21.728 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.029 * * * [progress]: [2/2] Setting up program. 0.031 * [progress]: [Phase 2 of 3] Improving. 0.032 * [simplify]: Simplifying using # : (- (atan (+ N 1.0)) (atan N)) 0.034 * * [simplify]: iteration 0 : 9 enodes (cost 4 ) 0.035 * * [simplify]: iteration 1 : 10 enodes (cost 4 ) 0.037 * * [simplify]: iteration 2 : 10 enodes (cost 4 ) 0.037 * [simplify]: Simplified to: (- (atan (+ N 1.0)) (atan N)) 0.037 * * [progress]: iteration 1 / 4 0.037 * * * [progress]: picking best candidate 0.039 * * * * [pick]: Picked # 0.039 * * * [progress]: localizing error 0.045 * * * [progress]: generating rewritten candidates 0.045 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.048 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 0.049 * * * [progress]: generating series expansions 0.049 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.049 * [approximate]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in (N) around 0 0.050 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.050 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.051 * [taylor]: Taking taylor expansion of (atan N) in N 0.051 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.051 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.051 * [taylor]: Taking taylor expansion of (atan N) in N 0.054 * [approximate]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in (N) around 0 0.054 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.054 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.054 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.054 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.054 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.054 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.057 * [approximate]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in (N) around 0 0.057 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.057 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.058 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.058 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.058 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.058 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.061 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 0.061 * [approximate]: Taking taylor expansion of (atan (+ N 1.0)) in (N) around 0 0.061 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.061 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.061 * [approximate]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in (N) around 0 0.061 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.061 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.062 * [approximate]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in (N) around 0 0.062 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.062 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.062 * * * [progress]: simplifying candidates 0.062 * [simplify]: Simplifying using # : (- (+ N 1.0) N) (+ 1 (* (+ N 1.0) N)) (/ (exp (atan (+ N 1.0))) (exp (atan N))) (log (- (atan (+ N 1.0)) (atan N))) (exp (- (atan (+ N 1.0)) (atan N))) (* (cbrt (- (atan (+ N 1.0)) (atan N))) (cbrt (- (atan (+ N 1.0)) (atan N)))) (cbrt (- (atan (+ N 1.0)) (atan N))) (* (* (- (atan (+ N 1.0)) (atan N)) (- (atan (+ N 1.0)) (atan N))) (- (atan (+ N 1.0)) (atan N))) (sqrt (- (atan (+ N 1.0)) (atan N))) (sqrt (- (atan (+ N 1.0)) (atan N))) (- (pow (atan (+ N 1.0)) 3) (pow (atan N) 3)) (+ (* (atan (+ N 1.0)) (atan (+ N 1.0))) (+ (* (atan N) (atan N)) (* (atan (+ N 1.0)) (atan N)))) (neg (atan N)) (- (* (atan (+ N 1.0)) (atan (+ N 1.0))) (* (atan N) (atan N))) (+ (atan (+ N 1.0)) (atan N)) (+ (sqrt (atan (+ N 1.0))) (sqrt (atan N))) (- (sqrt (atan (+ N 1.0))) (sqrt (atan N))) (- (atan (+ N 1.0)) (atan N)) (neg (atan N)) (log (atan (+ N 1.0))) (exp (atan (+ N 1.0))) (* (cbrt (atan (+ N 1.0))) (cbrt (atan (+ N 1.0)))) (cbrt (atan (+ N 1.0))) (* (* (atan (+ N 1.0)) (atan (+ N 1.0))) (atan (+ N 1.0))) (sqrt (atan (+ N 1.0))) (sqrt (atan (+ N 1.0))) (- (atan (+ N 1.0)) (atan N)) (- (atan (+ N 1.0)) (atan N)) (- (atan (+ N 1.0)) (atan N)) (atan (+ N 1.0)) (atan (+ N 1.0)) (atan (+ N 1.0)) 0.065 * * [simplify]: iteration 0 : 75 enodes (cost 154 ) 0.067 * * [simplify]: iteration 1 : 145 enodes (cost 145 ) 0.070 * * [simplify]: iteration 2 : 289 enodes (cost 143 ) 0.075 * * [simplify]: iteration 3 : 681 enodes (cost 142 ) 0.089 * * [simplify]: iteration 4 : 2447 enodes (cost 142 ) 0.139 * * [simplify]: iteration 5 : 5001 enodes (cost 142 ) 0.140 * [simplify]: Simplified to: 1.0 (+ 1 (* (+ N 1.0) N)) (exp (- (atan (+ N 1.0)) (atan N))) (log (- (atan (+ N 1.0)) (atan N))) (exp (- (atan (+ N 1.0)) (atan N))) (* (cbrt (- (atan (+ N 1.0)) (atan N))) (cbrt (- (atan (+ N 1.0)) (atan N)))) (cbrt (- (atan (+ N 1.0)) (atan N))) (pow (- (atan (+ N 1.0)) (atan N)) 3) (sqrt (- (atan (+ N 1.0)) (atan N))) (sqrt (- (atan (+ N 1.0)) (atan N))) (- (pow (atan (+ N 1.0)) 3) (pow (atan N) 3)) (+ (* (atan (+ N 1.0)) (+ (atan (+ N 1.0)) (atan N))) (* (atan N) (atan N))) (- 0 (atan N)) (- (* (atan (+ N 1.0)) (atan (+ N 1.0))) (* (atan N) (atan N))) (+ (atan (+ N 1.0)) (atan N)) (+ (sqrt (atan (+ N 1.0))) (sqrt (atan N))) (- (sqrt (atan (+ N 1.0))) (sqrt (atan N))) (- (atan (+ N 1.0)) (atan N)) (- 0 (atan N)) (log (atan (+ N 1.0))) (exp (atan (+ N 1.0))) (* (cbrt (atan (+ N 1.0))) (cbrt (atan (+ N 1.0)))) (cbrt (atan (+ N 1.0))) (pow (atan (+ N 1.0)) 3) (sqrt (atan (+ N 1.0))) (sqrt (atan (+ N 1.0))) (- (atan (+ N 1.0)) (atan N)) (- (atan (+ N 1.0)) (atan N)) (- (atan (+ N 1.0)) (atan N)) (atan (+ N 1.0)) (atan (+ N 1.0)) (atan (+ N 1.0)) 0.140 * * * [progress]: adding candidates to table 0.183 * * [progress]: iteration 2 / 4 0.183 * * * [progress]: picking best candidate 0.185 * * * * [pick]: Picked # 0.185 * * * [progress]: localizing error 0.191 * * * [progress]: generating rewritten candidates 0.191 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.191 * * * * [progress]: [ 2 / 2 ] rewriting at (2 2 2) 0.198 * * * [progress]: generating series expansions 0.198 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.198 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.198 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.198 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.199 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.199 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.199 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.200 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.200 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.200 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.201 * * * * [progress]: [ 2 / 2 ] generating series at (2 2 2) 0.201 * [approximate]: Taking taylor expansion of (* N (+ N 1.0)) in (N) around 0 0.201 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.201 * [taylor]: Taking taylor expansion of N in N 0.201 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.201 * [taylor]: Taking taylor expansion of N in N 0.201 * [taylor]: Taking taylor expansion of 1.0 in N 0.201 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.201 * [taylor]: Taking taylor expansion of N in N 0.201 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.201 * [taylor]: Taking taylor expansion of N in N 0.201 * [taylor]: Taking taylor expansion of 1.0 in N 0.211 * [approximate]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in (N) around 0 0.211 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.211 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.211 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.211 * [taylor]: Taking taylor expansion of N in N 0.212 * [taylor]: Taking taylor expansion of 1.0 in N 0.212 * [taylor]: Taking taylor expansion of N in N 0.212 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.212 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.212 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.212 * [taylor]: Taking taylor expansion of N in N 0.212 * [taylor]: Taking taylor expansion of 1.0 in N 0.212 * [taylor]: Taking taylor expansion of N in N 0.223 * [approximate]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in (N) around 0 0.223 * [taylor]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in N 0.223 * [taylor]: Taking taylor expansion of -1 in N 0.223 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.223 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.223 * [taylor]: Taking taylor expansion of 1.0 in N 0.223 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.223 * [taylor]: Taking taylor expansion of N in N 0.223 * [taylor]: Taking taylor expansion of N in N 0.224 * [taylor]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in N 0.224 * [taylor]: Taking taylor expansion of -1 in N 0.224 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.224 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.224 * [taylor]: Taking taylor expansion of 1.0 in N 0.224 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.224 * [taylor]: Taking taylor expansion of N in N 0.224 * [taylor]: Taking taylor expansion of N in N 0.243 * * * [progress]: simplifying candidates 0.243 * [simplify]: Simplifying using # : (log (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (exp (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (* (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (+ N 1.0) N) (+ (log (+ N 1.0)) (log N)) (log (* (+ N 1.0) N)) (exp (* (+ N 1.0) N)) (* (* (* (+ N 1.0) (+ N 1.0)) (+ N 1.0)) (* (* N N) N)) (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)) (* (* (* (+ N 1.0) N) (* (+ N 1.0) N)) (* (+ N 1.0) N)) (sqrt (* (+ N 1.0) N)) (sqrt (* (+ N 1.0) N)) (* (sqrt (+ N 1.0)) (sqrt N)) (* (sqrt (+ N 1.0)) (sqrt N)) (* (+ N 1.0) (* (cbrt N) (cbrt N))) (* (+ N 1.0) (sqrt N)) (* (+ N 1.0) 1) (* (cbrt (+ N 1.0)) N) (* (sqrt (+ N 1.0)) N) (* (+ N 1.0) N) (* (+ N 1.0) N) (* (+ (pow N 3) (pow 1.0 3)) N) (* (- (* N N) (* 1.0 1.0)) N) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (+ (pow N 2) (* 1.0 N)) (+ (pow N 2) (* 1.0 N)) (+ (pow N 2) (* 1.0 N)) 0.247 * * [simplify]: iteration 0 : 121 enodes (cost 151 ) 0.252 * * [simplify]: iteration 1 : 432 enodes (cost 127 ) 0.262 * * [simplify]: iteration 2 : 2321 enodes (cost 127 ) 0.301 * * [simplify]: iteration 3 : 5002 enodes (cost 127 ) 0.303 * [simplify]: Simplified to: (log (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (exp (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 3) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (+ N 1.0) N) (log (* (+ N 1.0) N)) (log (* (+ N 1.0) N)) (exp (* (+ N 1.0) N)) (pow (* (+ N 1.0) N) 3) (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)) (pow (* (+ N 1.0) N) 3) (sqrt (* (+ N 1.0) N)) (sqrt (* (+ N 1.0) N)) (* (sqrt (+ N 1.0)) (sqrt N)) (* (sqrt (+ N 1.0)) (sqrt N)) (* (+ N 1.0) (* (cbrt N) (cbrt N))) (* (+ N 1.0) (sqrt N)) (+ N 1.0) (* (cbrt (+ N 1.0)) N) (* (sqrt (+ N 1.0)) N) (* (+ N 1.0) N) (* (+ N 1.0) N) (* (+ (pow N 3) (pow 1.0 3)) N) (* (- (* N N) (* 1.0 1.0)) N) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (* (+ N 1.0) N) (* (+ N 1.0) N) (* (+ N 1.0) N) 0.303 * * * [progress]: adding candidates to table 0.354 * * [progress]: iteration 3 / 4 0.354 * * * [progress]: picking best candidate 0.366 * * * * [pick]: Picked # 0.366 * * * [progress]: localizing error 0.380 * * * [progress]: generating rewritten candidates 0.380 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 2) 0.385 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1 2) 0.389 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1 1) 0.394 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.395 * * * [progress]: generating series expansions 0.395 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 2) 0.395 * [approximate]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in (N) around 0 0.395 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.395 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.395 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.395 * [taylor]: Taking taylor expansion of 1/3 in N 0.395 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.395 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.395 * [taylor]: Taking taylor expansion of N in N 0.395 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.396 * [taylor]: Taking taylor expansion of N in N 0.396 * [taylor]: Taking taylor expansion of 1.0 in N 0.399 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.399 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.399 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.399 * [taylor]: Taking taylor expansion of 1/3 in N 0.399 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.399 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.399 * [taylor]: Taking taylor expansion of N in N 0.399 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.399 * [taylor]: Taking taylor expansion of N in N 0.399 * [taylor]: Taking taylor expansion of 1.0 in N 0.430 * [approximate]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in (N) around 0 0.430 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.430 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.430 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.430 * [taylor]: Taking taylor expansion of 1/3 in N 0.430 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.430 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.430 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.430 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.430 * [taylor]: Taking taylor expansion of N in N 0.430 * [taylor]: Taking taylor expansion of 1.0 in N 0.431 * [taylor]: Taking taylor expansion of N in N 0.432 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.432 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.432 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.432 * [taylor]: Taking taylor expansion of 1/3 in N 0.432 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.432 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.432 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.432 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.432 * [taylor]: Taking taylor expansion of N in N 0.432 * [taylor]: Taking taylor expansion of 1.0 in N 0.432 * [taylor]: Taking taylor expansion of N in N 0.453 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in (N) around 0 0.453 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.453 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.453 * [taylor]: Taking taylor expansion of -1 in N 0.453 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.453 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.454 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.454 * [taylor]: Taking taylor expansion of 1/3 in N 0.454 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.454 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.454 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.454 * [taylor]: Taking taylor expansion of 1.0 in N 0.454 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.454 * [taylor]: Taking taylor expansion of N in N 0.454 * [taylor]: Taking taylor expansion of N in N 0.456 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.456 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.456 * [taylor]: Taking taylor expansion of -1 in N 0.457 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.457 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.457 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.457 * [taylor]: Taking taylor expansion of 1/3 in N 0.457 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.457 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.457 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.457 * [taylor]: Taking taylor expansion of 1.0 in N 0.457 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.457 * [taylor]: Taking taylor expansion of N in N 0.457 * [taylor]: Taking taylor expansion of N in N 0.496 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1 2) 0.497 * [approximate]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in (N) around 0 0.497 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.497 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.497 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.497 * [taylor]: Taking taylor expansion of 1/3 in N 0.497 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.497 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.497 * [taylor]: Taking taylor expansion of N in N 0.497 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.497 * [taylor]: Taking taylor expansion of N in N 0.497 * [taylor]: Taking taylor expansion of 1.0 in N 0.500 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.500 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.500 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.500 * [taylor]: Taking taylor expansion of 1/3 in N 0.500 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.500 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.500 * [taylor]: Taking taylor expansion of N in N 0.500 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.500 * [taylor]: Taking taylor expansion of N in N 0.500 * [taylor]: Taking taylor expansion of 1.0 in N 0.530 * [approximate]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in (N) around 0 0.530 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.530 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.530 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.530 * [taylor]: Taking taylor expansion of 1/3 in N 0.530 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.530 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.530 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.530 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.530 * [taylor]: Taking taylor expansion of N in N 0.530 * [taylor]: Taking taylor expansion of 1.0 in N 0.530 * [taylor]: Taking taylor expansion of N in N 0.531 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.531 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.531 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.531 * [taylor]: Taking taylor expansion of 1/3 in N 0.531 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.531 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.531 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.531 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.531 * [taylor]: Taking taylor expansion of N in N 0.532 * [taylor]: Taking taylor expansion of 1.0 in N 0.532 * [taylor]: Taking taylor expansion of N in N 0.559 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in (N) around 0 0.559 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.559 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.559 * [taylor]: Taking taylor expansion of -1 in N 0.560 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.560 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.560 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.560 * [taylor]: Taking taylor expansion of 1/3 in N 0.560 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.560 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.560 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.560 * [taylor]: Taking taylor expansion of 1.0 in N 0.560 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.560 * [taylor]: Taking taylor expansion of N in N 0.560 * [taylor]: Taking taylor expansion of N in N 0.562 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.562 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.562 * [taylor]: Taking taylor expansion of -1 in N 0.563 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.563 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.563 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.563 * [taylor]: Taking taylor expansion of 1/3 in N 0.563 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.563 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.563 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.563 * [taylor]: Taking taylor expansion of 1.0 in N 0.563 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.563 * [taylor]: Taking taylor expansion of N in N 0.564 * [taylor]: Taking taylor expansion of N in N 0.597 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1 1) 0.597 * [approximate]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in (N) around 0 0.597 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.597 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.597 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.597 * [taylor]: Taking taylor expansion of 1/3 in N 0.597 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.597 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.597 * [taylor]: Taking taylor expansion of N in N 0.597 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.597 * [taylor]: Taking taylor expansion of N in N 0.597 * [taylor]: Taking taylor expansion of 1.0 in N 0.600 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.600 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.600 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.600 * [taylor]: Taking taylor expansion of 1/3 in N 0.600 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.600 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.600 * [taylor]: Taking taylor expansion of N in N 0.600 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.600 * [taylor]: Taking taylor expansion of N in N 0.600 * [taylor]: Taking taylor expansion of 1.0 in N 0.630 * [approximate]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in (N) around 0 0.630 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.630 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.630 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.630 * [taylor]: Taking taylor expansion of 1/3 in N 0.630 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.630 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.630 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.630 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.630 * [taylor]: Taking taylor expansion of N in N 0.630 * [taylor]: Taking taylor expansion of 1.0 in N 0.630 * [taylor]: Taking taylor expansion of N in N 0.631 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.631 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.631 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.631 * [taylor]: Taking taylor expansion of 1/3 in N 0.632 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.632 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.632 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.632 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.632 * [taylor]: Taking taylor expansion of N in N 0.632 * [taylor]: Taking taylor expansion of 1.0 in N 0.632 * [taylor]: Taking taylor expansion of N in N 0.660 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in (N) around 0 0.660 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.660 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.660 * [taylor]: Taking taylor expansion of -1 in N 0.661 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.661 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.661 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.661 * [taylor]: Taking taylor expansion of 1/3 in N 0.661 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.661 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.661 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.661 * [taylor]: Taking taylor expansion of 1.0 in N 0.661 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.661 * [taylor]: Taking taylor expansion of N in N 0.661 * [taylor]: Taking taylor expansion of N in N 0.664 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.664 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.664 * [taylor]: Taking taylor expansion of -1 in N 0.664 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.665 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.665 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.665 * [taylor]: Taking taylor expansion of 1/3 in N 0.665 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.665 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.665 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.665 * [taylor]: Taking taylor expansion of 1.0 in N 0.665 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.665 * [taylor]: Taking taylor expansion of N in N 0.665 * [taylor]: Taking taylor expansion of N in N 0.698 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.698 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.698 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.698 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.699 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.699 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.699 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.701 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (* 1.0 (/ (pow (cbrt -1) 3) N)) 1) (/ (pow (cbrt -1) 3) (pow N 2)))) in (N) around 0 0.701 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (* 1.0 (/ (pow (cbrt -1) 3) N)) 1) (/ (pow (cbrt -1) 3) (pow N 2)))) in N 0.702 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (* 1.0 (/ (pow (cbrt -1) 3) N)) 1) (/ (pow (cbrt -1) 3) (pow N 2)))) in N 0.704 * * * [progress]: simplifying candidates 0.705 * [simplify]: Simplifying using # : (log (cbrt (* (+ N 1.0) N))) (exp (cbrt (* (+ N 1.0) N))) (cbrt (+ N 1.0)) (cbrt N) (cbrt (* (+ (pow N 3) (pow 1.0 3)) N)) (cbrt (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (cbrt (* (- (* N N) (* 1.0 1.0)) N)) (cbrt (- N 1.0)) (* (cbrt (cbrt (* (+ N 1.0) N))) (cbrt (cbrt (* (+ N 1.0) N)))) (cbrt (cbrt (* (+ N 1.0) N))) (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (log (cbrt (* (+ N 1.0) N))) (exp (cbrt (* (+ N 1.0) N))) (cbrt (+ N 1.0)) (cbrt N) (cbrt (* (+ (pow N 3) (pow 1.0 3)) N)) (cbrt (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (cbrt (* (- (* N N) (* 1.0 1.0)) N)) (cbrt (- N 1.0)) (* (cbrt (cbrt (* (+ N 1.0) N))) (cbrt (cbrt (* (+ N 1.0) N)))) (cbrt (cbrt (* (+ N 1.0) N))) (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (log (cbrt (* (+ N 1.0) N))) (exp (cbrt (* (+ N 1.0) N))) (cbrt (+ N 1.0)) (cbrt N) (cbrt (* (+ (pow N 3) (pow 1.0 3)) N)) (cbrt (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (cbrt (* (- (* N N) (* 1.0 1.0)) N)) (cbrt (- N 1.0)) (* (cbrt (cbrt (* (+ N 1.0) N))) (cbrt (cbrt (* (+ N 1.0) N)))) (cbrt (cbrt (* (+ N 1.0) N))) (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (log (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (exp (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (* (cbrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (cbrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N))))))) (cbrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (* (* (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N))))) (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (sqrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (sqrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (- (+ (exp (* 1/3 (+ (log 1.0) (log N)))) (+ (* 0.05555555555555555 (* (exp (* 1/3 (+ (log 1.0) (log N)))) (pow N 2))) (* 0.3333333333333333 (* (exp (* 1/3 (+ (log 1.0) (log N)))) N)))) (* 1/6 (/ (* (exp (* 1/3 (+ (log 1.0) (log N)))) (pow N 2)) (pow 1.0 2)))) (- (+ (pow (/ 1 N) -2/3) (* 0.3333333333333333 (pow (/ 1 N) 1/3))) (* 0.1111111111111111 (pow (/ 1 (pow N 4)) 1/3))) (- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 0.3333333333333333 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 0.1111111111111111 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2)))) (- (+ (exp (* 1/3 (+ (log 1.0) (log N)))) (+ (* 0.05555555555555555 (* (exp (* 1/3 (+ (log 1.0) (log N)))) (pow N 2))) (* 0.3333333333333333 (* (exp (* 1/3 (+ (log 1.0) (log N)))) N)))) (* 1/6 (/ (* (exp (* 1/3 (+ (log 1.0) (log N)))) (pow N 2)) (pow 1.0 2)))) (- (+ (pow (/ 1 N) -2/3) (* 0.3333333333333333 (pow (/ 1 N) 1/3))) (* 0.1111111111111111 (pow (/ 1 (pow N 4)) 1/3))) (- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 0.3333333333333333 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 0.1111111111111111 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2)))) (- (+ (exp (* 1/3 (+ (log 1.0) (log N)))) (+ (* 0.05555555555555555 (* (exp (* 1/3 (+ (log 1.0) (log N)))) (pow N 2))) (* 0.3333333333333333 (* (exp (* 1/3 (+ (log 1.0) (log N)))) N)))) (* 1/6 (/ (* (exp (* 1/3 (+ (log 1.0) (log N)))) (pow N 2)) (pow 1.0 2)))) (- (+ (pow (/ 1 N) -2/3) (* 0.3333333333333333 (pow (/ 1 N) 1/3))) (* 0.1111111111111111 (pow (/ 1 (pow N 4)) 1/3))) (- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 0.3333333333333333 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 0.1111111111111111 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2)))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.711 * * [simplify]: iteration 0 : 208 enodes (cost 572 ) 0.715 * * [simplify]: iteration 1 : 609 enodes (cost 524 ) 0.727 * * [simplify]: iteration 2 : 2254 enodes (cost 482 ) 0.775 * * [simplify]: iteration 3 : 5001 enodes (cost 474 ) 0.778 * [simplify]: Simplified to: (log (cbrt (* (+ N 1.0) N))) (exp (cbrt (* (+ N 1.0) N))) (cbrt (+ N 1.0)) (pow N 1/3) (cbrt (* (+ (pow N 3) (pow 1.0 3)) N)) (cbrt (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (cbrt (* (- (* N N) (* 1.0 1.0)) N)) (cbrt (- N 1.0)) (* (cbrt (cbrt (* (+ N 1.0) N))) (cbrt (cbrt (* (+ N 1.0) N)))) (cbrt (cbrt (* (+ N 1.0) N))) (* (+ N 1.0) N) (sqrt (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (log (cbrt (* (+ N 1.0) N))) (exp (cbrt (* (+ N 1.0) N))) (cbrt (+ N 1.0)) (pow N 1/3) (cbrt (* (+ (pow N 3) (pow 1.0 3)) N)) (cbrt (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (cbrt (* (- (* N N) (* 1.0 1.0)) N)) (cbrt (- N 1.0)) (* (cbrt (cbrt (* (+ N 1.0) N))) (cbrt (cbrt (* (+ N 1.0) N)))) (cbrt (cbrt (* (+ N 1.0) N))) (* (+ N 1.0) N) (sqrt (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (log (cbrt (* (+ N 1.0) N))) (exp (cbrt (* (+ N 1.0) N))) (cbrt (+ N 1.0)) (pow N 1/3) (cbrt (* (+ (pow N 3) (pow 1.0 3)) N)) (cbrt (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (cbrt (* (- (* N N) (* 1.0 1.0)) N)) (cbrt (- N 1.0)) (* (cbrt (cbrt (* (+ N 1.0) N))) (cbrt (cbrt (* (+ N 1.0) N)))) (cbrt (cbrt (* (+ N 1.0) N))) (* (+ N 1.0) N) (sqrt (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (log (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (exp (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (* (cbrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (cbrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N))))))) (cbrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 3) (sqrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (sqrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (+ (+ (/ -1/6 (* (/ 1.0 (pow N 2)) (/ 1.0 (* (pow N 1/3) (pow 1.0 1/3))))) (* (pow N 1/3) (pow 1.0 1/3))) (* (* (pow N 1/3) (pow 1.0 1/3)) (+ (* N 0.3333333333333333) (* (pow N 2) 0.05555555555555555)))) (- (+ (pow (/ 1 N) -2/3) (* 0.3333333333333333 (pow (/ 1 N) 1/3))) (* 0.1111111111111111 (pow (/ 1 (pow N 4)) 1/3))) (- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 0.3333333333333333 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 0.1111111111111111 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2)))) (+ (+ (/ -1/6 (* (/ 1.0 (pow N 2)) (/ 1.0 (* (pow N 1/3) (pow 1.0 1/3))))) (* (pow N 1/3) (pow 1.0 1/3))) (* (* (pow N 1/3) (pow 1.0 1/3)) (+ (* N 0.3333333333333333) (* (pow N 2) 0.05555555555555555)))) (- (+ (pow (/ 1 N) -2/3) (* 0.3333333333333333 (pow (/ 1 N) 1/3))) (* 0.1111111111111111 (pow (/ 1 (pow N 4)) 1/3))) (- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 0.3333333333333333 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 0.1111111111111111 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2)))) (+ (+ (/ -1/6 (* (/ 1.0 (pow N 2)) (/ 1.0 (* (pow N 1/3) (pow 1.0 1/3))))) (* (pow N 1/3) (pow 1.0 1/3))) (* (* (pow N 1/3) (pow 1.0 1/3)) (+ (* N 0.3333333333333333) (* (pow N 2) 0.05555555555555555)))) (- (+ (pow (/ 1 N) -2/3) (* 0.3333333333333333 (pow (/ 1 N) 1/3))) (* 0.1111111111111111 (pow (/ 1 (pow N 4)) 1/3))) (- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 0.3333333333333333 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 0.1111111111111111 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2)))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.779 * * * [progress]: adding candidates to table 0.924 * * [progress]: iteration 4 / 4 0.924 * * * [progress]: picking best candidate 0.939 * * * * [pick]: Picked # 0.939 * * * [progress]: localizing error 0.947 * * * [progress]: generating rewritten candidates 0.947 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.948 * * * * [progress]: [ 2 / 2 ] rewriting at (2 2) 0.955 * * * [progress]: generating series expansions 0.955 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.956 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.956 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.956 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.956 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.956 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.957 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.957 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.957 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.958 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.958 * * * * [progress]: [ 2 / 2 ] generating series at (2 2) 0.958 * [approximate]: Taking taylor expansion of (+ (pow N 2) (+ (* 1.0 N) 1)) in (N) around 0 0.958 * [taylor]: Taking taylor expansion of (+ (pow N 2) (+ (* 1.0 N) 1)) in N 0.958 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.958 * [taylor]: Taking taylor expansion of N in N 0.958 * [taylor]: Taking taylor expansion of (+ (* 1.0 N) 1) in N 0.958 * [taylor]: Taking taylor expansion of (* 1.0 N) in N 0.958 * [taylor]: Taking taylor expansion of 1.0 in N 0.958 * [taylor]: Taking taylor expansion of N in N 0.958 * [taylor]: Taking taylor expansion of 1 in N 0.958 * [taylor]: Taking taylor expansion of (+ (pow N 2) (+ (* 1.0 N) 1)) in N 0.958 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.958 * [taylor]: Taking taylor expansion of N in N 0.958 * [taylor]: Taking taylor expansion of (+ (* 1.0 N) 1) in N 0.958 * [taylor]: Taking taylor expansion of (* 1.0 N) in N 0.959 * [taylor]: Taking taylor expansion of 1.0 in N 0.959 * [taylor]: Taking taylor expansion of N in N 0.959 * [taylor]: Taking taylor expansion of 1 in N 0.963 * [approximate]: Taking taylor expansion of (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)) in (N) around 0 0.963 * [taylor]: Taking taylor expansion of (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)) in N 0.963 * [taylor]: Taking taylor expansion of (* 1.0 (/ 1 N)) in N 0.963 * [taylor]: Taking taylor expansion of 1.0 in N 0.963 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.963 * [taylor]: Taking taylor expansion of N in N 0.963 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow N 2)) 1) in N 0.963 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.963 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.963 * [taylor]: Taking taylor expansion of N in N 0.964 * [taylor]: Taking taylor expansion of 1 in N 0.964 * [taylor]: Taking taylor expansion of (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)) in N 0.964 * [taylor]: Taking taylor expansion of (* 1.0 (/ 1 N)) in N 0.964 * [taylor]: Taking taylor expansion of 1.0 in N 0.964 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.964 * [taylor]: Taking taylor expansion of N in N 0.964 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow N 2)) 1) in N 0.964 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.964 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.964 * [taylor]: Taking taylor expansion of N in N 0.964 * [taylor]: Taking taylor expansion of 1 in N 0.969 * [approximate]: Taking taylor expansion of (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))) in (N) around 0 0.969 * [taylor]: Taking taylor expansion of (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))) in N 0.969 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow N 2)) 1) in N 0.969 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.970 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.970 * [taylor]: Taking taylor expansion of N in N 0.970 * [taylor]: Taking taylor expansion of 1 in N 0.970 * [taylor]: Taking taylor expansion of (* 1.0 (/ 1 N)) in N 0.970 * [taylor]: Taking taylor expansion of 1.0 in N 0.970 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.970 * [taylor]: Taking taylor expansion of N in N 0.970 * [taylor]: Taking taylor expansion of (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))) in N 0.970 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow N 2)) 1) in N 0.970 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.970 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.970 * [taylor]: Taking taylor expansion of N in N 0.971 * [taylor]: Taking taylor expansion of 1 in N 0.971 * [taylor]: Taking taylor expansion of (* 1.0 (/ 1 N)) in N 0.971 * [taylor]: Taking taylor expansion of 1.0 in N 0.971 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.971 * [taylor]: Taking taylor expansion of N in N 0.977 * * * [progress]: simplifying candidates 0.978 * [simplify]: Simplifying using # : (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (exp (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (* (cbrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (cbrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))))) (cbrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (* (* (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (* (exp (pow N 2)) (* (exp (* 1.0 N)) (exp 1))) (* (exp (pow N 2)) (exp (+ (* 1.0 N) 1))) (log (+ (pow N 2) (+ (* 1.0 N) 1))) (exp (+ (pow N 2) (+ (* 1.0 N) 1))) (* (cbrt (+ (pow N 2) (+ (* 1.0 N) 1))) (cbrt (+ (pow N 2) (+ (* 1.0 N) 1)))) (cbrt (+ (pow N 2) (+ (* 1.0 N) 1))) (* (* (+ (pow N 2) (+ (* 1.0 N) 1)) (+ (pow N 2) (+ (* 1.0 N) 1))) (+ (pow N 2) (+ (* 1.0 N) 1))) (sqrt (+ (pow N 2) (+ (* 1.0 N) 1))) (sqrt (+ (pow N 2) (+ (* 1.0 N) 1))) (+ (pow (pow N 2) 3) (pow (+ (* 1.0 N) 1) 3)) (+ (* (pow N 2) (pow N 2)) (- (* (+ (* 1.0 N) 1) (+ (* 1.0 N) 1)) (* (pow N 2) (+ (* 1.0 N) 1)))) (- (* (pow N 2) (pow N 2)) (* (+ (* 1.0 N) 1) (+ (* 1.0 N) 1))) (- (pow N 2) (+ (* 1.0 N) 1)) (+ (pow N 2) (+ (* 1.0 N) 1)) (+ (pow N 2) (* 1.0 N)) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (+ (pow N 2) (+ (* 1.0 N) 1)) (+ (pow N 2) (+ (* 1.0 N) 1)) (+ (pow N 2) (+ (* 1.0 N) 1)) 0.982 * * [simplify]: iteration 0 : 114 enodes (cost 181 ) 0.985 * * [simplify]: iteration 1 : 447 enodes (cost 154 ) 0.997 * * [simplify]: iteration 2 : 2686 enodes (cost 153 ) 1.055 * * [simplify]: iteration 3 : 5001 enodes (cost 150 ) 1.057 * [simplify]: Simplified to: (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (exp (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (* (cbrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (cbrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))))) (cbrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 3) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (pow E (+ 1 (* N (+ 1.0 N)))) (pow E (+ 1 (* N (+ 1.0 N)))) (log (+ (pow N 2) (+ (* 1.0 N) 1))) (pow E (+ 1 (* N (+ 1.0 N)))) (* (cbrt (+ (pow N 2) (+ (* 1.0 N) 1))) (cbrt (+ (pow N 2) (+ (* 1.0 N) 1)))) (cbrt (+ (pow N 2) (+ (* 1.0 N) 1))) (pow (+ 1 (* N (+ 1.0 N))) 3) (sqrt (+ (pow N 2) (+ (* 1.0 N) 1))) (sqrt (+ (pow N 2) (+ (* 1.0 N) 1))) (+ (pow (pow N 2) 3) (pow (+ (* 1.0 N) 1) 3)) (+ (* (+ (* 1.0 N) 1) (- (+ (* 1.0 N) 1) (pow N 2))) (pow N 4)) (* (+ (* N (- N 1.0)) -1) (+ 1 (* N (+ 1.0 N)))) (+ (* N (- N 1.0)) -1) (+ 1 (* N (+ 1.0 N))) (* N (+ 1.0 N)) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (+ 1 (* N (+ 1.0 N))) (+ 1 (* N (+ 1.0 N))) (+ 1 (* N (+ 1.0 N))) 1.057 * * * [progress]: adding candidates to table 1.099 * [progress]: [Phase 3 of 3] Extracting. 1.099 * * [regime]: Finding splitpoints for: (# # # # # # #) 1.100 * * * [regime-changes]: Trying 1 branch expressions: (N) 1.100 * * * * [regimes]: Trying to branch on N from (# # # # # # #) 1.122 * * * [regime]: Found split indices: #