into 0 15.535 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 15.536 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 15.536 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 15.537 * [backup-simplify]: Simplify (* (exp (* -0.5 (* (- 1.0 (/ 1 k)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 15.537 * [taylor]: Taking taylor expansion of 0 in k 15.537 * [backup-simplify]: Simplify 0 into 0 15.537 * [backup-simplify]: Simplify 0 into 0 15.537 * [backup-simplify]: Simplify (exp (* -0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log (/ 1 n))))) into (exp (* -0.5 (* (- 1.0 k) (log (/ 1 n))))) 15.538 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) 15.538 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 15.538 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in k 15.538 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in k 15.538 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in k 15.538 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 15.538 * [taylor]: Taking taylor expansion of 0.5 in k 15.538 * [backup-simplify]: Simplify 0.5 into 0.5 15.538 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 15.538 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.538 * [taylor]: Taking taylor expansion of k in k 15.538 * [backup-simplify]: Simplify 0 into 0 15.538 * [backup-simplify]: Simplify 1 into 1 15.538 * [backup-simplify]: Simplify (/ 1 1) into 1 15.538 * [taylor]: Taking taylor expansion of 1.0 in k 15.538 * [backup-simplify]: Simplify 1.0 into 1.0 15.538 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 15.538 * [taylor]: Taking taylor expansion of (/ -1 n) in k 15.538 * [taylor]: Taking taylor expansion of -1 in k 15.538 * [backup-simplify]: Simplify -1 into -1 15.538 * [taylor]: Taking taylor expansion of n in k 15.538 * [backup-simplify]: Simplify n into n 15.538 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 15.538 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 15.539 * [backup-simplify]: Simplify (+ 1 0) into 1 15.539 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 15.539 * [backup-simplify]: Simplify (* 0.5 (log (/ -1 n))) into (* 0.5 (log (/ -1 n))) 15.539 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) into (exp (* 0.5 (* (log (/ -1 n)) (+ (/ 1 k) 1.0)))) 15.539 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in n 15.539 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in n 15.539 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in n 15.539 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 15.539 * [taylor]: Taking taylor expansion of 0.5 in n 15.539 * [backup-simplify]: Simplify 0.5 into 0.5 15.539 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 15.539 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.539 * [taylor]: Taking taylor expansion of k in n 15.539 * [backup-simplify]: Simplify k into k 15.539 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.539 * [taylor]: Taking taylor expansion of 1.0 in n 15.539 * [backup-simplify]: Simplify 1.0 into 1.0 15.540 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 15.540 * [taylor]: Taking taylor expansion of (/ -1 n) in n 15.540 * [taylor]: Taking taylor expansion of -1 in n 15.540 * [backup-simplify]: Simplify -1 into -1 15.540 * [taylor]: Taking taylor expansion of n in n 15.540 * [backup-simplify]: Simplify 0 into 0 15.540 * [backup-simplify]: Simplify 1 into 1 15.540 * [backup-simplify]: Simplify (/ -1 1) into -1 15.540 * [backup-simplify]: Simplify (log -1) into (log -1) 15.540 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 15.540 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 15.541 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 15.541 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log -1) (log n))) into (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) 15.541 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 15.542 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.5 (+ (/ 1 k) 1.0))) in n 15.542 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in n 15.542 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in n 15.542 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 15.542 * [taylor]: Taking taylor expansion of 0.5 in n 15.542 * [backup-simplify]: Simplify 0.5 into 0.5 15.542 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 15.542 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.542 * [taylor]: Taking taylor expansion of k in n 15.542 * [backup-simplify]: Simplify k into k 15.542 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.542 * [taylor]: Taking taylor expansion of 1.0 in n 15.542 * [backup-simplify]: Simplify 1.0 into 1.0 15.542 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 15.542 * [taylor]: Taking taylor expansion of (/ -1 n) in n 15.542 * [taylor]: Taking taylor expansion of -1 in n 15.542 * [backup-simplify]: Simplify -1 into -1 15.542 * [taylor]: Taking taylor expansion of n in n 15.542 * [backup-simplify]: Simplify 0 into 0 15.542 * [backup-simplify]: Simplify 1 into 1 15.542 * [backup-simplify]: Simplify (/ -1 1) into -1 15.542 * [backup-simplify]: Simplify (log -1) into (log -1) 15.542 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 15.543 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 15.543 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 15.543 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log -1) (log n))) into (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) 15.544 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 15.544 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) in k 15.544 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) in k 15.544 * [taylor]: Taking taylor expansion of 0.5 in k 15.544 * [backup-simplify]: Simplify 0.5 into 0.5 15.544 * [taylor]: Taking taylor expansion of (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)) in k 15.544 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 15.544 * [taylor]: Taking taylor expansion of (log -1) in k 15.544 * [taylor]: Taking taylor expansion of -1 in k 15.544 * [backup-simplify]: Simplify -1 into -1 15.544 * [backup-simplify]: Simplify (log -1) into (log -1) 15.544 * [taylor]: Taking taylor expansion of (log n) in k 15.544 * [taylor]: Taking taylor expansion of n in k 15.544 * [backup-simplify]: Simplify n into n 15.544 * [backup-simplify]: Simplify (log n) into (log n) 15.544 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 15.544 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.544 * [taylor]: Taking taylor expansion of k in k 15.544 * [backup-simplify]: Simplify 0 into 0 15.544 * [backup-simplify]: Simplify 1 into 1 15.545 * [backup-simplify]: Simplify (/ 1 1) into 1 15.545 * [taylor]: Taking taylor expansion of 1.0 in k 15.545 * [backup-simplify]: Simplify 1.0 into 1.0 15.545 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 15.545 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 15.545 * [backup-simplify]: Simplify (+ 1 0) into 1 15.546 * [backup-simplify]: Simplify (* (- (log -1) (log n)) 1) into (- (log -1) (log n)) 15.546 * [backup-simplify]: Simplify (* 0.5 (- (log -1) (log n))) into (* 0.5 (- (log -1) (log n))) 15.546 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 15.547 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 15.547 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 15.548 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 15.548 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 15.548 * [backup-simplify]: Simplify (+ 0 0) into 0 15.549 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 15.549 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 15.550 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log -1) (log n)))) into 0 15.551 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 15.551 * [taylor]: Taking taylor expansion of 0 in k 15.551 * [backup-simplify]: Simplify 0 into 0 15.551 * [backup-simplify]: Simplify 0 into 0 15.551 * [backup-simplify]: Simplify 0 into 0 15.552 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.555 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 15.555 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 15.556 * [backup-simplify]: Simplify (+ 0 0) into 0 15.556 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 15.557 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 15.558 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 15.560 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 15.560 * [taylor]: Taking taylor expansion of 0 in k 15.560 * [backup-simplify]: Simplify 0 into 0 15.560 * [backup-simplify]: Simplify 0 into 0 15.560 * [backup-simplify]: Simplify 0 into 0 15.560 * [backup-simplify]: Simplify 0 into 0 15.561 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.567 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -1 1)))) 6) into 0 15.567 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 15.567 * [backup-simplify]: Simplify (+ 0 0) into 0 15.569 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 15.570 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 15.570 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0 15.572 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 15.572 * [taylor]: Taking taylor expansion of 0 in k 15.572 * [backup-simplify]: Simplify 0 into 0 15.572 * [backup-simplify]: Simplify 0 into 0 15.572 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log -1) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- (log -1) (log (/ -1 n))) (- 1.0 k)))) 15.572 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 15.573 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) 15.573 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (k) around 0 15.573 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 15.573 * [taylor]: Taking taylor expansion of 1.0 in k 15.573 * [backup-simplify]: Simplify 1.0 into 1.0 15.573 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 15.573 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 15.573 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 15.573 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 15.573 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 15.573 * [taylor]: Taking taylor expansion of 0.5 in k 15.573 * [backup-simplify]: Simplify 0.5 into 0.5 15.573 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 15.573 * [taylor]: Taking taylor expansion of 1.0 in k 15.573 * [backup-simplify]: Simplify 1.0 into 1.0 15.573 * [taylor]: Taking taylor expansion of k in k 15.573 * [backup-simplify]: Simplify 0 into 0 15.573 * [backup-simplify]: Simplify 1 into 1 15.573 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 15.573 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 15.573 * [taylor]: Taking taylor expansion of 2.0 in k 15.573 * [backup-simplify]: Simplify 2.0 into 2.0 15.573 * [taylor]: Taking taylor expansion of PI in k 15.573 * [backup-simplify]: Simplify PI into PI 15.573 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.574 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.574 * [backup-simplify]: Simplify (- 0) into 0 15.575 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 15.575 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 15.576 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 15.578 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 15.578 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 15.578 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.578 * [taylor]: Taking taylor expansion of k in k 15.578 * [backup-simplify]: Simplify 0 into 0 15.578 * [backup-simplify]: Simplify 1 into 1 15.578 * [backup-simplify]: Simplify (/ 1 1) into 1 15.578 * [backup-simplify]: Simplify (sqrt 0) into 0 15.579 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 15.579 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 15.579 * [taylor]: Taking taylor expansion of 1.0 in k 15.579 * [backup-simplify]: Simplify 1.0 into 1.0 15.579 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 15.579 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 k))) in k 15.579 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI)))) in k 15.579 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 PI))) in k 15.579 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 15.579 * [taylor]: Taking taylor expansion of 0.5 in k 15.579 * [backup-simplify]: Simplify 0.5 into 0.5 15.579 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 15.579 * [taylor]: Taking taylor expansion of 1.0 in k 15.579 * [backup-simplify]: Simplify 1.0 into 1.0 15.579 * [taylor]: Taking taylor expansion of k in k 15.579 * [backup-simplify]: Simplify 0 into 0 15.579 * [backup-simplify]: Simplify 1 into 1 15.579 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 15.579 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 15.579 * [taylor]: Taking taylor expansion of 2.0 in k 15.579 * [backup-simplify]: Simplify 2.0 into 2.0 15.579 * [taylor]: Taking taylor expansion of PI in k 15.579 * [backup-simplify]: Simplify PI into PI 15.580 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.580 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.581 * [backup-simplify]: Simplify (- 0) into 0 15.581 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 15.581 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 15.583 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 15.585 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 PI)))) into (pow (* 2.0 PI) 0.5) 15.585 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 15.585 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.585 * [taylor]: Taking taylor expansion of k in k 15.585 * [backup-simplify]: Simplify 0 into 0 15.585 * [backup-simplify]: Simplify 1 into 1 15.585 * [backup-simplify]: Simplify (/ 1 1) into 1 15.585 * [backup-simplify]: Simplify (sqrt 0) into 0 15.589 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 15.590 * [backup-simplify]: Simplify (* (pow (* 2.0 PI) 0.5) 0) into 0 15.590 * [backup-simplify]: Simplify (* 1.0 0) into 0 15.591 * [backup-simplify]: Simplify 0 into 0 15.591 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 15.592 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 15.592 * [backup-simplify]: Simplify (- 1) into -1 15.593 * [backup-simplify]: Simplify (+ 0 -1) into -1 15.594 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 15.596 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 PI)))) into (- (* 0.5 (log (* 2.0 PI)))) 15.604 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 1) 1)))) into (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) 15.608 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 PI) 0.5) +nan.0) (* (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) 0)) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) 15.617 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) 15.623 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))) 15.624 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 15.627 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 15.628 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 15.632 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 15.632 * [backup-simplify]: Simplify (- 0) into 0 15.633 * [backup-simplify]: Simplify (+ 0 0) into 0 15.634 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 15.636 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 PI))))) into 0 15.652 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) 15.675 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 PI) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) +nan.0) (* (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))) 15.705 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))))) 15.718 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))) 15.719 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.722 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 15.722 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 15.726 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 15.726 * [backup-simplify]: Simplify (- 0) into 0 15.726 * [backup-simplify]: Simplify (+ 0 0) into 0 15.727 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 15.728 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 PI)))))) into 0 15.743 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 PI)))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 3))) 15.785 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 PI) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) +nan.0) (+ (* (* 0.125 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) +nan.0) (* (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 3))) 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))))) 15.838 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))))))) (+ (* 0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))))))) 15.876 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))))) 15.914 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))))) (pow k 2)) (+ (* (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (log (* 2.0 PI)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))) k) (- (* +nan.0 (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow k 2))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (log (* 2.0 PI)) k)))))))))))))) 15.915 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* 2.0 PI) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) 15.915 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (k) around 0 15.915 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 15.915 * [taylor]: Taking taylor expansion of 1.0 in k 15.915 * [backup-simplify]: Simplify 1.0 into 1.0 15.915 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 15.915 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 15.915 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 15.915 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 15.915 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 15.915 * [taylor]: Taking taylor expansion of 0.5 in k 15.915 * [backup-simplify]: Simplify 0.5 into 0.5 15.915 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 15.915 * [taylor]: Taking taylor expansion of 1.0 in k 15.915 * [backup-simplify]: Simplify 1.0 into 1.0 15.915 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.915 * [taylor]: Taking taylor expansion of k in k 15.915 * [backup-simplify]: Simplify 0 into 0 15.915 * [backup-simplify]: Simplify 1 into 1 15.915 * [backup-simplify]: Simplify (/ 1 1) into 1 15.915 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 15.915 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 15.915 * [taylor]: Taking taylor expansion of 2.0 in k 15.915 * [backup-simplify]: Simplify 2.0 into 2.0 15.915 * [taylor]: Taking taylor expansion of PI in k 15.915 * [backup-simplify]: Simplify PI into PI 15.916 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.916 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.917 * [backup-simplify]: Simplify (- 1) into -1 15.917 * [backup-simplify]: Simplify (+ 0 -1) into -1 15.917 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 15.919 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 15.920 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 15.920 * [taylor]: Taking taylor expansion of (sqrt k) in k 15.920 * [taylor]: Taking taylor expansion of k in k 15.920 * [backup-simplify]: Simplify 0 into 0 15.920 * [backup-simplify]: Simplify 1 into 1 15.921 * [backup-simplify]: Simplify (sqrt 0) into 0 15.922 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 15.922 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 15.922 * [taylor]: Taking taylor expansion of 1.0 in k 15.922 * [backup-simplify]: Simplify 1.0 into 1.0 15.922 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 15.922 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (- 1.0 (/ 1 k)))) in k 15.922 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) in k 15.922 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI))) in k 15.922 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 15.922 * [taylor]: Taking taylor expansion of 0.5 in k 15.922 * [backup-simplify]: Simplify 0.5 into 0.5 15.923 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 15.923 * [taylor]: Taking taylor expansion of 1.0 in k 15.923 * [backup-simplify]: Simplify 1.0 into 1.0 15.923 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.923 * [taylor]: Taking taylor expansion of k in k 15.923 * [backup-simplify]: Simplify 0 into 0 15.923 * [backup-simplify]: Simplify 1 into 1 15.923 * [backup-simplify]: Simplify (/ 1 1) into 1 15.923 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 15.923 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 15.923 * [taylor]: Taking taylor expansion of 2.0 in k 15.923 * [backup-simplify]: Simplify 2.0 into 2.0 15.923 * [taylor]: Taking taylor expansion of PI in k 15.923 * [backup-simplify]: Simplify PI into PI 15.924 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.925 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.926 * [backup-simplify]: Simplify (- 1) into -1 15.926 * [backup-simplify]: Simplify (+ 0 -1) into -1 15.926 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 15.928 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 PI))) into (* -0.5 (log (* 2.0 PI))) 15.929 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 PI)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 15.929 * [taylor]: Taking taylor expansion of (sqrt k) in k 15.929 * [taylor]: Taking taylor expansion of k in k 15.929 * [backup-simplify]: Simplify 0 into 0 15.929 * [backup-simplify]: Simplify 1 into 1 15.930 * [backup-simplify]: Simplify (sqrt 0) into 0 15.931 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 15.933 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) 0) into 0 15.933 * [backup-simplify]: Simplify (* 1.0 0) into 0 15.933 * [backup-simplify]: Simplify 0 into 0 15.935 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 15.937 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 15.938 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 15.940 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 15.941 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 15.943 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 15.944 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 15.946 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 15.947 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 15.950 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 15.951 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 PI))))))) 15.954 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log (* 2.0 PI))))))) (pow (/ 1 k) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log (* 2.0 PI))))))) (pow (/ 1 k) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log (* 2.0 PI))))))) (/ 1 k)))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (pow k 3))) (- (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (pow k 2)))))))) 15.954 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* 2.0 PI) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 15.954 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k) around 0 15.954 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 15.954 * [taylor]: Taking taylor expansion of 1.0 in k 15.954 * [backup-simplify]: Simplify 1.0 into 1.0 15.954 * [taylor]: Taking taylor expansion of (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 15.954 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 15.954 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 15.954 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 15.954 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 15.954 * [taylor]: Taking taylor expansion of 0.5 in k 15.954 * [backup-simplify]: Simplify 0.5 into 0.5 15.954 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 15.954 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.954 * [taylor]: Taking taylor expansion of k in k 15.954 * [backup-simplify]: Simplify 0 into 0 15.954 * [backup-simplify]: Simplify 1 into 1 15.955 * [backup-simplify]: Simplify (/ 1 1) into 1 15.955 * [taylor]: Taking taylor expansion of 1.0 in k 15.955 * [backup-simplify]: Simplify 1.0 into 1.0 15.955 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 15.955 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 15.955 * [taylor]: Taking taylor expansion of 2.0 in k 15.955 * [backup-simplify]: Simplify 2.0 into 2.0 15.955 * [taylor]: Taking taylor expansion of PI in k 15.955 * [backup-simplify]: Simplify PI into PI 15.955 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.956 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.956 * [backup-simplify]: Simplify (+ 1 0) into 1 15.956 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 15.957 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 15.958 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 15.958 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 15.958 * [taylor]: Taking taylor expansion of (/ -1 k) in k 15.958 * [taylor]: Taking taylor expansion of -1 in k 15.958 * [backup-simplify]: Simplify -1 into -1 15.958 * [taylor]: Taking taylor expansion of k in k 15.958 * [backup-simplify]: Simplify 0 into 0 15.958 * [backup-simplify]: Simplify 1 into 1 15.959 * [backup-simplify]: Simplify (/ -1 1) into -1 15.959 * [backup-simplify]: Simplify (sqrt 0) into 0 15.960 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 15.960 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) 15.960 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 15.960 * [taylor]: Taking taylor expansion of 1.0 in k 15.960 * [backup-simplify]: Simplify 1.0 into 1.0 15.960 * [taylor]: Taking taylor expansion of (/ (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 15.960 * [taylor]: Taking taylor expansion of (pow (* 2.0 PI) (* 0.5 (+ (/ 1 k) 1.0))) in k 15.961 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) in k 15.961 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI))) in k 15.961 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 15.961 * [taylor]: Taking taylor expansion of 0.5 in k 15.961 * [backup-simplify]: Simplify 0.5 into 0.5 15.961 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 15.961 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.961 * [taylor]: Taking taylor expansion of k in k 15.961 * [backup-simplify]: Simplify 0 into 0 15.961 * [backup-simplify]: Simplify 1 into 1 15.961 * [backup-simplify]: Simplify (/ 1 1) into 1 15.961 * [taylor]: Taking taylor expansion of 1.0 in k 15.961 * [backup-simplify]: Simplify 1.0 into 1.0 15.961 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 15.961 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 15.961 * [taylor]: Taking taylor expansion of 2.0 in k 15.961 * [backup-simplify]: Simplify 2.0 into 2.0 15.961 * [taylor]: Taking taylor expansion of PI in k 15.961 * [backup-simplify]: Simplify PI into PI 15.961 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.962 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.962 * [backup-simplify]: Simplify (+ 1 0) into 1 15.963 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 15.964 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 PI))) into (* 0.5 (log (* 2.0 PI))) 15.967 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 PI)))) into (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) 15.968 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 15.968 * [taylor]: Taking taylor expansion of (/ -1 k) in k 15.968 * [taylor]: Taking taylor expansion of -1 in k 15.968 * [backup-simplify]: Simplify -1 into -1 15.968 * [taylor]: Taking taylor expansion of k in k 15.968 * [backup-simplify]: Simplify 0 into 0 15.968 * [backup-simplify]: Simplify 1 into 1 15.968 * [backup-simplify]: Simplify (/ -1 1) into -1 15.968 * [backup-simplify]: Simplify (sqrt 0) into 0 15.969 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 15.970 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) 15.971 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) 15.971 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) 15.972 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 15.974 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 15.976 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 15.979 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 15.980 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 15.981 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.985 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 15.989 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 15.993 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 15.995 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 k) 1.0)))))) 15.999 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (/ 1 (- k))) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))))))))) 15.999 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 15.999 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 15.999 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 15.999 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 15.999 * [taylor]: Taking taylor expansion of 1.0 in k 15.999 * [backup-simplify]: Simplify 1.0 into 1.0 16.000 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 16.000 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.000 * [taylor]: Taking taylor expansion of k in k 16.000 * [backup-simplify]: Simplify 0 into 0 16.000 * [backup-simplify]: Simplify 1 into 1 16.000 * [backup-simplify]: Simplify (/ 1 1) into 1 16.000 * [backup-simplify]: Simplify (sqrt 0) into 0 16.002 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 16.002 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 16.002 * [taylor]: Taking taylor expansion of 1.0 in k 16.002 * [backup-simplify]: Simplify 1.0 into 1.0 16.002 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 16.002 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.002 * [taylor]: Taking taylor expansion of k in k 16.002 * [backup-simplify]: Simplify 0 into 0 16.002 * [backup-simplify]: Simplify 1 into 1 16.002 * [backup-simplify]: Simplify (/ 1 1) into 1 16.003 * [backup-simplify]: Simplify (sqrt 0) into 0 16.004 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 16.005 * [backup-simplify]: Simplify (* 1.0 0) into 0 16.005 * [backup-simplify]: Simplify 0 into 0 16.006 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 16.007 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 16.007 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 16.011 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 16.013 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 16.013 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 16.014 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.018 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 16.021 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 16.021 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 16.023 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 16.023 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 16.023 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 16.023 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 16.023 * [taylor]: Taking taylor expansion of 1.0 in k 16.023 * [backup-simplify]: Simplify 1.0 into 1.0 16.023 * [taylor]: Taking taylor expansion of (sqrt k) in k 16.023 * [taylor]: Taking taylor expansion of k in k 16.023 * [backup-simplify]: Simplify 0 into 0 16.023 * [backup-simplify]: Simplify 1 into 1 16.023 * [backup-simplify]: Simplify (sqrt 0) into 0 16.025 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 16.025 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 16.025 * [taylor]: Taking taylor expansion of 1.0 in k 16.025 * [backup-simplify]: Simplify 1.0 into 1.0 16.025 * [taylor]: Taking taylor expansion of (sqrt k) in k 16.025 * [taylor]: Taking taylor expansion of k in k 16.025 * [backup-simplify]: Simplify 0 into 0 16.025 * [backup-simplify]: Simplify 1 into 1 16.025 * [backup-simplify]: Simplify (sqrt 0) into 0 16.027 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 16.027 * [backup-simplify]: Simplify (* 1.0 0) into 0 16.027 * [backup-simplify]: Simplify 0 into 0 16.029 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 16.029 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 16.032 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 16.034 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 16.035 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 16.039 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 16.041 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 16.042 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 16.043 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 16.044 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 16.044 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 16.044 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 16.044 * [taylor]: Taking taylor expansion of 1.0 in k 16.044 * [backup-simplify]: Simplify 1.0 into 1.0 16.044 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 16.044 * [taylor]: Taking taylor expansion of (/ -1 k) in k 16.044 * [taylor]: Taking taylor expansion of -1 in k 16.044 * [backup-simplify]: Simplify -1 into -1 16.044 * [taylor]: Taking taylor expansion of k in k 16.044 * [backup-simplify]: Simplify 0 into 0 16.044 * [backup-simplify]: Simplify 1 into 1 16.044 * [backup-simplify]: Simplify (/ -1 1) into -1 16.045 * [backup-simplify]: Simplify (sqrt 0) into 0 16.046 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 16.047 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 16.047 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 16.047 * [taylor]: Taking taylor expansion of 1.0 in k 16.047 * [backup-simplify]: Simplify 1.0 into 1.0 16.047 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 16.047 * [taylor]: Taking taylor expansion of (/ -1 k) in k 16.047 * [taylor]: Taking taylor expansion of -1 in k 16.047 * [backup-simplify]: Simplify -1 into -1 16.047 * [taylor]: Taking taylor expansion of k in k 16.047 * [backup-simplify]: Simplify 0 into 0 16.047 * [backup-simplify]: Simplify 1 into 1 16.047 * [backup-simplify]: Simplify (/ -1 1) into -1 16.048 * [backup-simplify]: Simplify (sqrt 0) into 0 16.049 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 16.050 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 16.050 * [backup-simplify]: Simplify +nan.0 into +nan.0 16.051 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 16.054 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 16.057 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 16.057 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 16.059 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.063 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 16.067 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 16.068 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 16.069 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 16.069 * * * [progress]: simplifying candidates 16.074 * [simplify]: Simplifying: (* (+ (log 2.0) (log PI)) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ 1.0 2.0)) (pow (* 2.0 PI) (/ k 2.0)) (pow (* 2.0 PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* 2.0 PI) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 PI) (/ (sqrt (- 1.0 k)) 1)) (pow (* 2.0 PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ 1 (sqrt 2.0))) (pow (* 2.0 PI) (/ 1 1)) (pow (* 2.0 PI) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 PI) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* 2.0 PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ 1 (sqrt 2.0))) (pow (* 2.0 PI) (/ 1 1)) (pow (* 2.0 PI) 1) (pow (* 2.0 PI) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (log (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (exp (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (* (log n) (/ (- 1.0 k) 2.0)) (* (log n) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow n (/ 1.0 2.0)) (pow n (/ k 2.0)) (pow n (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow n (sqrt (/ (- 1.0 k) 2.0))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow n (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow n (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow n (/ (sqrt (- 1.0 k)) 1)) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) (pow n (/ 1 1)) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) (pow n (/ 1 1)) (pow n 1) (pow n (- 1.0 k)) (pow (* (cbrt n) (cbrt n)) (/ (- 1.0 k) 2.0)) (pow (cbrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) (pow 1 (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow n (/ (- 1.0 k) 2.0))) (exp (pow n (/ (- 1.0 k) 2.0))) (* (cbrt (pow n (/ (- 1.0 k) 2.0))) (cbrt (pow n (/ (- 1.0 k) 2.0)))) (cbrt (pow n (/ (- 1.0 k) 2.0))) (* (* (pow n (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log 2.0) (log PI)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log 2.0) (log PI)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* 2.0 PI)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (log (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* 2.0 PI) (/ 1.0 2.0))) (* (sqrt k) (pow (* 2.0 PI) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) 1) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ 1.0 2.0))) (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (- (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (pow (* 2.0 PI) 0.5)) (* 0.5 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (* (log (* 2.0 PI)) k)))) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (- (+ (* 0.125 (* (pow (pow n 1.0) 0.5) (* (pow (log n) 2) (pow k 2)))) (pow n 0.5)) (* 0.5 (* (pow (pow n 1.0) 0.5) (* (log n) k)))) (exp (* -0.5 (* (- 1.0 k) (log (/ 1 n))))) (exp (* 0.5 (* (- (log -1) (log (/ -1 n))) (- 1.0 k)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) (pow k 2))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (pow PI 1.0)) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* (log (* 2.0 PI)) k)))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (pow k 3))) (- (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 PI)) (- 1.0 k)))))))))) (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 16.080 * * [simplify]: iteration 0: 326 enodes 16.224 * * [simplify]: iteration 1: 903 enodes 16.705 * * [simplify]: iteration 2: 3733 enodes 17.549 * * [simplify]: iteration complete: 5000 enodes 17.549 * * [simplify]: Extracting #0: cost 139 inf + 0 17.551 * * [simplify]: Extracting #1: cost 925 inf + 3 17.556 * * [simplify]: Extracting #2: cost 1492 inf + 8304 17.568 * * [simplify]: Extracting #3: cost 1605 inf + 75487 17.617 * * [simplify]: Extracting #4: cost 919 inf + 296488 17.705 * * [simplify]: Extracting #5: cost 433 inf + 487435 17.801 * * [simplify]: Extracting #6: cost 232 inf + 575515 17.898 * * [simplify]: Extracting #7: cost 50 inf + 689531 18.034 * * [simplify]: Extracting #8: cost 4 inf + 726681 18.194 * * [simplify]: Extracting #9: cost 0 inf + 731705 18.283 * [simplify]: Simplified to: (/ (log (* 2.0 PI)) (/ 2.0 (- 1.0 k))) (/ (log (* 2.0 PI)) (/ 2.0 (- 1.0 k))) (/ (log (* 2.0 PI)) (/ 2.0 (- 1.0 k))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* 2.0 PI) (/ 1.0 2.0)) (pow (* 2.0 PI) (/ k 2.0)) (pow (* 2.0 PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* 2.0 PI) (/ (cbrt (- 1.0 k)) (/ (sqrt 2.0) (cbrt (- 1.0 k))))) (pow (* 2.0 PI) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* 2.0 PI) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0))) (pow (* 2.0 PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 PI) (sqrt (- 1.0 k))) (pow (* 2.0 PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ 1 (sqrt 2.0))) (* 2.0 PI) (pow (* 2.0 PI) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 PI) (+ (sqrt 1.0) (sqrt k))) (pow (* 2.0 PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 PI) (/ 1 (sqrt 2.0))) (* 2.0 PI) (* 2.0 PI) (exp (* (log (* 2.0 PI)) (- 1.0 k))) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (/ (log (* 2.0 PI)) (/ 2.0 (- 1.0 k))) (exp (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2) 2.0)) (* (/ (- 1.0 k) 2.0) (log n)) (* (/ (- 1.0 k) 2.0) (log n)) (/ (- 1.0 k) 2.0) (pow n (/ 1.0 2.0)) (pow n (/ k 2.0)) (pow n (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow n (sqrt (/ (- 1.0 k) 2.0))) (pow n (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow n (/ (cbrt (- 1.0 k)) (/ (sqrt 2.0) (cbrt (- 1.0 k))))) (pow n (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow n (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0))) (pow n (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow n (sqrt (- 1.0 k))) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) n (pow n (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow n (+ (sqrt 1.0) (sqrt k))) (pow n (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow n (/ 1 (sqrt 2.0))) n n (pow n (- 1.0 k)) (pow (* (cbrt n) (cbrt n)) (/ (- 1.0 k) 2.0)) (pow (cbrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)) 1 (pow n (/ (- 1.0 k) 2.0)) (* (/ (- 1.0 k) 2.0) (log n)) (exp (pow n (/ (- 1.0 k) 2.0))) (* (cbrt (pow n (/ (- 1.0 k) 2.0))) (cbrt (pow n (/ (- 1.0 k) 2.0)))) (cbrt (pow n (/ (- 1.0 k) 2.0))) (* (pow n (/ (- 1.0 k) 2.0)) (* (pow n (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (sqrt (pow n (/ (- 1.0 k) 2.0))) (pow n (/ (/ (- 1.0 k) 2) 2.0)) (pow n (/ (/ (- 1.0 k) 2) 2.0)) (+ (/ (log (* 2.0 PI)) (/ 2.0 (- 1.0 k))) (log (/ 1.0 (sqrt k)))) (+ (/ (log (* 2.0 PI)) (/ 2.0 (- 1.0 k))) (log (/ 1.0 (sqrt k)))) (+ (/ (log (* 2.0 PI)) (/ 2.0 (- 1.0 k))) (log (/ 1.0 (sqrt k)))) (+ (/ (log (* 2.0 PI)) (/ 2.0 (- 1.0 k))) (log (/ 1.0 (sqrt k)))) (+ (/ (log (* 2.0 PI)) (/ 2.0 (- 1.0 k))) (log (/ 1.0 (sqrt k)))) (+ (/ (log (* 2.0 PI)) (/ 2.0 (- 1.0 k))) (log (/ 1.0 (sqrt k)))) (+ (/ (log (* 2.0 PI)) (/ 2.0 (- 1.0 k))) (log (/ 1.0 (sqrt k)))) (+ (/ (log (* 2.0 PI)) (/ 2.0 (- 1.0 k))) (log (/ 1.0 (sqrt k)))) (+ (/ (log (* 2.0 PI)) (/ 2.0 (- 1.0 k))) (log (/ 1.0 (sqrt k)))) (exp (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (/ (* 1.0 1.0) k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (pow (* 2.0 PI) (/ 1.0 2.0)) 1.0) (* (pow (* 2.0 PI) (/ k 2.0)) (sqrt k)) (* (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k)))) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2) 2.0))) (* (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2) 2.0))) (/ (* (pow 2.0 (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (* (* (/ 1.0 (sqrt k)) (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (/ (* 1.0 (sqrt (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (sqrt k)) (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2) 2.0))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (cbrt (sqrt k)))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (cbrt (sqrt k))) (/ (sqrt 1.0) (/ (sqrt (cbrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt k)) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt k)) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (/ 1.0 (cbrt (sqrt k)))) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (cbrt k)))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (sqrt k)) (/ 1.0 (/ (sqrt k) (pow (* 2.0 PI) (/ 1.0 2.0)))) (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (* (/ 1.0 (sqrt k)) (/ (* 1.0 1.0) k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (* (/ (cbrt 1.0) (fabs (cbrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (+ (exp (* (log (* 2.0 PI)) 0.5)) (- (* (* (* (log (* 2.0 PI)) k) (* (log (* 2.0 PI)) k)) (* 0.125 (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5))) (* (* 0.5 (* (log (* 2.0 PI)) k)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)))) (exp (* (* (log (* 2.0 PI)) (- 1.0 k)) 0.5)) (exp (* (* (log (* 2.0 PI)) (- 1.0 k)) 0.5)) (+ (pow n 0.5) (- (* (pow (pow n 1.0) 0.5) (* (* (* (log n) k) (* (log n) k)) 0.125)) (* (* (* (pow (pow n 1.0) 0.5) 0.5) (log n)) k))) (exp (* (* -0.5 (- (log n))) (- 1.0 k))) (exp (* (* 0.5 (- 1.0 k)) (+ (- (log -1) (log -1)) (log n)))) (+ (+ (- (* (* +nan.0 (* k k)) (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5)) (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) +nan.0)) (- (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) (* k +nan.0)) (* (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) +nan.0) (- (* (* k k) (log (* 2.0 PI))) (* (log (* 2.0 PI)) k))))) (* (* (pow (* (pow PI 1.0) (pow 2.0 1.0)) 0.5) +nan.0) (- (* (* (log (* 2.0 PI)) k) (* (log (* 2.0 PI)) k))))) (- (- (* +nan.0 (/ (exp (* (* (log (* 2.0 PI)) (- 1.0 k)) 0.5)) k)) (- (* (/ +nan.0 (* k k)) (/ (exp (* (* (log (* 2.0 PI)) (- 1.0 k)) 0.5)) k)) (/ (* (exp (* (* (log (* 2.0 PI)) (- 1.0 k)) 0.5)) +nan.0) (* k k))))) (+ (* (/ (exp (* (* (log (* 2.0 PI)) (- 1.0 k)) 0.5)) k) (- +nan.0)) (- (/ (* (exp (* (* (log (* 2.0 PI)) (- 1.0 k)) 0.5)) +nan.0) (* k k)) (* (exp (* (* (log (* 2.0 PI)) (- 1.0 k)) 0.5)) +nan.0))) (+ (* (* k k) (- +nan.0)) (- +nan.0 (* k +nan.0))) (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ (/ +nan.0 k) (* k k)))) (+ (- (/ +nan.0 k) +nan.0) (/ (- +nan.0) (* k k))) 18.296 * * * [progress]: adding candidates to table 19.467 * [progress]: [Phase 3 of 3] Extracting. 19.467 * * [regime]: Finding splitpoints for: (# # # # # # # # #) 19.469 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 19.469 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # # #) 19.555 * * * * [regimes]: Trying to branch on n from (# # # # # # # # #) 19.658 * * * * [regimes]: Trying to branch on k from (# # # # # # # # #) 19.768 * * * [regime]: Found split indices: #