10.577 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.025 * * * [progress]: [2/2] Setting up program. 0.027 * [progress]: [Phase 2 of 3] Improving. 0.027 * [simplify]: Simplifying using # : (- (atan (+ N 1.0)) (atan N)) 0.029 * * [simplify]: iteration 0 : 9 enodes (cost 4 ) 0.030 * * [simplify]: iteration 1 : 10 enodes (cost 4 ) 0.031 * * [simplify]: iteration 2 : 10 enodes (cost 4 ) 0.031 * [simplify]: Simplified to: (- (atan (+ N 1.0)) (atan N)) 0.032 * * [progress]: iteration 1 / 4 0.032 * * * [progress]: picking best candidate 0.033 * * * * [pick]: Picked # 0.033 * * * [progress]: localizing error 0.039 * * * [progress]: generating rewritten candidates 0.039 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.042 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 0.043 * * * [progress]: generating series expansions 0.044 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.044 * [approximate]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in (N) around 0 0.044 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.044 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.044 * [taylor]: Taking taylor expansion of (atan N) in N 0.044 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.044 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.044 * [taylor]: Taking taylor expansion of (atan N) in N 0.047 * [approximate]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in (N) around 0 0.047 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.047 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.047 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.047 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.047 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.048 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.051 * [approximate]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in (N) around 0 0.051 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.051 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.051 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.051 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.051 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.051 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.054 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 0.054 * [approximate]: Taking taylor expansion of (atan (+ N 1.0)) in (N) around 0 0.054 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.054 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.054 * [approximate]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in (N) around 0 0.054 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.055 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.055 * [approximate]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in (N) around 0 0.055 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.055 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.055 * * * [progress]: simplifying candidates 0.056 * [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)))) (- (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)) (- (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)) 0.059 * * [simplify]: iteration 0 : 75 enodes (cost 154 ) 0.060 * * [simplify]: iteration 1 : 145 enodes (cost 145 ) 0.063 * * [simplify]: iteration 2 : 289 enodes (cost 143 ) 0.068 * * [simplify]: iteration 3 : 681 enodes (cost 142 ) 0.080 * * [simplify]: iteration 4 : 2491 enodes (cost 142 ) 0.128 * * [simplify]: iteration 5 : 5001 enodes (cost 142 ) 0.129 * [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)) 0.130 * * * [progress]: adding candidates to table 0.199 * * [progress]: iteration 2 / 4 0.199 * * * [progress]: picking best candidate 0.205 * * * * [pick]: Picked # 0.205 * * * [progress]: localizing error 0.215 * * * [progress]: generating rewritten candidates 0.215 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.217 * * * * [progress]: [ 2 / 2 ] rewriting at (2 2 2) 0.228 * * * [progress]: generating series expansions 0.228 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.228 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.228 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.228 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.230 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.230 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.230 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.231 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.231 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.231 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.232 * * * * [progress]: [ 2 / 2 ] generating series at (2 2 2) 0.233 * [approximate]: Taking taylor expansion of (* N (+ N 1.0)) in (N) around 0 0.233 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.233 * [taylor]: Taking taylor expansion of N in N 0.233 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.233 * [taylor]: Taking taylor expansion of N in N 0.233 * [taylor]: Taking taylor expansion of 1.0 in N 0.233 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.233 * [taylor]: Taking taylor expansion of N in N 0.233 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.233 * [taylor]: Taking taylor expansion of N in N 0.233 * [taylor]: Taking taylor expansion of 1.0 in N 0.248 * [approximate]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in (N) around 0 0.248 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.248 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.248 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.248 * [taylor]: Taking taylor expansion of N in N 0.249 * [taylor]: Taking taylor expansion of 1.0 in N 0.249 * [taylor]: Taking taylor expansion of N in N 0.250 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.250 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.250 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.250 * [taylor]: Taking taylor expansion of N in N 0.250 * [taylor]: Taking taylor expansion of 1.0 in N 0.250 * [taylor]: Taking taylor expansion of N in N 0.267 * [approximate]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in (N) around 0 0.267 * [taylor]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in N 0.267 * [taylor]: Taking taylor expansion of -1 in N 0.267 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.267 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.267 * [taylor]: Taking taylor expansion of 1.0 in N 0.267 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.267 * [taylor]: Taking taylor expansion of N in N 0.268 * [taylor]: Taking taylor expansion of N in N 0.268 * [taylor]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in N 0.268 * [taylor]: Taking taylor expansion of -1 in N 0.268 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.268 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.268 * [taylor]: Taking taylor expansion of 1.0 in N 0.268 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.268 * [taylor]: Taking taylor expansion of N in N 0.269 * [taylor]: Taking taylor expansion of N in N 0.288 * * * [progress]: simplifying candidates 0.289 * [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)) 0.292 * * [simplify]: iteration 0 : 121 enodes (cost 151 ) 0.295 * * [simplify]: iteration 1 : 432 enodes (cost 127 ) 0.304 * * [simplify]: iteration 2 : 2321 enodes (cost 127 ) 0.341 * * [simplify]: iteration 3 : 5002 enodes (cost 127 ) 0.342 * [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) 0.343 * * * [progress]: adding candidates to table 0.391 * * [progress]: iteration 3 / 4 0.391 * * * [progress]: picking best candidate 0.397 * * * * [pick]: Picked # 0.397 * * * [progress]: localizing error 0.407 * * * [progress]: generating rewritten candidates 0.407 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 2) 0.411 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1 2) 0.416 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1 1) 0.420 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.421 * * * [progress]: generating series expansions 0.421 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 2) 0.421 * [approximate]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in (N) around 0 0.421 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.421 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.421 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.421 * [taylor]: Taking taylor expansion of 1/3 in N 0.421 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.421 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.421 * [taylor]: Taking taylor expansion of N in N 0.421 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.421 * [taylor]: Taking taylor expansion of N in N 0.421 * [taylor]: Taking taylor expansion of 1.0 in N 0.425 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.425 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.425 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.425 * [taylor]: Taking taylor expansion of 1/3 in N 0.425 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.425 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.425 * [taylor]: Taking taylor expansion of N in N 0.425 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.425 * [taylor]: Taking taylor expansion of N in N 0.425 * [taylor]: Taking taylor expansion of 1.0 in N 0.454 * [approximate]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in (N) around 0 0.454 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.454 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.454 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.454 * [taylor]: Taking taylor expansion of 1/3 in N 0.454 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.454 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.454 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 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 0.455 * [taylor]: Taking taylor expansion of 1.0 in N 0.455 * [taylor]: Taking taylor expansion of N in N 0.456 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.456 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.456 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.456 * [taylor]: Taking taylor expansion of 1/3 in N 0.460 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.460 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.460 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.460 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.460 * [taylor]: Taking taylor expansion of N in N 0.461 * [taylor]: Taking taylor expansion of 1.0 in N 0.461 * [taylor]: Taking taylor expansion of N in N 0.481 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in (N) around 0 0.481 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.481 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.481 * [taylor]: Taking taylor expansion of -1 in N 0.482 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.482 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.482 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.482 * [taylor]: Taking taylor expansion of 1/3 in N 0.482 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.482 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.482 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.482 * [taylor]: Taking taylor expansion of 1.0 in N 0.482 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.482 * [taylor]: Taking taylor expansion of N in N 0.483 * [taylor]: Taking taylor expansion of N in N 0.485 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.485 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.485 * [taylor]: Taking taylor expansion of -1 in N 0.485 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.485 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.486 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.486 * [taylor]: Taking taylor expansion of 1/3 in N 0.486 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.486 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.486 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.486 * [taylor]: Taking taylor expansion of 1.0 in N 0.486 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.486 * [taylor]: Taking taylor expansion of N in N 0.486 * [taylor]: Taking taylor expansion of N in N 0.518 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1 2) 0.518 * [approximate]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in (N) around 0 0.518 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.518 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.518 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.518 * [taylor]: Taking taylor expansion of 1/3 in N 0.518 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.518 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.518 * [taylor]: Taking taylor expansion of N in N 0.518 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.518 * [taylor]: Taking taylor expansion of N in N 0.518 * [taylor]: Taking taylor expansion of 1.0 in N 0.521 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.521 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.521 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.521 * [taylor]: Taking taylor expansion of 1/3 in N 0.522 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.522 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.522 * [taylor]: Taking taylor expansion of N in N 0.522 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.522 * [taylor]: Taking taylor expansion of N in N 0.522 * [taylor]: Taking taylor expansion of 1.0 in N 0.557 * [approximate]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in (N) around 0 0.557 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.557 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.557 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.557 * [taylor]: Taking taylor expansion of 1/3 in N 0.557 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.557 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.557 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.557 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.557 * [taylor]: Taking taylor expansion of N in N 0.557 * [taylor]: Taking taylor expansion of 1.0 in N 0.557 * [taylor]: Taking taylor expansion of N in N 0.558 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.558 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.558 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.558 * [taylor]: Taking taylor expansion of 1/3 in N 0.558 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.558 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.558 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.558 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.558 * [taylor]: Taking taylor expansion of N in N 0.559 * [taylor]: Taking taylor expansion of 1.0 in N 0.559 * [taylor]: Taking taylor expansion of N in N 0.579 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in (N) around 0 0.579 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.579 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.579 * [taylor]: Taking taylor expansion of -1 in N 0.580 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.580 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.580 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.580 * [taylor]: Taking taylor expansion of 1/3 in N 0.580 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.580 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.580 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.580 * [taylor]: Taking taylor expansion of 1.0 in N 0.580 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.580 * [taylor]: Taking taylor expansion of N in N 0.580 * [taylor]: Taking taylor expansion of N in N 0.582 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.582 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.582 * [taylor]: Taking taylor expansion of -1 in N 0.583 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.583 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.583 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.583 * [taylor]: Taking taylor expansion of 1/3 in N 0.583 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.583 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.583 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.583 * [taylor]: Taking taylor expansion of 1.0 in N 0.583 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.583 * [taylor]: Taking taylor expansion of N in N 0.583 * [taylor]: Taking taylor expansion of N in N 0.615 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1 1) 0.615 * [approximate]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in (N) around 0 0.615 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.615 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.615 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.615 * [taylor]: Taking taylor expansion of 1/3 in N 0.616 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.616 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.616 * [taylor]: Taking taylor expansion of N in N 0.616 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.616 * [taylor]: Taking taylor expansion of N in N 0.616 * [taylor]: Taking taylor expansion of 1.0 in N 0.619 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.619 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.619 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.619 * [taylor]: Taking taylor expansion of 1/3 in N 0.619 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.619 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.619 * [taylor]: Taking taylor expansion of N in N 0.619 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.619 * [taylor]: Taking taylor expansion of N in N 0.619 * [taylor]: Taking taylor expansion of 1.0 in N 0.654 * [approximate]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in (N) around 0 0.654 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.655 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.655 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.655 * [taylor]: Taking taylor expansion of 1/3 in N 0.655 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.655 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.655 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.655 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.655 * [taylor]: Taking taylor expansion of N in N 0.655 * [taylor]: Taking taylor expansion of 1.0 in N 0.655 * [taylor]: Taking taylor expansion of N in N 0.656 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.656 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.656 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.656 * [taylor]: Taking taylor expansion of 1/3 in N 0.656 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.656 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.656 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.656 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.656 * [taylor]: Taking taylor expansion of N in N 0.656 * [taylor]: Taking taylor expansion of 1.0 in N 0.656 * [taylor]: Taking taylor expansion of N in N 0.677 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in (N) around 0 0.678 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.678 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.678 * [taylor]: Taking taylor expansion of -1 in N 0.678 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.678 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.678 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.678 * [taylor]: Taking taylor expansion of 1/3 in N 0.678 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.679 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.679 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.679 * [taylor]: Taking taylor expansion of 1.0 in N 0.679 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.679 * [taylor]: Taking taylor expansion of N in N 0.679 * [taylor]: Taking taylor expansion of N in N 0.681 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.681 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.681 * [taylor]: Taking taylor expansion of -1 in N 0.682 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.682 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.682 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.682 * [taylor]: Taking taylor expansion of 1/3 in N 0.682 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.682 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.682 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.682 * [taylor]: Taking taylor expansion of 1.0 in N 0.682 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.682 * [taylor]: Taking taylor expansion of N in N 0.682 * [taylor]: Taking taylor expansion of N in N 0.720 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.721 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.721 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.721 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.722 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.722 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.722 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.723 * [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 0.723 * [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 0.725 * [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 0.727 * * * [progress]: simplifying candidates 0.727 * [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))) 0.732 * * [simplify]: iteration 0 : 208 enodes (cost 572 ) 0.736 * * [simplify]: iteration 1 : 609 enodes (cost 524 ) 0.747 * * [simplify]: iteration 2 : 2244 enodes (cost 482 ) 0.792 * * [simplify]: iteration 3 : 5002 enodes (cost 474 ) 0.794 * [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)))))) (- (* (* (pow N 1/3) (pow 1.0 1/3)) (+ (* N 0.3333333333333333) (* (pow N 2) 0.05555555555555555))) (- (* (/ 1/6 (/ 1.0 N)) (/ (* (pow N 1/3) (pow 1.0 1/3)) (/ 1.0 N))) (* (pow N 1/3) (pow 1.0 1/3)))) (- (+ (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)))) (- (* (* (pow N 1/3) (pow 1.0 1/3)) (+ (* N 0.3333333333333333) (* (pow N 2) 0.05555555555555555))) (- (* (/ 1/6 (/ 1.0 N)) (/ (* (pow N 1/3) (pow 1.0 1/3)) (/ 1.0 N))) (* (pow N 1/3) (pow 1.0 1/3)))) (- (+ (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)))) (- (* (* (pow N 1/3) (pow 1.0 1/3)) (+ (* N 0.3333333333333333) (* (pow N 2) 0.05555555555555555))) (- (* (/ 1/6 (/ 1.0 N)) (/ (* (pow N 1/3) (pow 1.0 1/3)) (/ 1.0 N))) (* (pow N 1/3) (pow 1.0 1/3)))) (- (+ (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))) 0.795 * * * [progress]: adding candidates to table 0.935 * * [progress]: iteration 4 / 4 0.935 * * * [progress]: picking best candidate 0.942 * * * * [pick]: Picked # 0.942 * * * [progress]: localizing error 0.950 * * * [progress]: generating rewritten candidates 0.950 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.952 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 0.953 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 0.959 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 0.961 * * * [progress]: generating series expansions 0.961 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.962 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 0.962 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.962 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.962 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.962 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.966 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 0.966 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.966 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.967 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.967 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.971 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 0.971 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.971 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.971 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.971 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.976 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 0.976 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 0.976 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.976 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.976 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.976 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.980 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 0.980 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.980 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.980 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.981 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.985 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 0.985 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.985 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.985 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.985 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.989 * * * * [progress]: [ 3 / 4 ] generating series at (2) 0.990 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.990 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.990 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.990 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.990 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.991 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.991 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.991 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.992 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.992 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 0.992 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.992 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.993 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.993 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.993 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.993 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.994 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.994 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.994 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.995 * * * [progress]: simplifying candidates 1.000 * [simplify]: Simplifying using # : (log (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (sqrt (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))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt 1) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (/ 1 2) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (log (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (sqrt (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))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt 1) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (/ 1 2) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (+ 1/2 1/2) (+ 1/2 (/ 1 2)) (+ 1 1) (+ (/ 1 2) 1/2) (+ (/ 1 2) (/ 1 2)) (* (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))))) (* (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (+ 1 1) (+ (log (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (log (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (log (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (exp (* (sqrt (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)))) (sqrt (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)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (cbrt (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (cbrt (* (sqrt (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)))) (sqrt (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)))))) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (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 (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt 1) (sqrt 1)) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* 1 1) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* 2 1/2) (* 2 1) (* 2 (/ 1 2)) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt 1)) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 1) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (sqrt (sqrt (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)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (sqrt (sqrt (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)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (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)))) (sqrt (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)))) (sqrt (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)))) (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))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1.006 * * [simplify]: iteration 0 : 110 enodes (cost 649 ) 1.009 * * [simplify]: iteration 1 : 391 enodes (cost 565 ) 1.020 * * [simplify]: iteration 2 : 2248 enodes (cost 539 ) 1.101 * * [simplify]: iteration 3 : 5001 enodes (cost 520 ) 1.105 * [simplify]: Simplified to: (log (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (pow (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 3) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 1 (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 1/2 (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (log (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (pow (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 3) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 1 (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 1/2 (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 1 1 2 1 1 (pow (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 4) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (pow (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 4) 2 (log (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (log (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (exp (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 3) (pow (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 4) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 3) (pow (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 4) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (pow (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 4) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (pow (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 4) (cbrt (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)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 1 (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)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 1 (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)))) (sqrt (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)))) (sqrt (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)))) 1 2 1 (pow (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 5) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (pow (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 3) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (pow (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 3) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (pow (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 4) (* (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (pow (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 3) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (pow (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 3) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (log (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (exp (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (pow (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 4) (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)))) (sqrt (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)))) (sqrt (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)))) (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))) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 1.105 * * * [progress]: adding candidates to table 1.207 * [progress]: [Phase 3 of 3] Extracting. 1.207 * * [regime]: Finding splitpoints for: (# # # # # #) 1.210 * * * [regime-changes]: Trying 1 branch expressions: (N) 1.210 * * * * [regimes]: Trying to branch on N from (# # # # # #) 1.231 * * * [regime]: Found split indices: #