6.988 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.029 * * * [progress]: [2/2] Setting up program. 0.031 * [progress]: [Phase 2 of 3] Improving. 0.031 * [simplify]: Simplifying using # : (- (atan (+ N 1.0)) (atan N)) 0.033 * * [simplify]: iteration 0 : 9 enodes (cost 4 ) 0.034 * * [simplify]: iteration 1 : 10 enodes (cost 4 ) 0.035 * * [simplify]: iteration 2 : 10 enodes (cost 4 ) 0.036 * [simplify]: Simplified to: (- (atan (+ N 1.0)) (atan N)) 0.036 * * [progress]: iteration 1 / 4 0.036 * * * [progress]: picking best candidate 0.038 * * * * [pick]: Picked # 0.038 * * * [progress]: localizing error 0.044 * * * [progress]: generating rewritten candidates 0.044 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.048 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 0.049 * * * [progress]: generating series expansions 0.049 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.049 * [approximate]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in (N) around 0 0.049 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.049 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.050 * [taylor]: Taking taylor expansion of (atan N) in N 0.050 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.050 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.050 * [taylor]: Taking taylor expansion of (atan N) in N 0.054 * [approximate]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in (N) around 0 0.054 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.054 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.054 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.054 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.054 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.054 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.057 * [approximate]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in (N) around 0 0.057 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.057 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.057 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.057 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.057 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.057 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.061 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 0.061 * [approximate]: Taking taylor expansion of (atan (+ N 1.0)) in (N) around 0 0.061 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.061 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.061 * [approximate]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in (N) around 0 0.061 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.061 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.061 * [approximate]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in (N) around 0 0.061 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.061 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.062 * * * [progress]: simplifying candidates 0.062 * [simplify]: Simplifying using # : (- (+ N 1.0) N) (+ 1 (* (+ N 1.0) N)) (/ (exp (atan (+ N 1.0))) (exp (atan N))) (log (- (atan (+ N 1.0)) (atan N))) (exp (- (atan (+ N 1.0)) (atan N))) (* (cbrt (- (atan (+ N 1.0)) (atan N))) (cbrt (- (atan (+ N 1.0)) (atan N)))) (cbrt (- (atan (+ N 1.0)) (atan N))) (* (* (- (atan (+ N 1.0)) (atan N)) (- (atan (+ N 1.0)) (atan N))) (- (atan (+ N 1.0)) (atan N))) (sqrt (- (atan (+ N 1.0)) (atan N))) (sqrt (- (atan (+ N 1.0)) (atan N))) (- (pow (atan (+ N 1.0)) 3) (pow (atan N) 3)) (+ (* (atan (+ N 1.0)) (atan (+ N 1.0))) (+ (* (atan N) (atan N)) (* (atan (+ N 1.0)) (atan N)))) (- (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)) 0.065 * * [simplify]: iteration 0 : 75 enodes (cost 154 ) 0.067 * * [simplify]: iteration 1 : 145 enodes (cost 145 ) 0.070 * * [simplify]: iteration 2 : 289 enodes (cost 143 ) 0.074 * * [simplify]: iteration 3 : 681 enodes (cost 142 ) 0.087 * * [simplify]: iteration 4 : 2491 enodes (cost 142 ) 0.135 * * [simplify]: iteration 5 : 5001 enodes (cost 142 ) 0.137 * [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)) 0.137 * * * [progress]: adding candidates to table 0.183 * * [progress]: iteration 2 / 4 0.183 * * * [progress]: picking best candidate 0.186 * * * * [pick]: Picked # 0.186 * * * [progress]: localizing error 0.192 * * * [progress]: generating rewritten candidates 0.192 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.193 * * * * [progress]: [ 2 / 2 ] rewriting at (2 2 2) 0.199 * * * [progress]: generating series expansions 0.199 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.200 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.200 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.200 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.200 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.200 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.201 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.201 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.201 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.201 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.202 * * * * [progress]: [ 2 / 2 ] generating series at (2 2 2) 0.202 * [approximate]: Taking taylor expansion of (* N (+ N 1.0)) in (N) around 0 0.202 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.202 * [taylor]: Taking taylor expansion of N in N 0.202 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.202 * [taylor]: Taking taylor expansion of N in N 0.202 * [taylor]: Taking taylor expansion of 1.0 in N 0.202 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.202 * [taylor]: Taking taylor expansion of N in N 0.202 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.202 * [taylor]: Taking taylor expansion of N in N 0.202 * [taylor]: Taking taylor expansion of 1.0 in N 0.212 * [approximate]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in (N) around 0 0.212 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.212 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.212 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.212 * [taylor]: Taking taylor expansion of N in N 0.212 * [taylor]: Taking taylor expansion of 1.0 in N 0.212 * [taylor]: Taking taylor expansion of N in N 0.213 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.213 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.213 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.213 * [taylor]: Taking taylor expansion of N in N 0.213 * [taylor]: Taking taylor expansion of 1.0 in N 0.213 * [taylor]: Taking taylor expansion of N in N 0.223 * [approximate]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in (N) around 0 0.223 * [taylor]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in N 0.223 * [taylor]: Taking taylor expansion of -1 in N 0.223 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.223 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.223 * [taylor]: Taking taylor expansion of 1.0 in N 0.223 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.223 * [taylor]: Taking taylor expansion of N in N 0.224 * [taylor]: Taking taylor expansion of N in N 0.225 * [taylor]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in N 0.225 * [taylor]: Taking taylor expansion of -1 in N 0.225 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.225 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.225 * [taylor]: Taking taylor expansion of 1.0 in N 0.225 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.225 * [taylor]: Taking taylor expansion of N in N 0.225 * [taylor]: Taking taylor expansion of N in N 0.246 * * * [progress]: simplifying candidates 0.247 * [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)) 0.250 * * [simplify]: iteration 0 : 121 enodes (cost 151 ) 0.253 * * [simplify]: iteration 1 : 432 enodes (cost 127 ) 0.263 * * [simplify]: iteration 2 : 2321 enodes (cost 127 ) 0.300 * * [simplify]: iteration 3 : 5002 enodes (cost 127 ) 0.302 * [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) 0.302 * * * [progress]: adding candidates to table 0.353 * * [progress]: iteration 3 / 4 0.353 * * * [progress]: picking best candidate 0.368 * * * * [pick]: Picked # 0.368 * * * [progress]: localizing error 0.378 * * * [progress]: generating rewritten candidates 0.378 * * * * [progress]: [ 1 / 4 ] rewriting at (2) 0.379 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 2) 0.380 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1 2 2) 0.381 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2 1 2 1) 0.383 * * * [progress]: generating series expansions 0.383 * * * * [progress]: [ 1 / 4 ] generating series at (2) 0.384 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.384 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.384 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.384 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.384 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.385 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.386 * [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 0.386 * [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 0.388 * [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 0.390 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 2) 0.390 * [approximate]: Taking taylor expansion of (pow N 1/3) in (N) around 0 0.390 * [taylor]: Taking taylor expansion of (pow N 1/3) in N 0.390 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log N))) in N 0.390 * [taylor]: Taking taylor expansion of (* 1/3 (log N)) in N 0.390 * [taylor]: Taking taylor expansion of 1/3 in N 0.390 * [taylor]: Taking taylor expansion of (log N) in N 0.390 * [taylor]: Taking taylor expansion of N in N 0.390 * [taylor]: Taking taylor expansion of (pow N 1/3) in N 0.390 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log N))) in N 0.391 * [taylor]: Taking taylor expansion of (* 1/3 (log N)) in N 0.391 * [taylor]: Taking taylor expansion of 1/3 in N 0.391 * [taylor]: Taking taylor expansion of (log N) in N 0.391 * [taylor]: Taking taylor expansion of N in N 0.443 * [approximate]: Taking taylor expansion of (pow (/ 1 N) 1/3) in (N) around 0 0.443 * [taylor]: Taking taylor expansion of (pow (/ 1 N) 1/3) in N 0.443 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 N)))) in N 0.443 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 N))) in N 0.443 * [taylor]: Taking taylor expansion of 1/3 in N 0.443 * [taylor]: Taking taylor expansion of (log (/ 1 N)) in N 0.443 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.443 * [taylor]: Taking taylor expansion of N in N 0.444 * [taylor]: Taking taylor expansion of (pow (/ 1 N) 1/3) in N 0.444 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 N)))) in N 0.444 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 N))) in N 0.444 * [taylor]: Taking taylor expansion of 1/3 in N 0.444 * [taylor]: Taking taylor expansion of (log (/ 1 N)) in N 0.444 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.444 * [taylor]: Taking taylor expansion of N in N 0.497 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 N) 1/3)) in (N) around 0 0.497 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 N) 1/3)) in N 0.497 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.497 * [taylor]: Taking taylor expansion of -1 in N 0.498 * [taylor]: Taking taylor expansion of (pow (/ 1 N) 1/3) in N 0.498 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 N)))) in N 0.498 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 N))) in N 0.498 * [taylor]: Taking taylor expansion of 1/3 in N 0.498 * [taylor]: Taking taylor expansion of (log (/ 1 N)) in N 0.498 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.498 * [taylor]: Taking taylor expansion of N in N 0.499 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 N) 1/3)) in N 0.499 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.499 * [taylor]: Taking taylor expansion of -1 in N 0.499 * [taylor]: Taking taylor expansion of (pow (/ 1 N) 1/3) in N 0.499 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 N)))) in N 0.499 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 N))) in N 0.499 * [taylor]: Taking taylor expansion of 1/3 in N 0.499 * [taylor]: Taking taylor expansion of (log (/ 1 N)) in N 0.499 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.500 * [taylor]: Taking taylor expansion of N in N 0.567 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1 2 2) 0.567 * [approximate]: Taking taylor expansion of (pow N 1/3) in (N) around 0 0.567 * [taylor]: Taking taylor expansion of (pow N 1/3) in N 0.567 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log N))) in N 0.567 * [taylor]: Taking taylor expansion of (* 1/3 (log N)) in N 0.567 * [taylor]: Taking taylor expansion of 1/3 in N 0.567 * [taylor]: Taking taylor expansion of (log N) in N 0.567 * [taylor]: Taking taylor expansion of N in N 0.568 * [taylor]: Taking taylor expansion of (pow N 1/3) in N 0.568 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log N))) in N 0.568 * [taylor]: Taking taylor expansion of (* 1/3 (log N)) in N 0.568 * [taylor]: Taking taylor expansion of 1/3 in N 0.568 * [taylor]: Taking taylor expansion of (log N) in N 0.568 * [taylor]: Taking taylor expansion of N in N 0.621 * [approximate]: Taking taylor expansion of (pow (/ 1 N) 1/3) in (N) around 0 0.621 * [taylor]: Taking taylor expansion of (pow (/ 1 N) 1/3) in N 0.621 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 N)))) in N 0.621 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 N))) in N 0.621 * [taylor]: Taking taylor expansion of 1/3 in N 0.621 * [taylor]: Taking taylor expansion of (log (/ 1 N)) in N 0.621 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.621 * [taylor]: Taking taylor expansion of N in N 0.622 * [taylor]: Taking taylor expansion of (pow (/ 1 N) 1/3) in N 0.622 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 N)))) in N 0.622 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 N))) in N 0.622 * [taylor]: Taking taylor expansion of 1/3 in N 0.622 * [taylor]: Taking taylor expansion of (log (/ 1 N)) in N 0.622 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.622 * [taylor]: Taking taylor expansion of N in N 0.677 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 N) 1/3)) in (N) around 0 0.677 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 N) 1/3)) in N 0.677 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.677 * [taylor]: Taking taylor expansion of -1 in N 0.678 * [taylor]: Taking taylor expansion of (pow (/ 1 N) 1/3) in N 0.678 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 N)))) in N 0.678 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 N))) in N 0.678 * [taylor]: Taking taylor expansion of 1/3 in N 0.678 * [taylor]: Taking taylor expansion of (log (/ 1 N)) in N 0.678 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.678 * [taylor]: Taking taylor expansion of N in N 0.679 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 N) 1/3)) in N 0.679 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.679 * [taylor]: Taking taylor expansion of -1 in N 0.680 * [taylor]: Taking taylor expansion of (pow (/ 1 N) 1/3) in N 0.680 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 N)))) in N 0.680 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 N))) in N 0.680 * [taylor]: Taking taylor expansion of 1/3 in N 0.680 * [taylor]: Taking taylor expansion of (log (/ 1 N)) in N 0.680 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.680 * [taylor]: Taking taylor expansion of N in N 0.745 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2 1 2 1) 0.745 * [approximate]: Taking taylor expansion of (pow N 1/3) in (N) around 0 0.745 * [taylor]: Taking taylor expansion of (pow N 1/3) in N 0.745 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log N))) in N 0.745 * [taylor]: Taking taylor expansion of (* 1/3 (log N)) in N 0.745 * [taylor]: Taking taylor expansion of 1/3 in N 0.745 * [taylor]: Taking taylor expansion of (log N) in N 0.745 * [taylor]: Taking taylor expansion of N in N 0.745 * [taylor]: Taking taylor expansion of (pow N 1/3) in N 0.745 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log N))) in N 0.745 * [taylor]: Taking taylor expansion of (* 1/3 (log N)) in N 0.745 * [taylor]: Taking taylor expansion of 1/3 in N 0.745 * [taylor]: Taking taylor expansion of (log N) in N 0.746 * [taylor]: Taking taylor expansion of N in N 0.793 * [approximate]: Taking taylor expansion of (pow (/ 1 N) 1/3) in (N) around 0 0.793 * [taylor]: Taking taylor expansion of (pow (/ 1 N) 1/3) in N 0.793 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 N)))) in N 0.793 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 N))) in N 0.793 * [taylor]: Taking taylor expansion of 1/3 in N 0.793 * [taylor]: Taking taylor expansion of (log (/ 1 N)) in N 0.793 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.793 * [taylor]: Taking taylor expansion of N in N 0.794 * [taylor]: Taking taylor expansion of (pow (/ 1 N) 1/3) in N 0.794 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 N)))) in N 0.794 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 N))) in N 0.794 * [taylor]: Taking taylor expansion of 1/3 in N 0.794 * [taylor]: Taking taylor expansion of (log (/ 1 N)) in N 0.794 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.794 * [taylor]: Taking taylor expansion of N in N 0.848 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 N) 1/3)) in (N) around 0 0.848 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 N) 1/3)) in N 0.848 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.848 * [taylor]: Taking taylor expansion of -1 in N 0.849 * [taylor]: Taking taylor expansion of (pow (/ 1 N) 1/3) in N 0.849 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 N)))) in N 0.849 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 N))) in N 0.849 * [taylor]: Taking taylor expansion of 1/3 in N 0.849 * [taylor]: Taking taylor expansion of (log (/ 1 N)) in N 0.849 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.849 * [taylor]: Taking taylor expansion of N in N 0.850 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 N) 1/3)) in N 0.850 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.850 * [taylor]: Taking taylor expansion of -1 in N 0.850 * [taylor]: Taking taylor expansion of (pow (/ 1 N) 1/3) in N 0.850 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 N)))) in N 0.850 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 N))) in N 0.850 * [taylor]: Taking taylor expansion of 1/3 in N 0.850 * [taylor]: Taking taylor expansion of (log (/ 1 N)) in N 0.850 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.851 * [taylor]: Taking taylor expansion of N in N 0.915 * * * [progress]: simplifying candidates 0.916 * [simplify]: Simplifying using # : (log (atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))) (exp (atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))) (* (cbrt (atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))) (cbrt (atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N)))))) (cbrt (atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))) (* (* (atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N)))) (atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))) (atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))) (sqrt (atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))) (sqrt (atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))) (log (cbrt N)) (exp (cbrt N)) (cbrt (* (cbrt N) (cbrt N))) (cbrt (cbrt N)) (cbrt (sqrt N)) (cbrt (sqrt N)) (cbrt 1) (cbrt N) (* (cbrt (cbrt N)) (cbrt (cbrt N))) (cbrt (cbrt N)) (* (* (cbrt N) (cbrt N)) (cbrt N)) (sqrt (cbrt N)) (sqrt (cbrt N)) (log (cbrt N)) (exp (cbrt N)) (cbrt (* (cbrt N) (cbrt N))) (cbrt (cbrt N)) (cbrt (sqrt N)) (cbrt (sqrt N)) (cbrt 1) (cbrt N) (* (cbrt (cbrt N)) (cbrt (cbrt N))) (cbrt (cbrt N)) (* (* (cbrt N) (cbrt N)) (cbrt N)) (sqrt (cbrt N)) (sqrt (cbrt N)) (log (cbrt N)) (exp (cbrt N)) (cbrt (* (cbrt N) (cbrt N))) (cbrt (cbrt N)) (cbrt (sqrt N)) (cbrt (sqrt N)) (cbrt 1) (cbrt N) (* (cbrt (cbrt N)) (cbrt (cbrt N))) (cbrt (cbrt N)) (* (* (cbrt N) (cbrt N)) (cbrt N)) (sqrt (cbrt N)) (sqrt (cbrt N)) (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 1/3) (pow (/ 1 N) -1/3) (* (pow (* -1 N) 1/3) (cbrt -1)) (pow N 1/3) (pow (/ 1 N) -1/3) (* (pow (* -1 N) 1/3) (cbrt -1)) (pow N 1/3) (pow (/ 1 N) -1/3) (* (pow (* -1 N) 1/3) (cbrt -1)) 0.919 * * [simplify]: iteration 0 : 75 enodes (cost 232 ) 0.921 * * [simplify]: iteration 1 : 164 enodes (cost 204 ) 0.925 * * [simplify]: iteration 2 : 533 enodes (cost 198 ) 0.937 * * [simplify]: iteration 3 : 2411 enodes (cost 194 ) 0.999 * * [simplify]: iteration 4 : 5001 enodes (cost 191 ) 1.000 * [simplify]: Simplified to: (log (atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))) (exp (atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))) (* (cbrt (atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))) (cbrt (atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N)))))) (cbrt (atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))) (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 3) (sqrt (atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))) (sqrt (atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))) (log (cbrt N)) (exp (cbrt N)) (cbrt (* (cbrt N) (cbrt N))) (cbrt (cbrt N)) (cbrt (sqrt N)) (cbrt (sqrt N)) 1 (pow N 1/3) (* (cbrt (cbrt N)) (cbrt (cbrt N))) (cbrt (cbrt N)) N (sqrt (cbrt N)) (sqrt (cbrt N)) (log (cbrt N)) (exp (cbrt N)) (cbrt (* (cbrt N) (cbrt N))) (cbrt (cbrt N)) (cbrt (sqrt N)) (cbrt (sqrt N)) 1 (pow N 1/3) (* (cbrt (cbrt N)) (cbrt (cbrt N))) (cbrt (cbrt N)) N (sqrt (cbrt N)) (sqrt (cbrt N)) (log (cbrt N)) (exp (cbrt N)) (cbrt (* (cbrt N) (cbrt N))) (cbrt (cbrt N)) (cbrt (sqrt N)) (cbrt (sqrt N)) 1 (pow N 1/3) (* (cbrt (cbrt N)) (cbrt (cbrt N))) (cbrt (cbrt N)) N (sqrt (cbrt N)) (sqrt (cbrt 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 1/3) (pow (/ 1 N) -1/3) (* (pow (* -1 N) 1/3) (cbrt -1)) (pow N 1/3) (pow (/ 1 N) -1/3) (* (pow (* -1 N) 1/3) (cbrt -1)) (pow N 1/3) (pow (/ 1 N) -1/3) (* (pow (* -1 N) 1/3) (cbrt -1)) 1.001 * * * [progress]: adding candidates to table 1.144 * * [progress]: iteration 4 / 4 1.144 * * * [progress]: picking best candidate 1.156 * * * * [pick]: Picked # 1.156 * * * [progress]: localizing error 1.165 * * * [progress]: generating rewritten candidates 1.165 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 1.166 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 1.167 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 1.168 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 1.169 * * * [progress]: generating series expansions 1.169 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 1.169 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 1.169 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 1.169 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 1.170 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 1.170 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 1.174 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 1.174 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 1.174 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 1.174 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 1.174 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 1.179 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 1.179 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 1.179 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 1.179 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 1.179 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 1.183 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 1.183 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 1.183 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 1.183 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 1.184 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 1.184 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 1.188 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 1.188 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 1.188 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 1.188 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 1.188 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 1.193 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 1.193 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 1.193 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 1.193 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 1.193 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 1.197 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 1.197 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 1.197 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 1.197 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 1.198 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 1.198 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 1.198 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 1.199 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 1.199 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 1.199 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 1.200 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 1.200 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 1.200 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 1.200 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 1.201 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 1.201 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 1.201 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 1.201 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 1.201 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 1.202 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 1.202 * * * [progress]: simplifying candidates 1.203 * [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))))) (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)))) (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))) 1.206 * * [simplify]: iteration 0 : 49 enodes (cost 332 ) 1.208 * * [simplify]: iteration 1 : 79 enodes (cost 294 ) 1.210 * * [simplify]: iteration 2 : 159 enodes (cost 294 ) 1.213 * * [simplify]: iteration 3 : 330 enodes (cost 292 ) 1.222 * * [simplify]: iteration 4 : 1202 enodes (cost 292 ) 1.273 * * [simplify]: iteration 5 : 5002 enodes (cost 292 ) 1.275 * [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))))) (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)))) (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)))) (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))) 1.275 * * * [progress]: adding candidates to table 1.359 * [progress]: [Phase 3 of 3] Extracting. 1.359 * * [regime]: Finding splitpoints for: (# # # # # # # #) 1.360 * * * [regime-changes]: Trying 1 branch expressions: (N) 1.360 * * * * [regimes]: Trying to branch on N from (# # # # # # # #) 1.388 * * * [regime]: Found split indices: #