6.081 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.026 * * * [progress]: [2/2] Setting up program. 0.029 * [progress]: [Phase 2 of 3] Improving. 0.029 * [simplify]: Simplifying using # : (- (atan (+ N 1.0)) (atan N)) 0.031 * * [simplify]: iteration 0 : 9 enodes (cost 4 ) 0.032 * * [simplify]: iteration 1 : 10 enodes (cost 4 ) 0.033 * * [simplify]: iteration 2 : 10 enodes (cost 4 ) 0.033 * [simplify]: Simplified to: (- (atan (+ N 1.0)) (atan N)) 0.033 * * [progress]: iteration 1 / 4 0.033 * * * [progress]: picking best candidate 0.035 * * * * [pick]: Picked # 0.035 * * * [progress]: localizing error 0.041 * * * [progress]: generating rewritten candidates 0.041 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.044 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 0.045 * * * [progress]: generating series expansions 0.045 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.045 * [approximate]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in (N) around 0 0.045 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.045 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.046 * [taylor]: Taking taylor expansion of (atan N) in N 0.046 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.046 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.046 * [taylor]: Taking taylor expansion of (atan N) in N 0.046 * [approximate]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in (N) around 0 0.046 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.046 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.046 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.046 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.046 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.046 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.047 * [approximate]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in (N) around 0 0.047 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.047 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.047 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.047 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.047 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.047 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.047 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 0.047 * [approximate]: Taking taylor expansion of (atan (+ N 1.0)) in (N) around 0 0.047 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.047 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.048 * [approximate]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in (N) around 0 0.048 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.048 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.048 * [approximate]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in (N) around 0 0.048 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.048 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.048 * * * [progress]: simplifying candidates 0.049 * [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)) 0.051 * * [simplify]: iteration 0 : 75 enodes (cost 154 ) 0.053 * * [simplify]: iteration 1 : 145 enodes (cost 145 ) 0.055 * * [simplify]: iteration 2 : 289 enodes (cost 143 ) 0.060 * * [simplify]: iteration 3 : 681 enodes (cost 142 ) 0.072 * * [simplify]: iteration 4 : 2447 enodes (cost 142 ) 0.119 * * [simplify]: iteration 5 : 5001 enodes (cost 142 ) 0.120 * [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)) 0.121 * * * [progress]: adding candidates to table 0.155 * * [progress]: iteration 2 / 4 0.155 * * * [progress]: picking best candidate 0.160 * * * * [pick]: Picked # 0.160 * * * [progress]: localizing error 0.166 * * * [progress]: generating rewritten candidates 0.166 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.167 * * * * [progress]: [ 2 / 2 ] rewriting at (2 2 2) 0.173 * * * [progress]: generating series expansions 0.173 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.173 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.173 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.173 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.174 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.174 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.174 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.175 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.175 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.175 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.175 * * * * [progress]: [ 2 / 2 ] generating series at (2 2 2) 0.175 * [approximate]: Taking taylor expansion of (* N (+ N 1.0)) in (N) around 0 0.175 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.175 * [taylor]: Taking taylor expansion of N in N 0.175 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.175 * [taylor]: Taking taylor expansion of N in N 0.175 * [taylor]: Taking taylor expansion of 1.0 in N 0.175 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.175 * [taylor]: Taking taylor expansion of N in N 0.175 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.175 * [taylor]: Taking taylor expansion of N in N 0.175 * [taylor]: Taking taylor expansion of 1.0 in N 0.176 * [approximate]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in (N) around 0 0.176 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.176 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.176 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.176 * [taylor]: Taking taylor expansion of N in N 0.176 * [taylor]: Taking taylor expansion of 1.0 in N 0.176 * [taylor]: Taking taylor expansion of N in N 0.176 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.176 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.176 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.176 * [taylor]: Taking taylor expansion of N in N 0.176 * [taylor]: Taking taylor expansion of 1.0 in N 0.176 * [taylor]: Taking taylor expansion of N in N 0.178 * [approximate]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in (N) around 0 0.178 * [taylor]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in N 0.178 * [taylor]: Taking taylor expansion of -1 in N 0.178 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.178 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.178 * [taylor]: Taking taylor expansion of 1.0 in N 0.178 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.178 * [taylor]: Taking taylor expansion of N in N 0.178 * [taylor]: Taking taylor expansion of N in N 0.178 * [taylor]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in N 0.178 * [taylor]: Taking taylor expansion of -1 in N 0.178 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.178 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.178 * [taylor]: Taking taylor expansion of 1.0 in N 0.178 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.178 * [taylor]: Taking taylor expansion of N in N 0.178 * [taylor]: Taking taylor expansion of N in N 0.180 * * * [progress]: simplifying candidates 0.180 * [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)) 0.183 * * [simplify]: iteration 0 : 121 enodes (cost 151 ) 0.186 * * [simplify]: iteration 1 : 432 enodes (cost 127 ) 0.195 * * [simplify]: iteration 2 : 2321 enodes (cost 127 ) 0.232 * * [simplify]: iteration 3 : 5002 enodes (cost 127 ) 0.233 * [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) 0.233 * * * [progress]: adding candidates to table 0.273 * * [progress]: iteration 3 / 4 0.273 * * * [progress]: picking best candidate 0.289 * * * * [pick]: Picked # 0.290 * * * [progress]: localizing error 0.298 * * * [progress]: generating rewritten candidates 0.298 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.299 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 0.300 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 0.306 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 0.309 * * * [progress]: generating series expansions 0.309 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.309 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 0.309 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.309 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.309 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.309 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.311 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 0.311 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.311 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.311 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.311 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.313 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 0.313 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.313 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.314 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.314 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.315 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 0.315 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 0.315 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.315 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.316 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.316 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.319 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 0.319 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.319 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.320 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.320 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.321 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 0.321 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.321 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.322 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.322 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.324 * * * * [progress]: [ 3 / 4 ] generating series at (2) 0.324 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.324 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.324 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.324 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.324 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.325 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.325 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.325 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.325 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.326 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 0.326 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.326 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.326 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.327 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.327 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.327 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.327 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.327 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.328 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.328 * * * [progress]: simplifying candidates 0.329 * [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))) 0.335 * * [simplify]: iteration 0 : 110 enodes (cost 649 ) 0.337 * * [simplify]: iteration 1 : 391 enodes (cost 565 ) 0.348 * * [simplify]: iteration 2 : 2248 enodes (cost 539 ) 0.429 * * [simplify]: iteration 3 : 5001 enodes (cost 520 ) 0.433 * [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))) 0.433 * * * [progress]: adding candidates to table 0.549 * * [progress]: iteration 4 / 4 0.549 * * * [progress]: picking best candidate 0.567 * * * * [pick]: Picked # 0.567 * * * [progress]: localizing error 0.580 * * * [progress]: generating rewritten candidates 0.580 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 1) 0.581 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 1) 0.584 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.585 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2) 0.592 * * * [progress]: generating series expansions 0.592 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 1) 0.592 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) in (N) around 0 0.593 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) in N 0.593 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) in N 0.593 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))))) in N 0.593 * [taylor]: Taking taylor expansion of 1/3 in N 0.593 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.593 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.593 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) in N 0.593 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) in N 0.593 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))))) in N 0.593 * [taylor]: Taking taylor expansion of 1/3 in N 0.593 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.593 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.603 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/3) in (N) around 0 0.603 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/3) in N 0.603 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) in N 0.603 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))))) in N 0.603 * [taylor]: Taking taylor expansion of 1/3 in N 0.603 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.603 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.603 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/3) in N 0.603 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) in N 0.603 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))))) in N 0.603 * [taylor]: Taking taylor expansion of 1/3 in N 0.603 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.603 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.614 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/3) in (N) around 0 0.614 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/3) in N 0.614 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) in N 0.614 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))))) in N 0.614 * [taylor]: Taking taylor expansion of 1/3 in N 0.614 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.614 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.615 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/3) in N 0.615 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) in N 0.615 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))))) in N 0.615 * [taylor]: Taking taylor expansion of 1/3 in N 0.615 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.615 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.625 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 1) 0.626 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) in (N) around 0 0.626 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) in N 0.626 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) in N 0.626 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))))) in N 0.626 * [taylor]: Taking taylor expansion of 1/3 in N 0.626 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.626 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.626 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) in N 0.626 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) in N 0.626 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))))) in N 0.626 * [taylor]: Taking taylor expansion of 1/3 in N 0.626 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.626 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.636 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/3) in (N) around 0 0.636 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/3) in N 0.636 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) in N 0.636 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))))) in N 0.636 * [taylor]: Taking taylor expansion of 1/3 in N 0.636 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.636 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.637 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/3) in N 0.637 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) in N 0.637 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))))) in N 0.637 * [taylor]: Taking taylor expansion of 1/3 in N 0.637 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.637 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.648 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/3) in (N) around 0 0.648 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/3) in N 0.648 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) in N 0.648 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))))) in N 0.648 * [taylor]: Taking taylor expansion of 1/3 in N 0.648 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.648 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.648 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/3) in N 0.648 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) in N 0.648 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))))) in N 0.648 * [taylor]: Taking taylor expansion of 1/3 in N 0.648 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.648 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.659 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 0.659 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 0.659 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.659 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.660 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.660 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.661 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 0.661 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.661 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.662 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.662 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.663 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 0.663 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.663 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.664 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.664 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.665 * * * * [progress]: [ 4 / 4 ] generating series at (2 2) 0.666 * [approximate]: Taking taylor expansion of (* (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/6) (fabs (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3))) in (N) around 0 0.666 * [taylor]: Taking taylor expansion of (* (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/6) (fabs (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3))) in N 0.666 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/6) in N 0.666 * [taylor]: Taking taylor expansion of (exp (* 1/6 (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) in N 0.666 * [taylor]: Taking taylor expansion of (* 1/6 (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))))) in N 0.666 * [taylor]: Taking taylor expansion of 1/6 in N 0.666 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.666 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.666 * [taylor]: Taking taylor expansion of (fabs (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3)) in N 0.666 * [taylor]: Taking taylor expansion of (* (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/6) (fabs (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3))) in N 0.666 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/6) in N 0.666 * [taylor]: Taking taylor expansion of (exp (* 1/6 (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) in N 0.667 * [taylor]: Taking taylor expansion of (* 1/6 (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))))) in N 0.667 * [taylor]: Taking taylor expansion of 1/6 in N 0.667 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.667 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.667 * [taylor]: Taking taylor expansion of (fabs (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3)) in N 0.680 * [approximate]: Taking taylor expansion of (* (fabs (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/3)) (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/6)) in (N) around 0 0.680 * [taylor]: Taking taylor expansion of (* (fabs (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/3)) (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/6)) in N 0.680 * [taylor]: Taking taylor expansion of (fabs (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/3)) in N 0.681 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/6) in N 0.681 * [taylor]: Taking taylor expansion of (exp (* 1/6 (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) in N 0.681 * [taylor]: Taking taylor expansion of (* 1/6 (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))))) in N 0.681 * [taylor]: Taking taylor expansion of 1/6 in N 0.681 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.681 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.681 * [taylor]: Taking taylor expansion of (* (fabs (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/3)) (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/6)) in N 0.681 * [taylor]: Taking taylor expansion of (fabs (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/3)) in N 0.681 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/6) in N 0.681 * [taylor]: Taking taylor expansion of (exp (* 1/6 (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) in N 0.681 * [taylor]: Taking taylor expansion of (* 1/6 (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))))) in N 0.682 * [taylor]: Taking taylor expansion of 1/6 in N 0.682 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.682 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.695 * [approximate]: Taking taylor expansion of (* (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/6) (fabs (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/3))) in (N) around 0 0.695 * [taylor]: Taking taylor expansion of (* (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/6) (fabs (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/3))) in N 0.695 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/6) in N 0.695 * [taylor]: Taking taylor expansion of (exp (* 1/6 (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) in N 0.695 * [taylor]: Taking taylor expansion of (* 1/6 (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))))) in N 0.695 * [taylor]: Taking taylor expansion of 1/6 in N 0.695 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.695 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.696 * [taylor]: Taking taylor expansion of (fabs (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/3)) in N 0.696 * [taylor]: Taking taylor expansion of (* (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/6) (fabs (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/3))) in N 0.696 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/6) in N 0.696 * [taylor]: Taking taylor expansion of (exp (* 1/6 (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) in N 0.696 * [taylor]: Taking taylor expansion of (* 1/6 (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))))) in N 0.696 * [taylor]: Taking taylor expansion of 1/6 in N 0.696 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.696 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.697 * [taylor]: Taking taylor expansion of (fabs (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/3)) in N 0.709 * * * [progress]: simplifying candidates 0.711 * [simplify]: Simplifying using # : (log (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (cbrt (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 1) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (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))))) (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))))) (log (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (cbrt (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 1) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (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))))) (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))))) (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))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (+ (log (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (log (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (log (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (exp (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (* (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (fabs (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 (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (cbrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (cbrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))) (cbrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (* (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (sqrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (sqrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (cbrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt 1))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (* (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt 1)) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 1) (* (cbrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) (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)))) (* (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/6) (fabs (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3))) (* (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/6) (fabs (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3))) (* (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/6) (fabs (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3))) 0.715 * * [simplify]: iteration 0 : 137 enodes (cost 815 ) 0.718 * * [simplify]: iteration 1 : 390 enodes (cost 742 ) 0.726 * * [simplify]: iteration 2 : 1504 enodes (cost 732 ) 0.756 * * [simplify]: iteration 3 : 5002 enodes (cost 724 ) 0.760 * [simplify]: Simplified to: (log (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (cbrt (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))))) 1 (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (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))))) (log (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (cbrt (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))))) 1 (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (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))))) (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))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (log (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (log (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (exp (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (pow (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) 3) (* (cbrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (cbrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))) (cbrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (pow (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) 3) (sqrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (sqrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (cbrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (fabs (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (cbrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (fabs (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)))) (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)))) (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 (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 1/6) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 1/6) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 1/6) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) 0.760 * * * [progress]: adding candidates to table 0.944 * [progress]: [Phase 3 of 3] Extracting. 0.944 * * [regime]: Finding splitpoints for: (# # # # # # # #) 0.945 * * * [regime-changes]: Trying 1 branch expressions: (N) 0.945 * * * * [regimes]: Trying to branch on N from (# # # # # # # #) 0.991 * * * [regime]: Found split indices: #