10.230 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.073 * * * [progress]: [2/2] Setting up program. 0.075 * [progress]: [Phase 2 of 3] Improving. 0.076 * [simplify]: Simplifying using # : (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.076 * [simplify]: Sending expressions to egg_math: (* (/ h0 (sqrt h1)) (pow (* (* h2 PI) h3) (/ (- h0 h1) h2))) 0.078 * * [simplify]: iteration 0 : 29 enodes (cost 8 ) 0.080 * * [simplify]: iteration 1 : 59 enodes (cost 8 ) 0.081 * * [simplify]: iteration 2 : 119 enodes (cost 8 ) 0.084 * * [simplify]: iteration 3 : 325 enodes (cost 8 ) 0.090 * * [simplify]: iteration 4 : 1044 enodes (cost 8 ) 0.113 * * [simplify]: iteration 5 : 5001 enodes (cost 8 ) 0.113 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.114 * * [progress]: iteration 1 / 4 0.114 * * * [progress]: picking best candidate 0.116 * * * * [pick]: Picked # 0.116 * * * [progress]: localizing error 0.134 * * * [progress]: generating rewritten candidates 0.134 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.155 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 0.171 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.177 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.222 * * * [progress]: generating series expansions 0.222 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.223 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 0.223 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.223 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.223 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.223 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.223 * [taylor]: Taking taylor expansion of 0.5 in k 0.223 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.223 * [taylor]: Taking taylor expansion of 1.0 in k 0.223 * [taylor]: Taking taylor expansion of k in k 0.223 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.224 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.224 * [taylor]: Taking taylor expansion of 2.0 in k 0.224 * [taylor]: Taking taylor expansion of (* n PI) in k 0.224 * [taylor]: Taking taylor expansion of n in k 0.224 * [taylor]: Taking taylor expansion of PI in k 0.224 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.224 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.225 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.225 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.225 * [taylor]: Taking taylor expansion of 0.5 in n 0.225 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.225 * [taylor]: Taking taylor expansion of 1.0 in n 0.225 * [taylor]: Taking taylor expansion of k in n 0.225 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.225 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.225 * [taylor]: Taking taylor expansion of 2.0 in n 0.225 * [taylor]: Taking taylor expansion of (* n PI) in n 0.225 * [taylor]: Taking taylor expansion of n in n 0.225 * [taylor]: Taking taylor expansion of PI in n 0.230 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.230 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.230 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.230 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.230 * [taylor]: Taking taylor expansion of 0.5 in n 0.230 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.230 * [taylor]: Taking taylor expansion of 1.0 in n 0.230 * [taylor]: Taking taylor expansion of k in n 0.230 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.230 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.230 * [taylor]: Taking taylor expansion of 2.0 in n 0.230 * [taylor]: Taking taylor expansion of (* n PI) in n 0.230 * [taylor]: Taking taylor expansion of n in n 0.230 * [taylor]: Taking taylor expansion of PI in n 0.235 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.235 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.235 * [taylor]: Taking taylor expansion of 0.5 in k 0.235 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.235 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.235 * [taylor]: Taking taylor expansion of 1.0 in k 0.235 * [taylor]: Taking taylor expansion of k in k 0.235 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.235 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.235 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.235 * [taylor]: Taking taylor expansion of 2.0 in k 0.235 * [taylor]: Taking taylor expansion of PI in k 0.236 * [taylor]: Taking taylor expansion of (log n) in k 0.236 * [taylor]: Taking taylor expansion of n in k 0.244 * [taylor]: Taking taylor expansion of 0 in k 0.259 * [taylor]: Taking taylor expansion of 0 in k 0.281 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.281 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.281 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.281 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.281 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.281 * [taylor]: Taking taylor expansion of 0.5 in k 0.281 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.281 * [taylor]: Taking taylor expansion of 1.0 in k 0.281 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.281 * [taylor]: Taking taylor expansion of k in k 0.282 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.282 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.282 * [taylor]: Taking taylor expansion of 2.0 in k 0.282 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.282 * [taylor]: Taking taylor expansion of PI in k 0.282 * [taylor]: Taking taylor expansion of n in k 0.283 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.283 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.283 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.283 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.283 * [taylor]: Taking taylor expansion of 0.5 in n 0.283 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.283 * [taylor]: Taking taylor expansion of 1.0 in n 0.283 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.283 * [taylor]: Taking taylor expansion of k in n 0.283 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.283 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.283 * [taylor]: Taking taylor expansion of 2.0 in n 0.283 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.283 * [taylor]: Taking taylor expansion of PI in n 0.283 * [taylor]: Taking taylor expansion of n in n 0.286 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.286 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.286 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.286 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.286 * [taylor]: Taking taylor expansion of 0.5 in n 0.286 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.286 * [taylor]: Taking taylor expansion of 1.0 in n 0.286 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.286 * [taylor]: Taking taylor expansion of k in n 0.286 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.286 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.286 * [taylor]: Taking taylor expansion of 2.0 in n 0.286 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.286 * [taylor]: Taking taylor expansion of PI in n 0.286 * [taylor]: Taking taylor expansion of n in n 0.290 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.290 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.290 * [taylor]: Taking taylor expansion of 0.5 in k 0.290 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.290 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.290 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.290 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.290 * [taylor]: Taking taylor expansion of 2.0 in k 0.290 * [taylor]: Taking taylor expansion of PI in k 0.291 * [taylor]: Taking taylor expansion of (log n) in k 0.291 * [taylor]: Taking taylor expansion of n in k 0.291 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.291 * [taylor]: Taking taylor expansion of 1.0 in k 0.291 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.291 * [taylor]: Taking taylor expansion of k in k 0.300 * [taylor]: Taking taylor expansion of 0 in k 0.306 * [taylor]: Taking taylor expansion of 0 in k 0.315 * [taylor]: Taking taylor expansion of 0 in k 0.316 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.316 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.316 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.316 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.316 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.316 * [taylor]: Taking taylor expansion of 0.5 in k 0.316 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.316 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.316 * [taylor]: Taking taylor expansion of k in k 0.316 * [taylor]: Taking taylor expansion of 1.0 in k 0.316 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.316 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.316 * [taylor]: Taking taylor expansion of -2.0 in k 0.316 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.316 * [taylor]: Taking taylor expansion of PI in k 0.316 * [taylor]: Taking taylor expansion of n in k 0.317 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.317 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.317 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.317 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.317 * [taylor]: Taking taylor expansion of 0.5 in n 0.317 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.317 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.317 * [taylor]: Taking taylor expansion of k in n 0.317 * [taylor]: Taking taylor expansion of 1.0 in n 0.317 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.317 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.317 * [taylor]: Taking taylor expansion of -2.0 in n 0.317 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.317 * [taylor]: Taking taylor expansion of PI in n 0.317 * [taylor]: Taking taylor expansion of n in n 0.321 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.321 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.321 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.321 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.321 * [taylor]: Taking taylor expansion of 0.5 in n 0.321 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.321 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.321 * [taylor]: Taking taylor expansion of k in n 0.321 * [taylor]: Taking taylor expansion of 1.0 in n 0.321 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.321 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.321 * [taylor]: Taking taylor expansion of -2.0 in n 0.321 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.321 * [taylor]: Taking taylor expansion of PI in n 0.321 * [taylor]: Taking taylor expansion of n in n 0.325 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 0.325 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 0.325 * [taylor]: Taking taylor expansion of 0.5 in k 0.325 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 0.325 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.325 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.325 * [taylor]: Taking taylor expansion of k in k 0.325 * [taylor]: Taking taylor expansion of 1.0 in k 0.325 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 0.325 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 0.325 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 0.325 * [taylor]: Taking taylor expansion of -2.0 in k 0.325 * [taylor]: Taking taylor expansion of PI in k 0.326 * [taylor]: Taking taylor expansion of (log n) in k 0.326 * [taylor]: Taking taylor expansion of n in k 0.334 * [taylor]: Taking taylor expansion of 0 in k 0.341 * [taylor]: Taking taylor expansion of 0 in k 0.354 * [taylor]: Taking taylor expansion of 0 in k 0.355 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 0.355 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.355 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.355 * [taylor]: Taking taylor expansion of 2.0 in n 0.355 * [taylor]: Taking taylor expansion of (* n PI) in n 0.355 * [taylor]: Taking taylor expansion of n in n 0.356 * [taylor]: Taking taylor expansion of PI in n 0.356 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.356 * [taylor]: Taking taylor expansion of 2.0 in n 0.356 * [taylor]: Taking taylor expansion of (* n PI) in n 0.356 * [taylor]: Taking taylor expansion of n in n 0.356 * [taylor]: Taking taylor expansion of PI in n 0.367 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 0.367 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.367 * [taylor]: Taking taylor expansion of 2.0 in n 0.367 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.367 * [taylor]: Taking taylor expansion of PI in n 0.367 * [taylor]: Taking taylor expansion of n in n 0.367 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.367 * [taylor]: Taking taylor expansion of 2.0 in n 0.367 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.367 * [taylor]: Taking taylor expansion of PI in n 0.367 * [taylor]: Taking taylor expansion of n in n 0.375 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.376 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.376 * [taylor]: Taking taylor expansion of -2.0 in n 0.376 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.376 * [taylor]: Taking taylor expansion of PI in n 0.376 * [taylor]: Taking taylor expansion of n in n 0.376 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.376 * [taylor]: Taking taylor expansion of -2.0 in n 0.376 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.376 * [taylor]: Taking taylor expansion of PI in n 0.376 * [taylor]: Taking taylor expansion of n in n 0.384 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 0.384 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.384 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.384 * [taylor]: Taking taylor expansion of 1.0 in k 0.384 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.384 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.384 * [taylor]: Taking taylor expansion of k in k 0.386 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.386 * [taylor]: Taking taylor expansion of 1.0 in k 0.386 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.386 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.386 * [taylor]: Taking taylor expansion of k in k 0.396 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 0.396 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.396 * [taylor]: Taking taylor expansion of 1.0 in k 0.396 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.396 * [taylor]: Taking taylor expansion of k in k 0.397 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.397 * [taylor]: Taking taylor expansion of 1.0 in k 0.397 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.397 * [taylor]: Taking taylor expansion of k in k 0.406 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.406 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.406 * [taylor]: Taking taylor expansion of 1.0 in k 0.406 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.406 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.406 * [taylor]: Taking taylor expansion of -1 in k 0.406 * [taylor]: Taking taylor expansion of k in k 0.407 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.407 * [taylor]: Taking taylor expansion of 1.0 in k 0.407 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.407 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.407 * [taylor]: Taking taylor expansion of -1 in k 0.407 * [taylor]: Taking taylor expansion of k in k 0.418 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.419 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0 0.419 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 0.419 * [taylor]: Taking taylor expansion of 1.0 in n 0.419 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 0.419 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.419 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.419 * [taylor]: Taking taylor expansion of k in n 0.419 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.419 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.419 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.419 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.419 * [taylor]: Taking taylor expansion of 0.5 in n 0.419 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.419 * [taylor]: Taking taylor expansion of 1.0 in n 0.419 * [taylor]: Taking taylor expansion of k in n 0.419 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.419 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.419 * [taylor]: Taking taylor expansion of 2.0 in n 0.419 * [taylor]: Taking taylor expansion of (* n PI) in n 0.419 * [taylor]: Taking taylor expansion of n in n 0.419 * [taylor]: Taking taylor expansion of PI in n 0.424 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.424 * [taylor]: Taking taylor expansion of 1.0 in k 0.424 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.424 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.424 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.424 * [taylor]: Taking taylor expansion of k in k 0.425 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.425 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.425 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.425 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.425 * [taylor]: Taking taylor expansion of 0.5 in k 0.425 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.425 * [taylor]: Taking taylor expansion of 1.0 in k 0.425 * [taylor]: Taking taylor expansion of k in k 0.425 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.425 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.425 * [taylor]: Taking taylor expansion of 2.0 in k 0.425 * [taylor]: Taking taylor expansion of (* n PI) in k 0.425 * [taylor]: Taking taylor expansion of n in k 0.425 * [taylor]: Taking taylor expansion of PI in k 0.426 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.426 * [taylor]: Taking taylor expansion of 1.0 in k 0.426 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.426 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.426 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.426 * [taylor]: Taking taylor expansion of k in k 0.427 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.427 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.427 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.427 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.427 * [taylor]: Taking taylor expansion of 0.5 in k 0.427 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.427 * [taylor]: Taking taylor expansion of 1.0 in k 0.427 * [taylor]: Taking taylor expansion of k in k 0.427 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.427 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.427 * [taylor]: Taking taylor expansion of 2.0 in k 0.427 * [taylor]: Taking taylor expansion of (* n PI) in k 0.427 * [taylor]: Taking taylor expansion of n in k 0.428 * [taylor]: Taking taylor expansion of PI in k 0.429 * [taylor]: Taking taylor expansion of 0 in n 0.439 * [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 0.439 * [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 0.439 * [taylor]: Taking taylor expansion of +nan.0 in n 0.439 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.439 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.439 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.439 * [taylor]: Taking taylor expansion of 0.5 in n 0.439 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.439 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.439 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.439 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.439 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.439 * [taylor]: Taking taylor expansion of 1.0 in n 0.439 * [taylor]: Taking taylor expansion of (log PI) in n 0.439 * [taylor]: Taking taylor expansion of PI in n 0.441 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.441 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.441 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.441 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.441 * [taylor]: Taking taylor expansion of 1.0 in n 0.441 * [taylor]: Taking taylor expansion of (log n) in n 0.441 * [taylor]: Taking taylor expansion of n in n 0.442 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.442 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.442 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.442 * [taylor]: Taking taylor expansion of 1.0 in n 0.442 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.442 * [taylor]: Taking taylor expansion of 2.0 in n 0.460 * [taylor]: Taking taylor expansion of (- (+ (* +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 PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) in n 0.460 * [taylor]: Taking taylor expansion of (+ (* +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 PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))) in n 0.460 * [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 0.460 * [taylor]: Taking taylor expansion of +nan.0 in n 0.460 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.460 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.460 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.460 * [taylor]: Taking taylor expansion of 0.5 in n 0.460 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.460 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.460 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.460 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.460 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.460 * [taylor]: Taking taylor expansion of 1.0 in n 0.460 * [taylor]: Taking taylor expansion of (log PI) in n 0.460 * [taylor]: Taking taylor expansion of PI in n 0.462 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.462 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.462 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.462 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.462 * [taylor]: Taking taylor expansion of 1.0 in n 0.462 * [taylor]: Taking taylor expansion of (log n) in n 0.462 * [taylor]: Taking taylor expansion of n in n 0.462 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.463 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.463 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.463 * [taylor]: Taking taylor expansion of 1.0 in n 0.463 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.463 * [taylor]: Taking taylor expansion of 2.0 in n 0.467 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))) in n 0.467 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 0.467 * [taylor]: Taking taylor expansion of +nan.0 in n 0.467 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 0.467 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.467 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.468 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.468 * [taylor]: Taking taylor expansion of 0.5 in n 0.468 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.468 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.468 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.468 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.468 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.468 * [taylor]: Taking taylor expansion of 1.0 in n 0.468 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.468 * [taylor]: Taking taylor expansion of 2.0 in n 0.469 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.469 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.469 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.469 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.469 * [taylor]: Taking taylor expansion of 1.0 in n 0.469 * [taylor]: Taking taylor expansion of (log PI) in n 0.469 * [taylor]: Taking taylor expansion of PI in n 0.471 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.471 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.471 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.471 * [taylor]: Taking taylor expansion of 1.0 in n 0.471 * [taylor]: Taking taylor expansion of (log n) in n 0.471 * [taylor]: Taking taylor expansion of n in n 0.475 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.475 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.475 * [taylor]: Taking taylor expansion of 2.0 in n 0.475 * [taylor]: Taking taylor expansion of (* n PI) in n 0.475 * [taylor]: Taking taylor expansion of n in n 0.475 * [taylor]: Taking taylor expansion of PI in n 0.522 * [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 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n 0.522 * [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 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n 0.522 * [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 0.522 * [taylor]: Taking taylor expansion of +nan.0 in n 0.522 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 0.522 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 0.522 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 0.522 * [taylor]: Taking taylor expansion of 0.5 in n 0.522 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 0.522 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 0.522 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.522 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.522 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.523 * [taylor]: Taking taylor expansion of 1.0 in n 0.523 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.523 * [taylor]: Taking taylor expansion of 2.0 in n 0.524 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 0.524 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.524 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.524 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.524 * [taylor]: Taking taylor expansion of 1.0 in n 0.524 * [taylor]: Taking taylor expansion of (log n) in n 0.524 * [taylor]: Taking taylor expansion of n in n 0.525 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.525 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.525 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.525 * [taylor]: Taking taylor expansion of 1.0 in n 0.525 * [taylor]: Taking taylor expansion of (log PI) in n 0.525 * [taylor]: Taking taylor expansion of PI in n 0.536 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n 0.536 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n 0.536 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 0.536 * [taylor]: Taking taylor expansion of +nan.0 in n 0.536 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 0.536 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.536 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.536 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.536 * [taylor]: Taking taylor expansion of 0.5 in n 0.536 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.536 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.536 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.536 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.536 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.536 * [taylor]: Taking taylor expansion of 1.0 in n 0.536 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.536 * [taylor]: Taking taylor expansion of 2.0 in n 0.538 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.538 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.538 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.538 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.538 * [taylor]: Taking taylor expansion of 1.0 in n 0.538 * [taylor]: Taking taylor expansion of (log PI) in n 0.538 * [taylor]: Taking taylor expansion of PI in n 0.539 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.539 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.539 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.539 * [taylor]: Taking taylor expansion of 1.0 in n 0.539 * [taylor]: Taking taylor expansion of (log n) in n 0.539 * [taylor]: Taking taylor expansion of n in n 0.543 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.543 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.543 * [taylor]: Taking taylor expansion of 2.0 in n 0.543 * [taylor]: Taking taylor expansion of (* n PI) in n 0.543 * [taylor]: Taking taylor expansion of n in n 0.543 * [taylor]: Taking taylor expansion of PI in n 0.546 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n 0.546 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n 0.546 * [taylor]: Taking taylor expansion of +nan.0 in n 0.546 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 0.546 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.546 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.546 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.546 * [taylor]: Taking taylor expansion of 0.5 in n 0.546 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.546 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.546 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.546 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.546 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.546 * [taylor]: Taking taylor expansion of 1.0 in n 0.546 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.546 * [taylor]: Taking taylor expansion of 2.0 in n 0.548 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.548 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.548 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.548 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.548 * [taylor]: Taking taylor expansion of 1.0 in n 0.548 * [taylor]: Taking taylor expansion of (log PI) in n 0.548 * [taylor]: Taking taylor expansion of PI in n 0.550 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.550 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.550 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.550 * [taylor]: Taking taylor expansion of 1.0 in n 0.550 * [taylor]: Taking taylor expansion of (log n) in n 0.550 * [taylor]: Taking taylor expansion of n in n 0.553 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 0.553 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.554 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.554 * [taylor]: Taking taylor expansion of 2.0 in n 0.554 * [taylor]: Taking taylor expansion of (* n PI) in n 0.554 * [taylor]: Taking taylor expansion of n in n 0.554 * [taylor]: Taking taylor expansion of PI in n 0.628 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0 0.628 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 0.628 * [taylor]: Taking taylor expansion of 1.0 in n 0.628 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 0.629 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.629 * [taylor]: Taking taylor expansion of k in n 0.629 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.629 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.629 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.629 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.629 * [taylor]: Taking taylor expansion of 0.5 in n 0.629 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.629 * [taylor]: Taking taylor expansion of 1.0 in n 0.629 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.629 * [taylor]: Taking taylor expansion of k in n 0.629 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.629 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.629 * [taylor]: Taking taylor expansion of 2.0 in n 0.629 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.629 * [taylor]: Taking taylor expansion of PI in n 0.629 * [taylor]: Taking taylor expansion of n in n 0.632 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.632 * [taylor]: Taking taylor expansion of 1.0 in k 0.632 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.632 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.632 * [taylor]: Taking taylor expansion of k in k 0.633 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.633 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.633 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.633 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.633 * [taylor]: Taking taylor expansion of 0.5 in k 0.633 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.634 * [taylor]: Taking taylor expansion of 1.0 in k 0.634 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.634 * [taylor]: Taking taylor expansion of k in k 0.634 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.634 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.634 * [taylor]: Taking taylor expansion of 2.0 in k 0.634 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.634 * [taylor]: Taking taylor expansion of PI in k 0.634 * [taylor]: Taking taylor expansion of n in k 0.635 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 0.635 * [taylor]: Taking taylor expansion of 1.0 in k 0.635 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 0.635 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.635 * [taylor]: Taking taylor expansion of k in k 0.636 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.636 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.636 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.636 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.636 * [taylor]: Taking taylor expansion of 0.5 in k 0.636 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.636 * [taylor]: Taking taylor expansion of 1.0 in k 0.636 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.636 * [taylor]: Taking taylor expansion of k in k 0.636 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.636 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.636 * [taylor]: Taking taylor expansion of 2.0 in k 0.636 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.636 * [taylor]: Taking taylor expansion of PI in k 0.636 * [taylor]: Taking taylor expansion of n in k 0.638 * [taylor]: Taking taylor expansion of 0 in n 0.638 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.638 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.638 * [taylor]: Taking taylor expansion of +nan.0 in n 0.638 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.638 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.638 * [taylor]: Taking taylor expansion of 0.5 in n 0.638 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.638 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.639 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.639 * [taylor]: Taking taylor expansion of 2.0 in n 0.639 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.639 * [taylor]: Taking taylor expansion of PI in n 0.639 * [taylor]: Taking taylor expansion of n in n 0.640 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.640 * [taylor]: Taking taylor expansion of 1.0 in n 0.640 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.640 * [taylor]: Taking taylor expansion of k in n 0.648 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.648 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.648 * [taylor]: Taking taylor expansion of +nan.0 in n 0.648 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.648 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.648 * [taylor]: Taking taylor expansion of 0.5 in n 0.648 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.648 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.648 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.648 * [taylor]: Taking taylor expansion of 2.0 in n 0.648 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.648 * [taylor]: Taking taylor expansion of PI in n 0.648 * [taylor]: Taking taylor expansion of n in n 0.649 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.649 * [taylor]: Taking taylor expansion of 1.0 in n 0.649 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.649 * [taylor]: Taking taylor expansion of k in n 0.664 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 0.664 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 0.664 * [taylor]: Taking taylor expansion of +nan.0 in n 0.664 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 0.664 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 0.664 * [taylor]: Taking taylor expansion of 0.5 in n 0.664 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 0.664 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.664 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.664 * [taylor]: Taking taylor expansion of 2.0 in n 0.664 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.664 * [taylor]: Taking taylor expansion of PI in n 0.664 * [taylor]: Taking taylor expansion of n in n 0.665 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.665 * [taylor]: Taking taylor expansion of 1.0 in n 0.665 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.665 * [taylor]: Taking taylor expansion of k in n 0.673 * [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 0.674 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 0.674 * [taylor]: Taking taylor expansion of 1.0 in n 0.674 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 0.674 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.674 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.674 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.674 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.674 * [taylor]: Taking taylor expansion of 0.5 in n 0.674 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.674 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.674 * [taylor]: Taking taylor expansion of k in n 0.674 * [taylor]: Taking taylor expansion of 1.0 in n 0.674 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.674 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.674 * [taylor]: Taking taylor expansion of -2.0 in n 0.674 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.674 * [taylor]: Taking taylor expansion of PI in n 0.674 * [taylor]: Taking taylor expansion of n in n 0.677 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.677 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.677 * [taylor]: Taking taylor expansion of -1 in n 0.677 * [taylor]: Taking taylor expansion of k in n 0.678 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.678 * [taylor]: Taking taylor expansion of 1.0 in k 0.678 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.678 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.678 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.678 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.678 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.678 * [taylor]: Taking taylor expansion of 0.5 in k 0.678 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.678 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.678 * [taylor]: Taking taylor expansion of k in k 0.678 * [taylor]: Taking taylor expansion of 1.0 in k 0.679 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.679 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.679 * [taylor]: Taking taylor expansion of -2.0 in k 0.679 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.679 * [taylor]: Taking taylor expansion of PI in k 0.679 * [taylor]: Taking taylor expansion of n in k 0.679 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.679 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.679 * [taylor]: Taking taylor expansion of -1 in k 0.679 * [taylor]: Taking taylor expansion of k in k 0.681 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 0.681 * [taylor]: Taking taylor expansion of 1.0 in k 0.681 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 0.681 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.681 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.681 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.681 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.681 * [taylor]: Taking taylor expansion of 0.5 in k 0.681 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.681 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.681 * [taylor]: Taking taylor expansion of k in k 0.681 * [taylor]: Taking taylor expansion of 1.0 in k 0.681 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.681 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.681 * [taylor]: Taking taylor expansion of -2.0 in k 0.681 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.681 * [taylor]: Taking taylor expansion of PI in k 0.681 * [taylor]: Taking taylor expansion of n in k 0.682 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.682 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.682 * [taylor]: Taking taylor expansion of -1 in k 0.682 * [taylor]: Taking taylor expansion of k in k 0.683 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.683 * [taylor]: Taking taylor expansion of +nan.0 in n 0.683 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.683 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.684 * [taylor]: Taking taylor expansion of 0.5 in n 0.684 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.684 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.684 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.684 * [taylor]: Taking taylor expansion of k in n 0.684 * [taylor]: Taking taylor expansion of 1.0 in n 0.684 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.684 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.684 * [taylor]: Taking taylor expansion of -2.0 in n 0.684 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.684 * [taylor]: Taking taylor expansion of PI in n 0.684 * [taylor]: Taking taylor expansion of n in n 0.692 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.692 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.692 * [taylor]: Taking taylor expansion of +nan.0 in n 0.692 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.692 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.692 * [taylor]: Taking taylor expansion of 0.5 in n 0.692 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.692 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.692 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.692 * [taylor]: Taking taylor expansion of k in n 0.692 * [taylor]: Taking taylor expansion of 1.0 in n 0.692 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.692 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.692 * [taylor]: Taking taylor expansion of -2.0 in n 0.692 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.692 * [taylor]: Taking taylor expansion of PI in n 0.693 * [taylor]: Taking taylor expansion of n in n 0.716 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 0.716 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 0.716 * [taylor]: Taking taylor expansion of +nan.0 in n 0.716 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 0.716 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 0.716 * [taylor]: Taking taylor expansion of 0.5 in n 0.716 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 0.716 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.716 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.716 * [taylor]: Taking taylor expansion of k in n 0.716 * [taylor]: Taking taylor expansion of 1.0 in n 0.716 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.716 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.716 * [taylor]: Taking taylor expansion of -2.0 in n 0.716 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.716 * [taylor]: Taking taylor expansion of PI in n 0.716 * [taylor]: Taking taylor expansion of n in n 0.725 * * * [progress]: simplifying candidates 0.727 * [simplify]: Simplifying using # : (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (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)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 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) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (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) (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 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(* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (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) (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))) (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))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (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))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (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 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 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(- +nan.0))))) (- (+ (* +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) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (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 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 0.729 * [simplify]: Sending expressions to egg_math: (expm1 (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (log1p (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (+ (+ (log h0) (log PI)) (log h1)) (/ (- h2 h3) h0)) (* (+ (log (* h0 PI)) (log h1)) (/ (- h2 h3) h0)) (* (log (* 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(pow h3 3))) (- (+ (* h8 (/ (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) h3)) (- (* h8 (/ (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (pow h3 2)))))))) (- (+ (* h8 (/ (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) h3)) (- (+ (* h8 (/ (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (pow h3 2))) (- (* h8 (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))))))))) 0.738 * * [simplify]: iteration 0 : 981 enodes (cost 1502 ) 0.755 * * [simplify]: iteration 1 : 4021 enodes (cost 1398 ) 0.818 * * [simplify]: iteration 2 : 5003 enodes (cost 1383 ) 0.825 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 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)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 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(* (/ (cbrt 1.0) (sqrt (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) (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))) (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))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (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))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (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 (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))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (fma (- 0.5) (fma (* k (log (* 2.0 PI))) (pow (exp 0.5) (log (* (* 2.0 PI) n))) (* (* k (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (log n))) (fma (* (* 0.125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.5)) (pow (log (* 2.0 PI)) 2) (fma (* (* 0.125 (pow k 2)) (pow (log n) 2)) (pow (* (* 2.0 PI) n) 0.5) (fma (* (* 0.25 (pow k 2)) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (pow (* (* 2.0 PI) n) 0.5))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (fma (- k) +nan.0 (fma +nan.0 (pow k 2) (- +nan.0))) (fma +nan.0 (- (/ 1 k) (/ 1 (pow k 3))) (/ (- +nan.0) (pow k 2))) (+ (fma +nan.0 (/ 1 k) (- +nan.0)) (/ (- +nan.0) (pow k 2))) (fma (- (* +nan.0 (* (pow k 2) (pow (log (* 2.0 PI)) 2)))) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (fma +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (fma (- (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (log n))))) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (fma +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)) (fma (- (* +nan.0 (* k (log (* 2.0 PI))))) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (fma +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)) (fma (- (* +nan.0 (* k (log n)))) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (fma (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0 (fma (- (* +nan.0 (pow k 2))) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))) (fma (- +nan.0) (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3)) (* +nan.0 (- (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k) (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2))))) (fma (- +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)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))) 0.826 * * * [progress]: adding candidates to table 1.260 * * [progress]: iteration 2 / 4 1.260 * * * [progress]: picking best candidate 1.277 * * * * [pick]: Picked # 1.277 * * * [progress]: localizing error 1.292 * * * [progress]: generating rewritten candidates 1.292 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 1) 1.312 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 1) 1.335 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1 1) 1.352 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 1) 1.373 * * * [progress]: generating series expansions 1.373 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 1) 1.374 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.374 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.374 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.374 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.374 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.374 * [taylor]: Taking taylor expansion of 0.5 in k 1.374 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.374 * [taylor]: Taking taylor expansion of 1.0 in k 1.374 * [taylor]: Taking taylor expansion of k in k 1.374 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.374 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.374 * [taylor]: Taking taylor expansion of 2.0 in k 1.374 * [taylor]: Taking taylor expansion of (* n PI) in k 1.374 * [taylor]: Taking taylor expansion of n in k 1.374 * [taylor]: Taking taylor expansion of PI in k 1.375 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.375 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.375 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.375 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.375 * [taylor]: Taking taylor expansion of 0.5 in n 1.375 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.375 * [taylor]: Taking taylor expansion of 1.0 in n 1.375 * [taylor]: Taking taylor expansion of k in n 1.375 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.375 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.375 * [taylor]: Taking taylor expansion of 2.0 in n 1.375 * [taylor]: Taking taylor expansion of (* n PI) in n 1.375 * [taylor]: Taking taylor expansion of n in n 1.375 * [taylor]: Taking taylor expansion of PI in n 1.383 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.383 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.383 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.383 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.383 * [taylor]: Taking taylor expansion of 0.5 in n 1.383 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.383 * [taylor]: Taking taylor expansion of 1.0 in n 1.383 * [taylor]: Taking taylor expansion of k in n 1.383 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.383 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.383 * [taylor]: Taking taylor expansion of 2.0 in n 1.383 * [taylor]: Taking taylor expansion of (* n PI) in n 1.383 * [taylor]: Taking taylor expansion of n in n 1.383 * [taylor]: Taking taylor expansion of PI in n 1.388 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.388 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.388 * [taylor]: Taking taylor expansion of 0.5 in k 1.388 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.388 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.388 * [taylor]: Taking taylor expansion of 1.0 in k 1.388 * [taylor]: Taking taylor expansion of k in k 1.388 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.388 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.388 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.388 * [taylor]: Taking taylor expansion of 2.0 in k 1.388 * [taylor]: Taking taylor expansion of PI in k 1.389 * [taylor]: Taking taylor expansion of (log n) in k 1.389 * [taylor]: Taking taylor expansion of n in k 1.398 * [taylor]: Taking taylor expansion of 0 in k 1.413 * [taylor]: Taking taylor expansion of 0 in k 1.430 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.430 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.430 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.430 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.430 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.430 * [taylor]: Taking taylor expansion of 0.5 in k 1.430 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.430 * [taylor]: Taking taylor expansion of 1.0 in k 1.430 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.430 * [taylor]: Taking taylor expansion of k in k 1.430 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.431 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.431 * [taylor]: Taking taylor expansion of 2.0 in k 1.431 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.431 * [taylor]: Taking taylor expansion of PI in k 1.431 * [taylor]: Taking taylor expansion of n in k 1.431 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.432 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.432 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.432 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.432 * [taylor]: Taking taylor expansion of 0.5 in n 1.432 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.432 * [taylor]: Taking taylor expansion of 1.0 in n 1.432 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.432 * [taylor]: Taking taylor expansion of k in n 1.432 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.432 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.432 * [taylor]: Taking taylor expansion of 2.0 in n 1.432 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.432 * [taylor]: Taking taylor expansion of PI in n 1.432 * [taylor]: Taking taylor expansion of n in n 1.435 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.435 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.435 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.435 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.435 * [taylor]: Taking taylor expansion of 0.5 in n 1.435 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.435 * [taylor]: Taking taylor expansion of 1.0 in n 1.435 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.435 * [taylor]: Taking taylor expansion of k in n 1.435 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.435 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.435 * [taylor]: Taking taylor expansion of 2.0 in n 1.435 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.435 * [taylor]: Taking taylor expansion of PI in n 1.435 * [taylor]: Taking taylor expansion of n in n 1.439 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.439 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.439 * [taylor]: Taking taylor expansion of 0.5 in k 1.439 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.439 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.439 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.439 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.439 * [taylor]: Taking taylor expansion of 2.0 in k 1.439 * [taylor]: Taking taylor expansion of PI in k 1.440 * [taylor]: Taking taylor expansion of (log n) in k 1.440 * [taylor]: Taking taylor expansion of n in k 1.440 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.440 * [taylor]: Taking taylor expansion of 1.0 in k 1.440 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.440 * [taylor]: Taking taylor expansion of k in k 1.449 * [taylor]: Taking taylor expansion of 0 in k 1.455 * [taylor]: Taking taylor expansion of 0 in k 1.470 * [taylor]: Taking taylor expansion of 0 in k 1.471 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.471 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.471 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.471 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.471 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.471 * [taylor]: Taking taylor expansion of 0.5 in k 1.471 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.471 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.471 * [taylor]: Taking taylor expansion of k in k 1.471 * [taylor]: Taking taylor expansion of 1.0 in k 1.471 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.471 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.471 * [taylor]: Taking taylor expansion of -2.0 in k 1.471 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.471 * [taylor]: Taking taylor expansion of PI in k 1.471 * [taylor]: Taking taylor expansion of n in k 1.472 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.472 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.472 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.472 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.472 * [taylor]: Taking taylor expansion of 0.5 in n 1.472 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.472 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.472 * [taylor]: Taking taylor expansion of k in n 1.472 * [taylor]: Taking taylor expansion of 1.0 in n 1.472 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.472 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.472 * [taylor]: Taking taylor expansion of -2.0 in n 1.472 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.472 * [taylor]: Taking taylor expansion of PI in n 1.473 * [taylor]: Taking taylor expansion of n in n 1.476 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.476 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.476 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.476 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.476 * [taylor]: Taking taylor expansion of 0.5 in n 1.476 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.476 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.476 * [taylor]: Taking taylor expansion of k in n 1.476 * [taylor]: Taking taylor expansion of 1.0 in n 1.476 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.476 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.476 * [taylor]: Taking taylor expansion of -2.0 in n 1.476 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.476 * [taylor]: Taking taylor expansion of PI in n 1.476 * [taylor]: Taking taylor expansion of n in n 1.479 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.479 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.480 * [taylor]: Taking taylor expansion of 0.5 in k 1.480 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.480 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.480 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.480 * [taylor]: Taking taylor expansion of k in k 1.480 * [taylor]: Taking taylor expansion of 1.0 in k 1.480 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.480 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.480 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.480 * [taylor]: Taking taylor expansion of -2.0 in k 1.480 * [taylor]: Taking taylor expansion of PI in k 1.481 * [taylor]: Taking taylor expansion of (log n) in k 1.481 * [taylor]: Taking taylor expansion of n in k 1.489 * [taylor]: Taking taylor expansion of 0 in k 1.496 * [taylor]: Taking taylor expansion of 0 in k 1.504 * [taylor]: Taking taylor expansion of 0 in k 1.505 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 1) 1.505 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.505 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.505 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.505 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.505 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.505 * [taylor]: Taking taylor expansion of 0.5 in k 1.505 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.505 * [taylor]: Taking taylor expansion of 1.0 in k 1.505 * [taylor]: Taking taylor expansion of k in k 1.505 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.505 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.505 * [taylor]: Taking taylor expansion of 2.0 in k 1.505 * [taylor]: Taking taylor expansion of (* n PI) in k 1.505 * [taylor]: Taking taylor expansion of n in k 1.505 * [taylor]: Taking taylor expansion of PI in k 1.506 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.506 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.506 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.506 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.506 * [taylor]: Taking taylor expansion of 0.5 in n 1.506 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.506 * [taylor]: Taking taylor expansion of 1.0 in n 1.506 * [taylor]: Taking taylor expansion of k in n 1.506 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.506 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.506 * [taylor]: Taking taylor expansion of 2.0 in n 1.506 * [taylor]: Taking taylor expansion of (* n PI) in n 1.506 * [taylor]: Taking taylor expansion of n in n 1.506 * [taylor]: Taking taylor expansion of PI in n 1.511 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.511 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.511 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.511 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.511 * [taylor]: Taking taylor expansion of 0.5 in n 1.511 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.511 * [taylor]: Taking taylor expansion of 1.0 in n 1.511 * [taylor]: Taking taylor expansion of k in n 1.511 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.511 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.511 * [taylor]: Taking taylor expansion of 2.0 in n 1.511 * [taylor]: Taking taylor expansion of (* n PI) in n 1.511 * [taylor]: Taking taylor expansion of n in n 1.511 * [taylor]: Taking taylor expansion of PI in n 1.516 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.516 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.516 * [taylor]: Taking taylor expansion of 0.5 in k 1.516 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.516 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.516 * [taylor]: Taking taylor expansion of 1.0 in k 1.516 * [taylor]: Taking taylor expansion of k in k 1.516 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.516 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.516 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.516 * [taylor]: Taking taylor expansion of 2.0 in k 1.516 * [taylor]: Taking taylor expansion of PI in k 1.517 * [taylor]: Taking taylor expansion of (log n) in k 1.517 * [taylor]: Taking taylor expansion of n in k 1.526 * [taylor]: Taking taylor expansion of 0 in k 1.540 * [taylor]: Taking taylor expansion of 0 in k 1.564 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.564 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.564 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.564 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.564 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.564 * [taylor]: Taking taylor expansion of 0.5 in k 1.564 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.564 * [taylor]: Taking taylor expansion of 1.0 in k 1.564 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.564 * [taylor]: Taking taylor expansion of k in k 1.564 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.564 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.564 * [taylor]: Taking taylor expansion of 2.0 in k 1.564 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.564 * [taylor]: Taking taylor expansion of PI in k 1.564 * [taylor]: Taking taylor expansion of n in k 1.565 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.565 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.565 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.565 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.565 * [taylor]: Taking taylor expansion of 0.5 in n 1.565 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.565 * [taylor]: Taking taylor expansion of 1.0 in n 1.565 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.565 * [taylor]: Taking taylor expansion of k in n 1.565 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.565 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.565 * [taylor]: Taking taylor expansion of 2.0 in n 1.565 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.565 * [taylor]: Taking taylor expansion of PI in n 1.565 * [taylor]: Taking taylor expansion of n in n 1.569 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.569 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.569 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.569 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.569 * [taylor]: Taking taylor expansion of 0.5 in n 1.569 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.569 * [taylor]: Taking taylor expansion of 1.0 in n 1.569 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.569 * [taylor]: Taking taylor expansion of k in n 1.569 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.569 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.569 * [taylor]: Taking taylor expansion of 2.0 in n 1.569 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.569 * [taylor]: Taking taylor expansion of PI in n 1.569 * [taylor]: Taking taylor expansion of n in n 1.572 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.572 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.572 * [taylor]: Taking taylor expansion of 0.5 in k 1.572 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.572 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.572 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.572 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.572 * [taylor]: Taking taylor expansion of 2.0 in k 1.572 * [taylor]: Taking taylor expansion of PI in k 1.573 * [taylor]: Taking taylor expansion of (log n) in k 1.573 * [taylor]: Taking taylor expansion of n in k 1.573 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.573 * [taylor]: Taking taylor expansion of 1.0 in k 1.573 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.573 * [taylor]: Taking taylor expansion of k in k 1.582 * [taylor]: Taking taylor expansion of 0 in k 1.589 * [taylor]: Taking taylor expansion of 0 in k 1.597 * [taylor]: Taking taylor expansion of 0 in k 1.599 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.599 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.599 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.599 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.599 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.599 * [taylor]: Taking taylor expansion of 0.5 in k 1.599 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.599 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.599 * [taylor]: Taking taylor expansion of k in k 1.599 * [taylor]: Taking taylor expansion of 1.0 in k 1.599 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.599 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.599 * [taylor]: Taking taylor expansion of -2.0 in k 1.599 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.599 * [taylor]: Taking taylor expansion of PI in k 1.599 * [taylor]: Taking taylor expansion of n in k 1.600 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.600 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.600 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.600 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.600 * [taylor]: Taking taylor expansion of 0.5 in n 1.600 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.600 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.600 * [taylor]: Taking taylor expansion of k in n 1.600 * [taylor]: Taking taylor expansion of 1.0 in n 1.600 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.600 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.600 * [taylor]: Taking taylor expansion of -2.0 in n 1.600 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.600 * [taylor]: Taking taylor expansion of PI in n 1.600 * [taylor]: Taking taylor expansion of n in n 1.603 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.603 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.604 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.604 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.604 * [taylor]: Taking taylor expansion of 0.5 in n 1.604 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.604 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.604 * [taylor]: Taking taylor expansion of k in n 1.604 * [taylor]: Taking taylor expansion of 1.0 in n 1.604 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.604 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.604 * [taylor]: Taking taylor expansion of -2.0 in n 1.604 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.604 * [taylor]: Taking taylor expansion of PI in n 1.604 * [taylor]: Taking taylor expansion of n in n 1.607 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.607 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.607 * [taylor]: Taking taylor expansion of 0.5 in k 1.607 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.607 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.607 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.607 * [taylor]: Taking taylor expansion of k in k 1.607 * [taylor]: Taking taylor expansion of 1.0 in k 1.607 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.607 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.607 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.608 * [taylor]: Taking taylor expansion of -2.0 in k 1.608 * [taylor]: Taking taylor expansion of PI in k 1.608 * [taylor]: Taking taylor expansion of (log n) in k 1.608 * [taylor]: Taking taylor expansion of n in k 1.617 * [taylor]: Taking taylor expansion of 0 in k 1.624 * [taylor]: Taking taylor expansion of 0 in k 1.632 * [taylor]: Taking taylor expansion of 0 in k 1.633 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1 1) 1.633 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.633 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.633 * [taylor]: Taking taylor expansion of 2.0 in n 1.633 * [taylor]: Taking taylor expansion of (* n PI) in n 1.633 * [taylor]: Taking taylor expansion of n in n 1.633 * [taylor]: Taking taylor expansion of PI in n 1.633 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.633 * [taylor]: Taking taylor expansion of 2.0 in n 1.633 * [taylor]: Taking taylor expansion of (* n PI) in n 1.633 * [taylor]: Taking taylor expansion of n in n 1.633 * [taylor]: Taking taylor expansion of PI in n 1.651 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.651 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.651 * [taylor]: Taking taylor expansion of 2.0 in n 1.651 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.651 * [taylor]: Taking taylor expansion of PI in n 1.651 * [taylor]: Taking taylor expansion of n in n 1.651 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.651 * [taylor]: Taking taylor expansion of 2.0 in n 1.651 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.651 * [taylor]: Taking taylor expansion of PI in n 1.651 * [taylor]: Taking taylor expansion of n in n 1.660 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.660 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.660 * [taylor]: Taking taylor expansion of -2.0 in n 1.660 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.660 * [taylor]: Taking taylor expansion of PI in n 1.660 * [taylor]: Taking taylor expansion of n in n 1.660 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.660 * [taylor]: Taking taylor expansion of -2.0 in n 1.660 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.660 * [taylor]: Taking taylor expansion of PI in n 1.660 * [taylor]: Taking taylor expansion of n in n 1.669 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 1) 1.669 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.669 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.669 * [taylor]: Taking taylor expansion of 2.0 in n 1.669 * [taylor]: Taking taylor expansion of (* n PI) in n 1.669 * [taylor]: Taking taylor expansion of n in n 1.669 * [taylor]: Taking taylor expansion of PI in n 1.669 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.669 * [taylor]: Taking taylor expansion of 2.0 in n 1.669 * [taylor]: Taking taylor expansion of (* n PI) in n 1.669 * [taylor]: Taking taylor expansion of n in n 1.669 * [taylor]: Taking taylor expansion of PI in n 1.681 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.681 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.681 * [taylor]: Taking taylor expansion of 2.0 in n 1.681 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.681 * [taylor]: Taking taylor expansion of PI in n 1.681 * [taylor]: Taking taylor expansion of n in n 1.681 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.681 * [taylor]: Taking taylor expansion of 2.0 in n 1.681 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.681 * [taylor]: Taking taylor expansion of PI in n 1.681 * [taylor]: Taking taylor expansion of n in n 1.690 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.690 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.690 * [taylor]: Taking taylor expansion of -2.0 in n 1.690 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.690 * [taylor]: Taking taylor expansion of PI in n 1.690 * [taylor]: Taking taylor expansion of n in n 1.690 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.690 * [taylor]: Taking taylor expansion of -2.0 in n 1.690 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.690 * [taylor]: Taking taylor expansion of PI in n 1.690 * [taylor]: Taking taylor expansion of n in n 1.698 * * * [progress]: simplifying candidates 1.700 * [simplify]: Simplifying using # : (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (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)) (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (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)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 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) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 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) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 1.701 * [simplify]: Sending expressions to egg_math: (expm1 (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (log1p (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (+ (+ (log h0) (log PI)) (log h1)) (/ (- h2 h3) h0)) (* (+ (log (* h0 PI)) (log h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ h2 h0)) (pow (* (* h0 PI) h1) (/ h3 h0)) (pow (* (* h0 PI) h1) (* (cbrt (/ (- h2 h3) h0)) (cbrt (/ (- h2 h3) h0)))) (pow (* (* h0 PI) h1) (sqrt (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) 1)) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) 1) (pow (* (* h0 PI) h1) (- h2 h3)) (pow (* h0 PI) (/ (- h2 h3) h0)) (pow h1 (/ (- h2 h3) h0)) (log (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (exp (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (* (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (expm1 (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (log1p (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (+ (+ (log h0) (log PI)) (log h1)) (/ (- h2 h3) h0)) (* (+ (log (* h0 PI)) (log h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ h2 h0)) (pow (* (* h0 PI) h1) (/ h3 h0)) (pow (* (* h0 PI) h1) (* (cbrt (/ (- h2 h3) h0)) (cbrt (/ (- h2 h3) h0)))) (pow (* (* h0 PI) h1) (sqrt (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) 1)) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) 1) (pow (* (* h0 PI) h1) (- h2 h3)) (pow (* h0 PI) (/ (- h2 h3) h0)) (pow h1 (/ (- h2 h3) h0)) (log (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (exp (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (* (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (expm1 (* (* h0 PI) h1)) (log1p (* (* h0 PI) h1)) (* (* h0 PI) h1) (* (* h0 PI) h1) (+ (+ (log h0) (log PI)) (log h1)) (+ (log (* h0 PI)) (log h1)) (log (* (* h0 PI) h1)) (exp (* (* h0 PI) h1)) (* (* (* (* h0 h0) h0) (* (* PI PI) PI)) (* (* h1 h1) h1)) (* (* (* (* h0 PI) (* h0 PI)) (* h0 PI)) (* (* h1 h1) h1)) (* (cbrt (* (* h0 PI) h1)) (cbrt (* (* h0 PI) h1))) (cbrt (* (* h0 PI) h1)) (* (* (* (* h0 PI) h1) (* (* h0 PI) h1)) (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (* (* h0 PI) (sqrt h1)) (* (* h0 PI) 1) (* PI h1) (expm1 (* (* h0 PI) h1)) (log1p (* (* h0 PI) h1)) (* (* h0 PI) h1) (* (* h0 PI) h1) (+ (+ (log h0) (log PI)) (log h1)) (+ (log (* h0 PI)) (log h1)) (log (* (* h0 PI) h1)) (exp (* (* h0 PI) h1)) (* (* (* (* h0 h0) h0) (* (* PI PI) PI)) (* (* h1 h1) h1)) (* (* (* (* h0 PI) (* h0 PI)) (* h0 PI)) (* (* h1 h1) h1)) (* (cbrt (* (* h0 PI) h1)) (cbrt (* (* h0 PI) h1))) (cbrt (* (* h0 PI) h1)) (* (* (* (* h0 PI) h1) (* (* h0 PI) h1)) (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (sqrt (* (* h0 PI) h1)) (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (* (* h0 PI) (sqrt h1)) (* (* h0 PI) 1) (* PI h1) (- (+ (* h4 (* (pow h3 2) (* (pow (log (* h0 PI)) 2) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h4 (* (pow h3 2) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (pow (log h1) 2)))) (+ (* h6 (* (pow h3 2) (* (log (* h0 PI)) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1))))) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h5 (* h3 (* (log (* h0 PI)) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (* h5 (* h3 (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1)))))) (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (- (+ (* h4 (* (pow h3 2) (* (pow (log (* h0 PI)) 2) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h4 (* (pow h3 2) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (pow (log h1) 2)))) (+ (* h6 (* (pow h3 2) (* (log (* h0 PI)) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1))))) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h5 (* h3 (* (log (* h0 PI)) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (* h5 (* h3 (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1)))))) (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h0 (* h1 PI)) 1.706 * * [simplify]: iteration 0 : 407 enodes (cost 832 ) 1.714 * * [simplify]: iteration 1 : 1658 enodes (cost 770 ) 1.746 * * [simplify]: iteration 2 : 5001 enodes (cost 732 ) 1.750 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 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)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 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 (- 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))) (* (* 2.0 PI) n) (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))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (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 (* (* 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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (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)) (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 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)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 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 (- 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))) (* (* 2.0 PI) n) (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))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (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 (* (* 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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (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)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 1/2) (pow (* (* 2.0 PI) n) 1/2) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 1/2) (pow (* (* 2.0 PI) n) 1/2) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (+ (+ (* (- (* 0.5 k)) (fma (pow (* (* 2.0 PI) n) 0.5) (log (* 2.0 PI)) (* (pow (* (* 2.0 PI) n) 0.5) (log n)))) (* (* (* 0.125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.5)) (+ (pow (log (* 2.0 PI)) 2) (pow (log n) 2)))) (fma (* (* 0.25 (pow k 2)) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (pow (* (* 2.0 PI) n) 0.5))) (pow (* (* 2.0 PI) n) (* 0.5 (- 1.0 k))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (+ (+ (* (- (* 0.5 k)) (fma (pow (* (* 2.0 PI) n) 0.5) (log (* 2.0 PI)) (* (pow (* (* 2.0 PI) n) 0.5) (log n)))) (* (* (* 0.125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.5)) (+ (pow (log (* 2.0 PI)) 2) (pow (log n) 2)))) (fma (* (* 0.25 (pow k 2)) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (pow (* (* 2.0 PI) n) 0.5))) (pow (* (* 2.0 PI) n) (* 0.5 (- 1.0 k))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) 1.751 * * * [progress]: adding candidates to table 2.149 * * [progress]: iteration 3 / 4 2.149 * * * [progress]: picking best candidate 2.165 * * * * [pick]: Picked # 2.165 * * * [progress]: localizing error 2.190 * * * [progress]: generating rewritten candidates 2.190 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1) 2.294 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 2.315 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1 1 2) 2.316 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 1 1 2 2) 2.321 * * * [progress]: generating series expansions 2.321 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1) 2.322 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 2.322 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.322 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.322 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.322 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.322 * [taylor]: Taking taylor expansion of 0.5 in k 2.322 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.322 * [taylor]: Taking taylor expansion of 1.0 in k 2.322 * [taylor]: Taking taylor expansion of k in k 2.322 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.322 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.322 * [taylor]: Taking taylor expansion of 2.0 in k 2.322 * [taylor]: Taking taylor expansion of (* n PI) in k 2.322 * [taylor]: Taking taylor expansion of n in k 2.322 * [taylor]: Taking taylor expansion of PI in k 2.323 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.323 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.323 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.323 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.323 * [taylor]: Taking taylor expansion of 0.5 in n 2.323 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.323 * [taylor]: Taking taylor expansion of 1.0 in n 2.323 * [taylor]: Taking taylor expansion of k in n 2.323 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.323 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.323 * [taylor]: Taking taylor expansion of 2.0 in n 2.323 * [taylor]: Taking taylor expansion of (* n PI) in n 2.323 * [taylor]: Taking taylor expansion of n in n 2.323 * [taylor]: Taking taylor expansion of PI in n 2.329 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.329 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.329 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.329 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.329 * [taylor]: Taking taylor expansion of 0.5 in n 2.329 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.329 * [taylor]: Taking taylor expansion of 1.0 in n 2.329 * [taylor]: Taking taylor expansion of k in n 2.329 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.329 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.329 * [taylor]: Taking taylor expansion of 2.0 in n 2.329 * [taylor]: Taking taylor expansion of (* n PI) in n 2.329 * [taylor]: Taking taylor expansion of n in n 2.329 * [taylor]: Taking taylor expansion of PI in n 2.334 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.334 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.334 * [taylor]: Taking taylor expansion of 0.5 in k 2.334 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.334 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.334 * [taylor]: Taking taylor expansion of 1.0 in k 2.334 * [taylor]: Taking taylor expansion of k in k 2.334 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.334 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.334 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.334 * [taylor]: Taking taylor expansion of 2.0 in k 2.334 * [taylor]: Taking taylor expansion of PI in k 2.335 * [taylor]: Taking taylor expansion of (log n) in k 2.335 * [taylor]: Taking taylor expansion of n in k 2.344 * [taylor]: Taking taylor expansion of 0 in k 2.358 * [taylor]: Taking taylor expansion of 0 in k 2.376 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.376 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.376 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.376 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.376 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.376 * [taylor]: Taking taylor expansion of 0.5 in k 2.376 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.376 * [taylor]: Taking taylor expansion of 1.0 in k 2.376 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.376 * [taylor]: Taking taylor expansion of k in k 2.376 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.376 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.376 * [taylor]: Taking taylor expansion of 2.0 in k 2.376 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.376 * [taylor]: Taking taylor expansion of PI in k 2.376 * [taylor]: Taking taylor expansion of n in k 2.377 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.377 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.377 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.377 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.377 * [taylor]: Taking taylor expansion of 0.5 in n 2.377 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.377 * [taylor]: Taking taylor expansion of 1.0 in n 2.377 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.377 * [taylor]: Taking taylor expansion of k in n 2.377 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.377 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.377 * [taylor]: Taking taylor expansion of 2.0 in n 2.377 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.377 * [taylor]: Taking taylor expansion of PI in n 2.377 * [taylor]: Taking taylor expansion of n in n 2.381 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.381 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.381 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.381 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.381 * [taylor]: Taking taylor expansion of 0.5 in n 2.381 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.381 * [taylor]: Taking taylor expansion of 1.0 in n 2.381 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.381 * [taylor]: Taking taylor expansion of k in n 2.381 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.381 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.381 * [taylor]: Taking taylor expansion of 2.0 in n 2.381 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.381 * [taylor]: Taking taylor expansion of PI in n 2.381 * [taylor]: Taking taylor expansion of n in n 2.385 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.385 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.385 * [taylor]: Taking taylor expansion of 0.5 in k 2.385 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.385 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.385 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.385 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.385 * [taylor]: Taking taylor expansion of 2.0 in k 2.385 * [taylor]: Taking taylor expansion of PI in k 2.386 * [taylor]: Taking taylor expansion of (log n) in k 2.386 * [taylor]: Taking taylor expansion of n in k 2.386 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.386 * [taylor]: Taking taylor expansion of 1.0 in k 2.386 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.386 * [taylor]: Taking taylor expansion of k in k 2.394 * [taylor]: Taking taylor expansion of 0 in k 2.407 * [taylor]: Taking taylor expansion of 0 in k 2.416 * [taylor]: Taking taylor expansion of 0 in k 2.417 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 2.417 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.417 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in k 2.417 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in k 2.417 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.417 * [taylor]: Taking taylor expansion of 0.5 in k 2.417 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.417 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.417 * [taylor]: Taking taylor expansion of k in k 2.418 * [taylor]: Taking taylor expansion of 1.0 in k 2.418 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in k 2.418 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in k 2.418 * [taylor]: Taking taylor expansion of 2.0 in k 2.418 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in k 2.418 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in k 2.418 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in k 2.418 * [taylor]: Taking taylor expansion of (cbrt -1) in k 2.418 * [taylor]: Taking taylor expansion of -1 in k 2.419 * [taylor]: Taking taylor expansion of PI in k 2.419 * [taylor]: Taking taylor expansion of n in k 2.424 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.424 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 2.424 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 2.424 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.424 * [taylor]: Taking taylor expansion of 0.5 in n 2.424 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.424 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.424 * [taylor]: Taking taylor expansion of k in n 2.424 * [taylor]: Taking taylor expansion of 1.0 in n 2.424 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 2.424 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 2.425 * [taylor]: Taking taylor expansion of 2.0 in n 2.425 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 2.425 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 2.425 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 2.425 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.425 * [taylor]: Taking taylor expansion of -1 in n 2.425 * [taylor]: Taking taylor expansion of PI in n 2.425 * [taylor]: Taking taylor expansion of n in n 2.432 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.432 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 2.432 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 2.432 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.432 * [taylor]: Taking taylor expansion of 0.5 in n 2.432 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.432 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.432 * [taylor]: Taking taylor expansion of k in n 2.432 * [taylor]: Taking taylor expansion of 1.0 in n 2.432 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 2.432 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 2.432 * [taylor]: Taking taylor expansion of 2.0 in n 2.432 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 2.433 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 2.433 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 2.433 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.433 * [taylor]: Taking taylor expansion of -1 in n 2.433 * [taylor]: Taking taylor expansion of PI in n 2.433 * [taylor]: Taking taylor expansion of n in n 2.440 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.440 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.440 * [taylor]: Taking taylor expansion of 0.5 in k 2.440 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.440 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.440 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.440 * [taylor]: Taking taylor expansion of k in k 2.441 * [taylor]: Taking taylor expansion of 1.0 in k 2.441 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.441 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.441 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.441 * [taylor]: Taking taylor expansion of -2.0 in k 2.441 * [taylor]: Taking taylor expansion of PI in k 2.442 * [taylor]: Taking taylor expansion of (log n) in k 2.442 * [taylor]: Taking taylor expansion of n in k 2.451 * [taylor]: Taking taylor expansion of 0 in k 2.461 * [taylor]: Taking taylor expansion of 0 in k 2.472 * [taylor]: Taking taylor expansion of 0 in k 2.473 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 2.474 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 2.474 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.474 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.474 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.474 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.474 * [taylor]: Taking taylor expansion of 0.5 in k 2.474 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.474 * [taylor]: Taking taylor expansion of 1.0 in k 2.474 * [taylor]: Taking taylor expansion of k in k 2.474 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.474 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.474 * [taylor]: Taking taylor expansion of 2.0 in k 2.474 * [taylor]: Taking taylor expansion of (* n PI) in k 2.474 * [taylor]: Taking taylor expansion of n in k 2.474 * [taylor]: Taking taylor expansion of PI in k 2.475 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.475 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.475 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.475 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.475 * [taylor]: Taking taylor expansion of 0.5 in n 2.475 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.475 * [taylor]: Taking taylor expansion of 1.0 in n 2.475 * [taylor]: Taking taylor expansion of k in n 2.475 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.475 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.475 * [taylor]: Taking taylor expansion of 2.0 in n 2.475 * [taylor]: Taking taylor expansion of (* n PI) in n 2.475 * [taylor]: Taking taylor expansion of n in n 2.475 * [taylor]: Taking taylor expansion of PI in n 2.480 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.480 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.480 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.480 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.480 * [taylor]: Taking taylor expansion of 0.5 in n 2.480 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.480 * [taylor]: Taking taylor expansion of 1.0 in n 2.480 * [taylor]: Taking taylor expansion of k in n 2.480 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.480 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.480 * [taylor]: Taking taylor expansion of 2.0 in n 2.480 * [taylor]: Taking taylor expansion of (* n PI) in n 2.480 * [taylor]: Taking taylor expansion of n in n 2.480 * [taylor]: Taking taylor expansion of PI in n 2.485 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.485 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.485 * [taylor]: Taking taylor expansion of 0.5 in k 2.485 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.485 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.485 * [taylor]: Taking taylor expansion of 1.0 in k 2.485 * [taylor]: Taking taylor expansion of k in k 2.485 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.485 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.485 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.485 * [taylor]: Taking taylor expansion of 2.0 in k 2.485 * [taylor]: Taking taylor expansion of PI in k 2.486 * [taylor]: Taking taylor expansion of (log n) in k 2.486 * [taylor]: Taking taylor expansion of n in k 2.501 * [taylor]: Taking taylor expansion of 0 in k 2.515 * [taylor]: Taking taylor expansion of 0 in k 2.534 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.534 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.534 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.534 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.534 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.534 * [taylor]: Taking taylor expansion of 0.5 in k 2.534 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.534 * [taylor]: Taking taylor expansion of 1.0 in k 2.534 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.534 * [taylor]: Taking taylor expansion of k in k 2.534 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.535 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.535 * [taylor]: Taking taylor expansion of 2.0 in k 2.535 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.535 * [taylor]: Taking taylor expansion of PI in k 2.535 * [taylor]: Taking taylor expansion of n in k 2.536 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.536 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.536 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.536 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.536 * [taylor]: Taking taylor expansion of 0.5 in n 2.536 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.536 * [taylor]: Taking taylor expansion of 1.0 in n 2.536 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.536 * [taylor]: Taking taylor expansion of k in n 2.536 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.536 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.536 * [taylor]: Taking taylor expansion of 2.0 in n 2.536 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.536 * [taylor]: Taking taylor expansion of PI in n 2.536 * [taylor]: Taking taylor expansion of n in n 2.539 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.539 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.539 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.539 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.539 * [taylor]: Taking taylor expansion of 0.5 in n 2.539 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.539 * [taylor]: Taking taylor expansion of 1.0 in n 2.539 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.539 * [taylor]: Taking taylor expansion of k in n 2.539 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.539 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.539 * [taylor]: Taking taylor expansion of 2.0 in n 2.539 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.539 * [taylor]: Taking taylor expansion of PI in n 2.539 * [taylor]: Taking taylor expansion of n in n 2.543 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.543 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.543 * [taylor]: Taking taylor expansion of 0.5 in k 2.543 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.543 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.543 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.543 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.543 * [taylor]: Taking taylor expansion of 2.0 in k 2.543 * [taylor]: Taking taylor expansion of PI in k 2.544 * [taylor]: Taking taylor expansion of (log n) in k 2.544 * [taylor]: Taking taylor expansion of n in k 2.544 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.544 * [taylor]: Taking taylor expansion of 1.0 in k 2.544 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.544 * [taylor]: Taking taylor expansion of k in k 2.553 * [taylor]: Taking taylor expansion of 0 in k 2.559 * [taylor]: Taking taylor expansion of 0 in k 2.568 * [taylor]: Taking taylor expansion of 0 in k 2.569 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 2.569 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.569 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.569 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.569 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.569 * [taylor]: Taking taylor expansion of 0.5 in k 2.569 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.569 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.569 * [taylor]: Taking taylor expansion of k in k 2.569 * [taylor]: Taking taylor expansion of 1.0 in k 2.569 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.569 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.569 * [taylor]: Taking taylor expansion of -2.0 in k 2.569 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.569 * [taylor]: Taking taylor expansion of PI in k 2.569 * [taylor]: Taking taylor expansion of n in k 2.570 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.570 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.570 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.570 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.570 * [taylor]: Taking taylor expansion of 0.5 in n 2.570 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.570 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.570 * [taylor]: Taking taylor expansion of k in n 2.570 * [taylor]: Taking taylor expansion of 1.0 in n 2.570 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.570 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.570 * [taylor]: Taking taylor expansion of -2.0 in n 2.570 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.570 * [taylor]: Taking taylor expansion of PI in n 2.570 * [taylor]: Taking taylor expansion of n in n 2.574 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.574 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.574 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.574 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.574 * [taylor]: Taking taylor expansion of 0.5 in n 2.574 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.574 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.574 * [taylor]: Taking taylor expansion of k in n 2.574 * [taylor]: Taking taylor expansion of 1.0 in n 2.574 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.574 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.574 * [taylor]: Taking taylor expansion of -2.0 in n 2.574 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.574 * [taylor]: Taking taylor expansion of PI in n 2.574 * [taylor]: Taking taylor expansion of n in n 2.577 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.577 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.577 * [taylor]: Taking taylor expansion of 0.5 in k 2.577 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.577 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.577 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.577 * [taylor]: Taking taylor expansion of k in k 2.578 * [taylor]: Taking taylor expansion of 1.0 in k 2.578 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.578 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.578 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.578 * [taylor]: Taking taylor expansion of -2.0 in k 2.578 * [taylor]: Taking taylor expansion of PI in k 2.585 * [taylor]: Taking taylor expansion of (log n) in k 2.585 * [taylor]: Taking taylor expansion of n in k 2.593 * [taylor]: Taking taylor expansion of 0 in k 2.600 * [taylor]: Taking taylor expansion of 0 in k 2.608 * [taylor]: Taking taylor expansion of 0 in k 2.609 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1 1 2) 2.609 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 2.609 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.609 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.609 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.609 * [taylor]: Taking taylor expansion of 1/3 in n 2.609 * [taylor]: Taking taylor expansion of (log n) in n 2.609 * [taylor]: Taking taylor expansion of n in n 2.609 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.610 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.610 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.610 * [taylor]: Taking taylor expansion of 1/3 in n 2.610 * [taylor]: Taking taylor expansion of (log n) in n 2.610 * [taylor]: Taking taylor expansion of n in n 2.656 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 2.656 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.656 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.656 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.656 * [taylor]: Taking taylor expansion of 1/3 in n 2.656 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.656 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.656 * [taylor]: Taking taylor expansion of n in n 2.657 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.657 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.657 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.657 * [taylor]: Taking taylor expansion of 1/3 in n 2.657 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.657 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.657 * [taylor]: Taking taylor expansion of n in n 2.714 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 2.714 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.714 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.714 * [taylor]: Taking taylor expansion of -1 in n 2.715 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.715 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.715 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.715 * [taylor]: Taking taylor expansion of 1/3 in n 2.715 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.715 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.715 * [taylor]: Taking taylor expansion of n in n 2.716 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.716 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.716 * [taylor]: Taking taylor expansion of -1 in n 2.717 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.717 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.717 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.717 * [taylor]: Taking taylor expansion of 1/3 in n 2.717 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.717 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.717 * [taylor]: Taking taylor expansion of n in n 2.783 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 1 1 2 2) 2.783 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 2.783 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.783 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.783 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.783 * [taylor]: Taking taylor expansion of 1/3 in n 2.783 * [taylor]: Taking taylor expansion of (log n) in n 2.783 * [taylor]: Taking taylor expansion of n in n 2.784 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 2.784 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 2.784 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 2.784 * [taylor]: Taking taylor expansion of 1/3 in n 2.784 * [taylor]: Taking taylor expansion of (log n) in n 2.784 * [taylor]: Taking taylor expansion of n in n 2.837 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 2.837 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.837 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.837 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.837 * [taylor]: Taking taylor expansion of 1/3 in n 2.837 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.837 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.837 * [taylor]: Taking taylor expansion of n in n 2.838 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.838 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.838 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.838 * [taylor]: Taking taylor expansion of 1/3 in n 2.838 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.838 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.838 * [taylor]: Taking taylor expansion of n in n 2.888 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 2.888 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.888 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.888 * [taylor]: Taking taylor expansion of -1 in n 2.888 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.888 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.888 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.888 * [taylor]: Taking taylor expansion of 1/3 in n 2.888 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.888 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.889 * [taylor]: Taking taylor expansion of n in n 2.889 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 2.889 * [taylor]: Taking taylor expansion of (cbrt -1) in n 2.889 * [taylor]: Taking taylor expansion of -1 in n 2.890 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 2.890 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 2.890 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 2.890 * [taylor]: Taking taylor expansion of 1/3 in n 2.890 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 2.890 * [taylor]: Taking taylor expansion of (/ 1 n) in n 2.890 * [taylor]: Taking taylor expansion of n in n 2.957 * * * [progress]: simplifying candidates 2.959 * [simplify]: Simplifying using # : (expm1 (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (* (+ (+ (+ (log 2.0) (log PI)) (+ (log (cbrt n)) (log (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (+ (+ (+ (log 2.0) (log PI)) (log (* (cbrt n) (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (+ (+ (log (* 2.0 PI)) (+ (log (cbrt n)) (log (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (+ (+ (log (* 2.0 PI)) (log (* (cbrt n) (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (+ (log (* (* 2.0 PI) (* (cbrt n) (cbrt n)))) (log (cbrt n))) (/ (- 1.0 k) 2.0)) (* (log (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n))) (/ (- 1.0 k) 2.0)) (* (log (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n))) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 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) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1.0 2.0)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ k 2.0)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 (sqrt 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ 1 1)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) 1) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (- 1.0 k)) (pow (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (/ (- 1.0 k) 2.0)) (pow (cbrt n) (/ (- 1.0 k) 2.0)) (log (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (exp (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1.0 k) 2.0))) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (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)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) (* (* (cbrt n) (cbrt n)) (cbrt n)) (sqrt (cbrt n)) (sqrt (cbrt n)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) (* (* (cbrt n) (cbrt n)) (cbrt n)) (sqrt (cbrt n)) (sqrt (cbrt n)) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) 2.960 * [simplify]: Sending expressions to egg_math: (expm1 (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (log1p (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (* (+ (+ (+ (log h0) (log PI)) (+ (log (cbrt h1)) (log (cbrt h1)))) (log (cbrt h1))) (/ (- h2 h3) h0)) (* (+ (+ (+ (log h0) (log PI)) (log (* (cbrt h1) (cbrt h1)))) (log (cbrt h1))) (/ (- h2 h3) h0)) (* (+ (+ (log (* h0 PI)) (+ (log (cbrt h1)) (log (cbrt h1)))) (log (cbrt h1))) (/ (- h2 h3) h0)) (* (+ (+ (log (* h0 PI)) (log (* (cbrt h1) (cbrt h1)))) (log (cbrt h1))) (/ (- h2 h3) h0)) (* (+ (log (* (* h0 PI) (* (cbrt h1) (cbrt h1)))) (log (cbrt h1))) (/ (- h2 h3) h0)) (* (log (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1))) (/ (- h2 h3) h0)) (* (log (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1))) (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ h2 h0)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ h3 h0)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (* (cbrt (/ (- h2 h3) h0)) (cbrt (/ (- h2 h3) h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (sqrt (/ (- h2 h3) h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (* (cbrt h0) (cbrt h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (sqrt h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) 1)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (sqrt (- h2 h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (sqrt (- h2 h3)) (sqrt h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (sqrt (- h2 h3)) 1)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 (sqrt h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 1)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (+ (sqrt h2) (sqrt h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (+ (sqrt h2) (sqrt h3)) (sqrt h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (+ (sqrt h2) (sqrt h3)) 1)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 (sqrt h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ 1 1)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) 1) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (- h2 h3)) (pow (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (/ (- h2 h3) h0)) (pow (cbrt h1) (/ (- h2 h3) h0)) (log (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (exp (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (* (cbrt (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (cbrt (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0)))) (cbrt (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (* (* (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (sqrt (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (sqrt (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (- h2 h3) h0))) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (/ (- h2 h3) h0) 2)) (pow (* (* (* h0 PI) (* (cbrt h1) (cbrt h1))) (cbrt h1)) (/ (/ (- h2 h3) h0) 2)) (expm1 (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (log1p (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (+ (+ (log h0) (log PI)) (log h1)) (/ (- h2 h3) h0)) (* (+ (log (* h0 PI)) (log h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* (log (* (* h0 PI) h1)) (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (* 1 (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ h2 h0)) (pow (* (* h0 PI) h1) (/ h3 h0)) (pow (* (* h0 PI) h1) (* (cbrt (/ (- h2 h3) h0)) (cbrt (/ (- h2 h3) h0)))) (pow (* (* h0 PI) h1) (sqrt (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (* (cbrt (- h2 h3)) (cbrt (- h2 h3))) 1)) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (sqrt (- h2 h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) (sqrt h0))) (pow (* (* h0 PI) h1) (/ (+ (sqrt h2) (sqrt h3)) 1)) (pow (* (* h0 PI) h1) (/ 1 (* (cbrt h0) (cbrt h0)))) (pow (* (* h0 PI) h1) (/ 1 (sqrt h0))) (pow (* (* h0 PI) h1) (/ 1 1)) (pow (* (* h0 PI) h1) 1) (pow (* (* h0 PI) h1) (- h2 h3)) (pow (* h0 PI) (/ (- h2 h3) h0)) (pow h1 (/ (- h2 h3) h0)) (log (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (exp (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)))) (cbrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (* (* (pow (* (* h0 PI) h1) (/ (- h2 h3) h0)) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (sqrt (pow (* (* h0 PI) h1) (/ (- h2 h3) h0))) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (pow (* (* h0 PI) h1) (/ (/ (- h2 h3) h0) 2)) (expm1 (cbrt h1)) (log1p (cbrt h1)) (log (cbrt h1)) (exp (cbrt h1)) (cbrt (* (cbrt h1) (cbrt h1))) (cbrt (cbrt h1)) (cbrt (sqrt h1)) (cbrt (sqrt h1)) (cbrt 1) (cbrt h1) (* (cbrt (cbrt h1)) (cbrt (cbrt h1))) (cbrt (cbrt h1)) (* (* (cbrt h1) (cbrt h1)) (cbrt h1)) (sqrt (cbrt h1)) (sqrt (cbrt h1)) (expm1 (cbrt h1)) (log1p (cbrt h1)) (log (cbrt h1)) (exp (cbrt h1)) (cbrt (* (cbrt h1) (cbrt h1))) (cbrt (cbrt h1)) (cbrt (sqrt h1)) (cbrt (sqrt h1)) (cbrt 1) (cbrt h1) (* (cbrt (cbrt h1)) (cbrt (cbrt h1))) (cbrt (cbrt h1)) (* (* (cbrt h1) (cbrt h1)) (cbrt h1)) (sqrt (cbrt h1)) (sqrt (cbrt h1)) (- (+ (* h4 (* (pow h3 2) (* (pow (log (* h0 PI)) 2) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h4 (* (pow h3 2) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (pow (log h1) 2)))) (+ (* h6 (* (pow h3 2) (* (log (* h0 PI)) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1))))) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h5 (* h3 (* (log (* h0 PI)) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (* h5 (* h3 (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1)))))) (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (- (+ (* h4 (* (pow h3 2) (* (pow (log (* h0 PI)) 2) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h4 (* (pow h3 2) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (pow (log h1) 2)))) (+ (* h6 (* (pow h3 2) (* (log (* h0 PI)) (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1))))) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h5 (* h3 (* (log (* h0 PI)) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (* h5 (* h3 (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1)))))) (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (pow h1 1/3) (pow (/ 1 h1) -1/3) (* (pow (* -1 h1) 1/3) (cbrt -1)) (pow h1 1/3) (pow (/ 1 h1) -1/3) (* (pow (* -1 h1) 1/3) (cbrt -1)) 2.966 * * [simplify]: iteration 0 : 511 enodes (cost 996 ) 2.973 * * [simplify]: iteration 1 : 1634 enodes (cost 936 ) 3.001 * * [simplify]: iteration 2 : 5001 enodes (cost 729 ) 3.005 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 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)) (* (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) (/ (- 1.0 k) 2.0) (/ (- 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 (- 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))) (* (* 2.0 PI) n) (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))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (/ (- 1.0 k) 2.0)) (pow (cbrt n) (/ (- 1.0 k) 2.0)) (* (log (* (* 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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (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)) (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 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)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 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 (- 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))) (* (* 2.0 PI) n) (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))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (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 (* (* 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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (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)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (pow n 1/3) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) n (sqrt (cbrt n)) (sqrt (cbrt n)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (pow n 1/3) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) n (sqrt (cbrt n)) (sqrt (cbrt n)) (fma (- 0.5) (fma (* k (log (* 2.0 PI))) (pow (exp 0.5) (log (* (* 2.0 PI) n))) (* (* k (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (log n))) (fma (* (* 0.125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.5)) (pow (log (* 2.0 PI)) 2) (fma (* (* 0.125 (pow k 2)) (pow (log n) 2)) (pow (* (* 2.0 PI) n) 0.5) (fma (* (* 0.25 (pow k 2)) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (pow (* (* 2.0 PI) n) 0.5))))) (pow (* (* 2.0 PI) n) (* 0.5 (- 1.0 k))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (fma (- 0.5) (fma (* k (log (* 2.0 PI))) (pow (exp 0.5) (log (* (* 2.0 PI) n))) (* (* k (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (log n))) (fma (* (* 0.125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.5)) (pow (log (* 2.0 PI)) 2) (fma (* (* 0.125 (pow k 2)) (pow (log n) 2)) (pow (* (* 2.0 PI) n) 0.5) (fma (* (* 0.25 (pow k 2)) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (pow (* (* 2.0 PI) n) 0.5))))) (pow (* (* 2.0 PI) n) (* 0.5 (- 1.0 k))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) 3.006 * * * [progress]: adding candidates to table 3.468 * * [progress]: iteration 4 / 4 3.468 * * * [progress]: picking best candidate 3.481 * * * * [pick]: Picked # 3.481 * * * [progress]: localizing error 3.496 * * * [progress]: generating rewritten candidates 3.496 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.519 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 3.543 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 3.560 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 3.599 * * * [progress]: generating series expansions 3.599 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 3.600 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 3.600 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.600 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.600 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.600 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.600 * [taylor]: Taking taylor expansion of 0.5 in k 3.600 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.600 * [taylor]: Taking taylor expansion of 1.0 in k 3.600 * [taylor]: Taking taylor expansion of k in k 3.600 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.600 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.601 * [taylor]: Taking taylor expansion of 2.0 in k 3.601 * [taylor]: Taking taylor expansion of (* n PI) in k 3.601 * [taylor]: Taking taylor expansion of n in k 3.601 * [taylor]: Taking taylor expansion of PI in k 3.601 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.602 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.602 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.602 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.602 * [taylor]: Taking taylor expansion of 0.5 in n 3.602 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.602 * [taylor]: Taking taylor expansion of 1.0 in n 3.602 * [taylor]: Taking taylor expansion of k in n 3.602 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.602 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.602 * [taylor]: Taking taylor expansion of 2.0 in n 3.602 * [taylor]: Taking taylor expansion of (* n PI) in n 3.602 * [taylor]: Taking taylor expansion of n in n 3.602 * [taylor]: Taking taylor expansion of PI in n 3.607 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.607 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.607 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.607 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.607 * [taylor]: Taking taylor expansion of 0.5 in n 3.607 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.607 * [taylor]: Taking taylor expansion of 1.0 in n 3.607 * [taylor]: Taking taylor expansion of k in n 3.607 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.607 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.607 * [taylor]: Taking taylor expansion of 2.0 in n 3.607 * [taylor]: Taking taylor expansion of (* n PI) in n 3.607 * [taylor]: Taking taylor expansion of n in n 3.607 * [taylor]: Taking taylor expansion of PI in n 3.612 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.612 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.612 * [taylor]: Taking taylor expansion of 0.5 in k 3.612 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.612 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.612 * [taylor]: Taking taylor expansion of 1.0 in k 3.612 * [taylor]: Taking taylor expansion of k in k 3.612 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.612 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.612 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.612 * [taylor]: Taking taylor expansion of 2.0 in k 3.612 * [taylor]: Taking taylor expansion of PI in k 3.613 * [taylor]: Taking taylor expansion of (log n) in k 3.613 * [taylor]: Taking taylor expansion of n in k 3.622 * [taylor]: Taking taylor expansion of 0 in k 3.636 * [taylor]: Taking taylor expansion of 0 in k 3.662 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 3.662 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.662 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.662 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.662 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.662 * [taylor]: Taking taylor expansion of 0.5 in k 3.662 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.662 * [taylor]: Taking taylor expansion of 1.0 in k 3.662 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.662 * [taylor]: Taking taylor expansion of k in k 3.663 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.663 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.663 * [taylor]: Taking taylor expansion of 2.0 in k 3.663 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.663 * [taylor]: Taking taylor expansion of PI in k 3.663 * [taylor]: Taking taylor expansion of n in k 3.664 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.664 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.664 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.664 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.664 * [taylor]: Taking taylor expansion of 0.5 in n 3.664 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.664 * [taylor]: Taking taylor expansion of 1.0 in n 3.664 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.664 * [taylor]: Taking taylor expansion of k in n 3.664 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.664 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.664 * [taylor]: Taking taylor expansion of 2.0 in n 3.664 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.664 * [taylor]: Taking taylor expansion of PI in n 3.664 * [taylor]: Taking taylor expansion of n in n 3.667 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.667 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.667 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.667 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.667 * [taylor]: Taking taylor expansion of 0.5 in n 3.667 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.667 * [taylor]: Taking taylor expansion of 1.0 in n 3.667 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.667 * [taylor]: Taking taylor expansion of k in n 3.667 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.667 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.667 * [taylor]: Taking taylor expansion of 2.0 in n 3.667 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.667 * [taylor]: Taking taylor expansion of PI in n 3.667 * [taylor]: Taking taylor expansion of n in n 3.671 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 3.671 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 3.671 * [taylor]: Taking taylor expansion of 0.5 in k 3.671 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 3.671 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 3.671 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.671 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.671 * [taylor]: Taking taylor expansion of 2.0 in k 3.671 * [taylor]: Taking taylor expansion of PI in k 3.672 * [taylor]: Taking taylor expansion of (log n) in k 3.672 * [taylor]: Taking taylor expansion of n in k 3.672 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.672 * [taylor]: Taking taylor expansion of 1.0 in k 3.672 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.672 * [taylor]: Taking taylor expansion of k in k 3.682 * [taylor]: Taking taylor expansion of 0 in k 3.689 * [taylor]: Taking taylor expansion of 0 in k 3.697 * [taylor]: Taking taylor expansion of 0 in k 3.698 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 3.698 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.698 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.698 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.698 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.699 * [taylor]: Taking taylor expansion of 0.5 in k 3.699 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.699 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.699 * [taylor]: Taking taylor expansion of k in k 3.699 * [taylor]: Taking taylor expansion of 1.0 in k 3.699 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.699 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.699 * [taylor]: Taking taylor expansion of -2.0 in k 3.699 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.699 * [taylor]: Taking taylor expansion of PI in k 3.699 * [taylor]: Taking taylor expansion of n in k 3.700 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.700 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.700 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.700 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.700 * [taylor]: Taking taylor expansion of 0.5 in n 3.700 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.700 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.700 * [taylor]: Taking taylor expansion of k in n 3.700 * [taylor]: Taking taylor expansion of 1.0 in n 3.700 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.700 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.700 * [taylor]: Taking taylor expansion of -2.0 in n 3.700 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.700 * [taylor]: Taking taylor expansion of PI in n 3.700 * [taylor]: Taking taylor expansion of n in n 3.703 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.703 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.703 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.703 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.703 * [taylor]: Taking taylor expansion of 0.5 in n 3.703 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.703 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.703 * [taylor]: Taking taylor expansion of k in n 3.703 * [taylor]: Taking taylor expansion of 1.0 in n 3.703 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.703 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.703 * [taylor]: Taking taylor expansion of -2.0 in n 3.703 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.704 * [taylor]: Taking taylor expansion of PI in n 3.704 * [taylor]: Taking taylor expansion of n in n 3.707 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 3.707 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 3.707 * [taylor]: Taking taylor expansion of 0.5 in k 3.707 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 3.707 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.707 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.707 * [taylor]: Taking taylor expansion of k in k 3.708 * [taylor]: Taking taylor expansion of 1.0 in k 3.708 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 3.708 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 3.708 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 3.708 * [taylor]: Taking taylor expansion of -2.0 in k 3.708 * [taylor]: Taking taylor expansion of PI in k 3.708 * [taylor]: Taking taylor expansion of (log n) in k 3.708 * [taylor]: Taking taylor expansion of n in k 3.717 * [taylor]: Taking taylor expansion of 0 in k 3.723 * [taylor]: Taking taylor expansion of 0 in k 3.731 * [taylor]: Taking taylor expansion of 0 in k 3.732 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 3.732 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 3.732 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.732 * [taylor]: Taking taylor expansion of 1.0 in k 3.732 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.732 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.732 * [taylor]: Taking taylor expansion of k in k 3.734 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.734 * [taylor]: Taking taylor expansion of 1.0 in k 3.734 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.734 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.734 * [taylor]: Taking taylor expansion of k in k 3.750 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 3.750 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.750 * [taylor]: Taking taylor expansion of 1.0 in k 3.750 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.750 * [taylor]: Taking taylor expansion of k in k 3.752 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.752 * [taylor]: Taking taylor expansion of 1.0 in k 3.752 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.752 * [taylor]: Taking taylor expansion of k in k 3.762 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 3.762 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.762 * [taylor]: Taking taylor expansion of 1.0 in k 3.762 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.762 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.762 * [taylor]: Taking taylor expansion of -1 in k 3.762 * [taylor]: Taking taylor expansion of k in k 3.763 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.763 * [taylor]: Taking taylor expansion of 1.0 in k 3.763 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.763 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.763 * [taylor]: Taking taylor expansion of -1 in k 3.763 * [taylor]: Taking taylor expansion of k in k 3.774 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 3.775 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 3.775 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.775 * [taylor]: Taking taylor expansion of 2.0 in n 3.775 * [taylor]: Taking taylor expansion of (* n PI) in n 3.775 * [taylor]: Taking taylor expansion of n in n 3.775 * [taylor]: Taking taylor expansion of PI in n 3.775 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.775 * [taylor]: Taking taylor expansion of 2.0 in n 3.775 * [taylor]: Taking taylor expansion of (* n PI) in n 3.775 * [taylor]: Taking taylor expansion of n in n 3.775 * [taylor]: Taking taylor expansion of PI in n 3.786 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 3.786 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.787 * [taylor]: Taking taylor expansion of 2.0 in n 3.787 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.787 * [taylor]: Taking taylor expansion of PI in n 3.787 * [taylor]: Taking taylor expansion of n in n 3.787 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.787 * [taylor]: Taking taylor expansion of 2.0 in n 3.787 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.787 * [taylor]: Taking taylor expansion of PI in n 3.787 * [taylor]: Taking taylor expansion of n in n 3.795 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 3.795 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.795 * [taylor]: Taking taylor expansion of -2.0 in n 3.795 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.795 * [taylor]: Taking taylor expansion of PI in n 3.795 * [taylor]: Taking taylor expansion of n in n 3.796 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.796 * [taylor]: Taking taylor expansion of -2.0 in n 3.796 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.796 * [taylor]: Taking taylor expansion of PI in n 3.796 * [taylor]: Taking taylor expansion of n in n 3.804 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 3.804 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0 3.804 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 3.804 * [taylor]: Taking taylor expansion of 1.0 in k 3.804 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 3.804 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 3.804 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 3.804 * [taylor]: Taking taylor expansion of 1/4 in k 3.804 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.804 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.804 * [taylor]: Taking taylor expansion of k in k 3.805 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 3.805 * [taylor]: Taking taylor expansion of 1.0 in k 3.805 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 3.805 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 3.805 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 3.805 * [taylor]: Taking taylor expansion of 1/4 in k 3.805 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 3.805 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.805 * [taylor]: Taking taylor expansion of k in k 3.869 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0 3.869 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 3.869 * [taylor]: Taking taylor expansion of 1.0 in k 3.869 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 3.869 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 3.869 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 3.869 * [taylor]: Taking taylor expansion of 1/4 in k 3.869 * [taylor]: Taking taylor expansion of (log k) in k 3.869 * [taylor]: Taking taylor expansion of k in k 3.870 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 3.870 * [taylor]: Taking taylor expansion of 1.0 in k 3.870 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 3.870 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 3.870 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 3.870 * [taylor]: Taking taylor expansion of 1/4 in k 3.870 * [taylor]: Taking taylor expansion of (log k) in k 3.870 * [taylor]: Taking taylor expansion of k in k 3.929 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0 3.929 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 3.929 * [taylor]: Taking taylor expansion of 1.0 in k 3.929 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 3.929 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 3.929 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.929 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.929 * [taylor]: Taking taylor expansion of -1 in k 3.929 * [taylor]: Taking taylor expansion of k in k 3.935 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 3.935 * [taylor]: Taking taylor expansion of 1.0 in k 3.935 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 3.935 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 3.935 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.935 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.935 * [taylor]: Taking taylor expansion of -1 in k 3.935 * [taylor]: Taking taylor expansion of k in k 3.970 * * * [progress]: simplifying candidates 3.978 * [simplify]: Simplifying using # : (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (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)) (expm1 (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (log1p (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (- (- (log 1.0) (log (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) (- (log (/ 1.0 (sqrt (sqrt k)))) (log (sqrt (sqrt k)))) (log (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (exp (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (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)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt 1))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt 1)) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) 1) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt 1))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt 1)) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) 1) (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt 1)) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1) (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (cbrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (cbrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt 1))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt 1)) (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) 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(exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (+ (* h5 (* h3 (* (log (* h0 PI)) (exp (* h5 (+ (log (* h0 PI)) (log h1))))))) (* h5 (* h3 (* (exp (* h5 (+ (log (* h0 PI)) (log h1)))) (log h1)))))) (exp (* h5 (* (- (log (* h0 PI)) (log (/ 1 h1))) (- h2 h3)))) (exp (* h5 (* (- h2 h3) (- (log (* h7 PI)) (log (/ -1 h1)))))) (- (+ (* h8 h3) (- (+ (* h8 (pow h3 2)) (- h8))))) (- (+ (* h8 (/ 1 (pow h3 2))) (- (+ (* h8 (/ 1 h3)) (- (* h8 (/ 1 (pow h3 3)))))))) (- (+ (* h8 (/ 1 (pow h3 2))) (- (+ (* h8 (/ 1 h3)) (- h8))))) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h0 (* h1 PI)) (* h2 (pow (/ 1 h3) 1/4)) (* h2 (pow (/ 1 h3) 1/4)) (- (* h2 (sqrt h8)) (+ (* h8 (/ 1 (* (sqrt h8) (pow h3 2)))) (- (+ (* h8 (/ 1 (* (sqrt h8) h3))) (- (* h8 (/ 1 (* (pow (sqrt h8) 3) (pow h3 2))))))))) 4.005 * * [simplify]: iteration 0 : 1355 enodes (cost 5833 ) 4.027 * * [simplify]: iteration 1 : 5001 enodes (cost 5050 ) 4.047 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 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(sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt (sqrt k)) (/ 1.0 (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt k) 1.0) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt k) 1.0) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k))))) (/ (sqrt k) 1.0) (/ (sqrt k) 1.0) (sqrt k) (sqrt k) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 1/2) (pow (* (* 2.0 PI) n) 1/2) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (expm1 (/ 1.0 (sqrt (sqrt k)))) (log1p (/ 1.0 (sqrt (sqrt k)))) (log (/ 1.0 (sqrt (sqrt k)))) (log (/ 1.0 (sqrt (sqrt k)))) (exp (/ 1.0 (sqrt (sqrt k)))) (pow (/ 1.0 (sqrt (sqrt k))) 3) (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (cbrt (/ 1.0 (sqrt (sqrt k)))) (pow (/ 1.0 (sqrt (sqrt k))) 3) (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))) (- 1.0) (- (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (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) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (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 k)))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (* 1 (fabs (cbrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1.0 (cbrt (sqrt (sqrt k)))) (/ 1 (* 1 (fabs (cbrt (sqrt k))))) (/ 1.0 (sqrt (cbrt (sqrt k)))) (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ 1.0 (sqrt (sqrt (cbrt k)))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1.0 (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 (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 (sqrt (* (cbrt k) (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) (+ (* (* 0.125 (pow k 2)) (+ (* (pow (exp 0.5) (log (* (* 2.0 PI) n))) (pow (log (* 2.0 PI)) 2)) (* (pow (log n) 2) (pow (exp 0.5) (log (* (* 2.0 PI) n)))))) (- (fma (* 0.25 (pow k 2)) (* (* (log n) (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (log (* 2.0 PI))) (pow (exp 0.5) (log (* (* 2.0 PI) n)))) (* (* 0.5 k) (+ (* (pow (exp 0.5) (log (* (* 2.0 PI) n))) (log (* 2.0 PI))) (* (log n) (pow (exp 0.5) (log (* (* 2.0 PI) n)))))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (+ (- (* +nan.0 k)) (fma +nan.0 (pow k 2) (- +nan.0))) (+ (- (* +nan.0 (/ 1 (pow k 2)))) (fma +nan.0 (/ 1 k) (- (* +nan.0 (/ 1 (pow k 3)))))) (+ (- (* +nan.0 (/ 1 (pow k 2)))) (fma +nan.0 (/ 1 k) (- +nan.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* 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) (pow k 2))))) (* +nan.0 (- (/ 1 (* (sqrt +nan.0) k)) (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))))) 4.051 * * * [progress]: adding candidates to table 4.838 * [progress]: [Phase 3 of 3] Extracting. 4.838 * * [regime]: Finding splitpoints for: (# # # # # #) 4.840 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 4.840 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # #) 4.873 * * * * [regimes]: Trying to branch on n from (# # # # # #) 4.904 * * * * [regimes]: Trying to branch on k from (# # # # # #) 4.933 * * * [regime]: Found split indices: #