8.177 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.024 * * * [progress]: [2/2] Setting up program. 0.026 * [progress]: [Phase 2 of 3] Improving. 0.026 * [simplify]: Simplifying using # : (- (atan (+ N 1.0)) (atan N)) 0.028 * * [simplify]: iteration 0 : 9 enodes (cost 4 ) 0.030 * * [simplify]: iteration 1 : 10 enodes (cost 4 ) 0.031 * * [simplify]: iteration 2 : 10 enodes (cost 4 ) 0.031 * [simplify]: Simplified to: (- (atan (+ N 1.0)) (atan N)) 0.031 * * [progress]: iteration 1 / 4 0.031 * * * [progress]: picking best candidate 0.033 * * * * [pick]: Picked # 0.033 * * * [progress]: localizing error 0.038 * * * [progress]: generating rewritten candidates 0.038 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.040 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 0.041 * * * [progress]: generating series expansions 0.041 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.042 * [approximate]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in (N) around 0 0.042 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.042 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.042 * [taylor]: Taking taylor expansion of (atan N) in N 0.042 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.042 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.042 * [taylor]: Taking taylor expansion of (atan N) in N 0.045 * [approximate]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in (N) around 0 0.045 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.045 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.045 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.045 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.045 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.045 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.049 * [approximate]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in (N) around 0 0.049 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.049 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.049 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.049 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.049 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.049 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.052 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 0.052 * [approximate]: Taking taylor expansion of (atan (+ N 1.0)) in (N) around 0 0.052 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.052 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.052 * [approximate]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in (N) around 0 0.052 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.052 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.053 * [approximate]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in (N) around 0 0.053 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.053 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.053 * * * [progress]: simplifying candidates 0.053 * [simplify]: Simplifying using # : (- (+ N 1.0) N) (+ 1 (* (+ N 1.0) 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)) (- (atan N)) (- (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)) 0.056 * * [simplify]: iteration 0 : 52 enodes (cost 58 ) 0.057 * * [simplify]: iteration 1 : 106 enodes (cost 58 ) 0.060 * * [simplify]: iteration 2 : 194 enodes (cost 56 ) 0.063 * * [simplify]: iteration 3 : 370 enodes (cost 55 ) 0.072 * * [simplify]: iteration 4 : 1482 enodes (cost 55 ) 0.106 * * [simplify]: iteration 5 : 5002 enodes (cost 55 ) 0.107 * [simplify]: Simplified to: 1.0 (+ 1 (* (+ N 1.0) 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))) (- (atan N)) (- (* (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)) (- (atan (+ N 1.0)) (atan N)) (- (atan (+ N 1.0)) (atan N)) (atan (+ N 1.0)) (atan (+ N 1.0)) (atan (+ N 1.0)) 0.107 * * * [progress]: adding candidates to table 0.121 * * [progress]: iteration 2 / 4 0.121 * * * [progress]: picking best candidate 0.122 * * * * [pick]: Picked # 0.122 * * * [progress]: localizing error 0.127 * * * [progress]: generating rewritten candidates 0.127 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.128 * * * * [progress]: [ 2 / 2 ] rewriting at (2 2 2) 0.132 * * * [progress]: generating series expansions 0.132 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.132 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.132 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.132 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.133 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.133 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.133 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.133 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.133 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.134 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.134 * * * * [progress]: [ 2 / 2 ] generating series at (2 2 2) 0.134 * [approximate]: Taking taylor expansion of (* N (+ N 1.0)) in (N) around 0 0.134 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.134 * [taylor]: Taking taylor expansion of N in N 0.134 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.134 * [taylor]: Taking taylor expansion of N in N 0.134 * [taylor]: Taking taylor expansion of 1.0 in N 0.134 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.134 * [taylor]: Taking taylor expansion of N in N 0.134 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.134 * [taylor]: Taking taylor expansion of N in N 0.134 * [taylor]: Taking taylor expansion of 1.0 in N 0.144 * [approximate]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in (N) around 0 0.144 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.144 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.144 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.144 * [taylor]: Taking taylor expansion of N in N 0.144 * [taylor]: Taking taylor expansion of 1.0 in N 0.144 * [taylor]: Taking taylor expansion of N in N 0.145 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.145 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.145 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.145 * [taylor]: Taking taylor expansion of N in N 0.145 * [taylor]: Taking taylor expansion of 1.0 in N 0.145 * [taylor]: Taking taylor expansion of N in N 0.155 * [approximate]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in (N) around 0 0.155 * [taylor]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in N 0.155 * [taylor]: Taking taylor expansion of -1 in N 0.155 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.155 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.155 * [taylor]: Taking taylor expansion of 1.0 in N 0.155 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.155 * [taylor]: Taking taylor expansion of N in N 0.156 * [taylor]: Taking taylor expansion of N in N 0.156 * [taylor]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in N 0.156 * [taylor]: Taking taylor expansion of -1 in N 0.157 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.157 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.157 * [taylor]: Taking taylor expansion of 1.0 in N 0.157 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.157 * [taylor]: Taking taylor expansion of N in N 0.157 * [taylor]: Taking taylor expansion of N in N 0.175 * * * [progress]: simplifying candidates 0.175 * [simplify]: Simplifying using # : (* (+ (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)) 0.178 * * [simplify]: iteration 0 : 44 enodes (cost 32 ) 0.179 * * [simplify]: iteration 1 : 100 enodes (cost 29 ) 0.182 * * [simplify]: iteration 2 : 305 enodes (cost 29 ) 0.188 * * [simplify]: iteration 3 : 913 enodes (cost 29 ) 0.215 * * [simplify]: iteration 4 : 4006 enodes (cost 29 ) 0.376 * * [simplify]: iteration 5 : 5001 enodes (cost 29 ) 0.376 * [simplify]: Simplified to: (* (+ (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))) (* N (+ 1.0 N)) (* N (+ 1.0 N)) (* N (+ 1.0 N)) 0.376 * * * [progress]: adding candidates to table 0.393 * * [progress]: iteration 3 / 4 0.393 * * * [progress]: picking best candidate 0.397 * * * * [pick]: Picked # 0.397 * * * [progress]: localizing error 0.407 * * * [progress]: generating rewritten candidates 0.407 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 0.416 * * * * [progress]: [ 2 / 4 ] rewriting at (2) 0.416 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1) 0.422 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2 1 1) 0.427 * * * [progress]: generating series expansions 0.428 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 0.428 * [approximate]: Taking taylor expansion of (/ (* (- (pow N 2) 1.0) N) (- N 1.0)) in (N) around 0 0.428 * [taylor]: Taking taylor expansion of (/ (* (- (pow N 2) 1.0) N) (- N 1.0)) in N 0.428 * [taylor]: Taking taylor expansion of (* (- (pow N 2) 1.0) N) in N 0.428 * [taylor]: Taking taylor expansion of (- (pow N 2) 1.0) in N 0.428 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.428 * [taylor]: Taking taylor expansion of N in N 0.428 * [taylor]: Taking taylor expansion of 1.0 in N 0.428 * [taylor]: Taking taylor expansion of N in N 0.428 * [taylor]: Taking taylor expansion of (- N 1.0) in N 0.428 * [taylor]: Taking taylor expansion of N in N 0.428 * [taylor]: Taking taylor expansion of 1.0 in N 0.433 * [taylor]: Taking taylor expansion of (/ (* (- (pow N 2) 1.0) N) (- N 1.0)) in N 0.433 * [taylor]: Taking taylor expansion of (* (- (pow N 2) 1.0) N) in N 0.433 * [taylor]: Taking taylor expansion of (- (pow N 2) 1.0) in N 0.433 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.433 * [taylor]: Taking taylor expansion of N in N 0.433 * [taylor]: Taking taylor expansion of 1.0 in N 0.433 * [taylor]: Taking taylor expansion of N in N 0.433 * [taylor]: Taking taylor expansion of (- N 1.0) in N 0.433 * [taylor]: Taking taylor expansion of N in N 0.433 * [taylor]: Taking taylor expansion of 1.0 in N 0.462 * [approximate]: Taking taylor expansion of (/ (- (/ 1 (pow N 2)) 1.0) (* (- (/ 1 N) 1.0) N)) in (N) around 0 0.462 * [taylor]: Taking taylor expansion of (/ (- (/ 1 (pow N 2)) 1.0) (* (- (/ 1 N) 1.0) N)) in N 0.462 * [taylor]: Taking taylor expansion of (- (/ 1 (pow N 2)) 1.0) in N 0.462 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.462 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.462 * [taylor]: Taking taylor expansion of N in N 0.462 * [taylor]: Taking taylor expansion of 1.0 in N 0.462 * [taylor]: Taking taylor expansion of (* (- (/ 1 N) 1.0) N) in N 0.462 * [taylor]: Taking taylor expansion of (- (/ 1 N) 1.0) in N 0.462 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.462 * [taylor]: Taking taylor expansion of N in N 0.463 * [taylor]: Taking taylor expansion of 1.0 in N 0.463 * [taylor]: Taking taylor expansion of N in N 0.465 * [taylor]: Taking taylor expansion of (/ (- (/ 1 (pow N 2)) 1.0) (* (- (/ 1 N) 1.0) N)) in N 0.465 * [taylor]: Taking taylor expansion of (- (/ 1 (pow N 2)) 1.0) in N 0.465 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.465 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.465 * [taylor]: Taking taylor expansion of N in N 0.466 * [taylor]: Taking taylor expansion of 1.0 in N 0.466 * [taylor]: Taking taylor expansion of (* (- (/ 1 N) 1.0) N) in N 0.466 * [taylor]: Taking taylor expansion of (- (/ 1 N) 1.0) in N 0.466 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.466 * [taylor]: Taking taylor expansion of N in N 0.466 * [taylor]: Taking taylor expansion of 1.0 in N 0.466 * [taylor]: Taking taylor expansion of N in N 0.508 * [approximate]: Taking taylor expansion of (/ (- (/ 1 (pow N 2)) 1.0) (* N (+ (/ 1 N) 1.0))) in (N) around 0 0.508 * [taylor]: Taking taylor expansion of (/ (- (/ 1 (pow N 2)) 1.0) (* N (+ (/ 1 N) 1.0))) in N 0.508 * [taylor]: Taking taylor expansion of (- (/ 1 (pow N 2)) 1.0) in N 0.508 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.508 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.508 * [taylor]: Taking taylor expansion of N in N 0.508 * [taylor]: Taking taylor expansion of 1.0 in N 0.508 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 0.508 * [taylor]: Taking taylor expansion of N in N 0.508 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.508 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.508 * [taylor]: Taking taylor expansion of N in N 0.509 * [taylor]: Taking taylor expansion of 1.0 in N 0.511 * [taylor]: Taking taylor expansion of (/ (- (/ 1 (pow N 2)) 1.0) (* N (+ (/ 1 N) 1.0))) in N 0.511 * [taylor]: Taking taylor expansion of (- (/ 1 (pow N 2)) 1.0) in N 0.511 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.511 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.511 * [taylor]: Taking taylor expansion of N in N 0.511 * [taylor]: Taking taylor expansion of 1.0 in N 0.511 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 0.511 * [taylor]: Taking taylor expansion of N in N 0.511 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.511 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.511 * [taylor]: Taking taylor expansion of N in N 0.512 * [taylor]: Taking taylor expansion of 1.0 in N 0.545 * * * * [progress]: [ 2 / 4 ] generating series at (2) 0.546 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ (pow N 3) (- N 1.0)) 1) (* 1.0 (/ N (- N 1.0))))) in (N) around 0 0.546 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ (pow N 3) (- N 1.0)) 1) (* 1.0 (/ N (- N 1.0))))) in N 0.546 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ (pow N 3) (- N 1.0)) 1) (* 1.0 (/ N (- N 1.0))))) in N 0.548 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (* (- (/ 1 N) 1.0) (pow N 3))) 1) (* 1.0 (/ 1 (* (- (/ 1 N) 1.0) N))))) in (N) around 0 0.548 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (* (- (/ 1 N) 1.0) (pow N 3))) 1) (* 1.0 (/ 1 (* (- (/ 1 N) 1.0) N))))) in N 0.548 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (* (- (/ 1 N) 1.0) (pow N 3))) 1) (* 1.0 (/ 1 (* (- (/ 1 N) 1.0) N))))) in N 0.549 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (* (pow N 3) (+ (/ 1 N) 1.0))) 1) (* 1.0 (/ 1 (* N (+ (/ 1 N) 1.0)))))) in (N) around 0 0.550 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (* (pow N 3) (+ (/ 1 N) 1.0))) 1) (* 1.0 (/ 1 (* N (+ (/ 1 N) 1.0)))))) in N 0.550 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (* (pow N 3) (+ (/ 1 N) 1.0))) 1) (* 1.0 (/ 1 (* N (+ (/ 1 N) 1.0)))))) in N 0.551 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1) 0.551 * [approximate]: Taking taylor expansion of (* (- (pow N 2) 1.0) N) in (N) around 0 0.551 * [taylor]: Taking taylor expansion of (* (- (pow N 2) 1.0) N) in N 0.551 * [taylor]: Taking taylor expansion of (- (pow N 2) 1.0) in N 0.551 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.551 * [taylor]: Taking taylor expansion of N in N 0.551 * [taylor]: Taking taylor expansion of 1.0 in N 0.551 * [taylor]: Taking taylor expansion of N in N 0.551 * [taylor]: Taking taylor expansion of (* (- (pow N 2) 1.0) N) in N 0.551 * [taylor]: Taking taylor expansion of (- (pow N 2) 1.0) in N 0.551 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.551 * [taylor]: Taking taylor expansion of N in N 0.551 * [taylor]: Taking taylor expansion of 1.0 in N 0.551 * [taylor]: Taking taylor expansion of N in N 0.576 * [approximate]: Taking taylor expansion of (/ (- (/ 1 (pow N 2)) 1.0) N) in (N) around 0 0.576 * [taylor]: Taking taylor expansion of (/ (- (/ 1 (pow N 2)) 1.0) N) in N 0.576 * [taylor]: Taking taylor expansion of (- (/ 1 (pow N 2)) 1.0) in N 0.576 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.576 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.576 * [taylor]: Taking taylor expansion of N in N 0.577 * [taylor]: Taking taylor expansion of 1.0 in N 0.577 * [taylor]: Taking taylor expansion of N in N 0.577 * [taylor]: Taking taylor expansion of (/ (- (/ 1 (pow N 2)) 1.0) N) in N 0.577 * [taylor]: Taking taylor expansion of (- (/ 1 (pow N 2)) 1.0) in N 0.577 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.577 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.577 * [taylor]: Taking taylor expansion of N in N 0.578 * [taylor]: Taking taylor expansion of 1.0 in N 0.578 * [taylor]: Taking taylor expansion of N in N 0.598 * [approximate]: Taking taylor expansion of (* -1 (/ (- (/ 1 (pow N 2)) 1.0) N)) in (N) around 0 0.598 * [taylor]: Taking taylor expansion of (* -1 (/ (- (/ 1 (pow N 2)) 1.0) N)) in N 0.598 * [taylor]: Taking taylor expansion of -1 in N 0.598 * [taylor]: Taking taylor expansion of (/ (- (/ 1 (pow N 2)) 1.0) N) in N 0.598 * [taylor]: Taking taylor expansion of (- (/ 1 (pow N 2)) 1.0) in N 0.598 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.598 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.598 * [taylor]: Taking taylor expansion of N in N 0.599 * [taylor]: Taking taylor expansion of 1.0 in N 0.599 * [taylor]: Taking taylor expansion of N in N 0.599 * [taylor]: Taking taylor expansion of (* -1 (/ (- (/ 1 (pow N 2)) 1.0) N)) in N 0.599 * [taylor]: Taking taylor expansion of -1 in N 0.600 * [taylor]: Taking taylor expansion of (/ (- (/ 1 (pow N 2)) 1.0) N) in N 0.600 * [taylor]: Taking taylor expansion of (- (/ 1 (pow N 2)) 1.0) in N 0.600 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.600 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.600 * [taylor]: Taking taylor expansion of N in N 0.600 * [taylor]: Taking taylor expansion of 1.0 in N 0.600 * [taylor]: Taking taylor expansion of N in N 0.627 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2 1 1) 0.628 * [approximate]: Taking taylor expansion of (- (pow N 2) 1.0) in (N) around 0 0.628 * [taylor]: Taking taylor expansion of (- (pow N 2) 1.0) in N 0.628 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.628 * [taylor]: Taking taylor expansion of N in N 0.628 * [taylor]: Taking taylor expansion of 1.0 in N 0.628 * [taylor]: Taking taylor expansion of (- (pow N 2) 1.0) in N 0.628 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.628 * [taylor]: Taking taylor expansion of N in N 0.628 * [taylor]: Taking taylor expansion of 1.0 in N 0.642 * [approximate]: Taking taylor expansion of (- (/ 1 (pow N 2)) 1.0) in (N) around 0 0.642 * [taylor]: Taking taylor expansion of (- (/ 1 (pow N 2)) 1.0) in N 0.642 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.642 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.642 * [taylor]: Taking taylor expansion of N in N 0.643 * [taylor]: Taking taylor expansion of 1.0 in N 0.643 * [taylor]: Taking taylor expansion of (- (/ 1 (pow N 2)) 1.0) in N 0.643 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.643 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.643 * [taylor]: Taking taylor expansion of N in N 0.643 * [taylor]: Taking taylor expansion of 1.0 in N 0.657 * [approximate]: Taking taylor expansion of (- (/ 1 (pow N 2)) 1.0) in (N) around 0 0.657 * [taylor]: Taking taylor expansion of (- (/ 1 (pow N 2)) 1.0) in N 0.657 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.657 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.657 * [taylor]: Taking taylor expansion of N in N 0.657 * [taylor]: Taking taylor expansion of 1.0 in N 0.658 * [taylor]: Taking taylor expansion of (- (/ 1 (pow N 2)) 1.0) in N 0.658 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.658 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.658 * [taylor]: Taking taylor expansion of N in N 0.658 * [taylor]: Taking taylor expansion of 1.0 in N 0.671 * * * [progress]: simplifying candidates 0.672 * [simplify]: Simplifying using # : (- (* (- (* N N) (* 1.0 1.0)) N)) (- (- N 1.0)) (/ 1 (- N 1.0)) (/ (- N 1.0) (* (- (* N N) (* 1.0 1.0)) N)) (/ (- N 1.0) N) (/ (- N 1.0) (* (- N 1.0) N)) (/ (- N 1.0) (* (- N 1.0) N)) (/ (- N 1.0) (* (- N 1.0) N)) (/ (- N 1.0) (* (- N 1.0) N)) (/ (- N 1.0) (- (* N N) (* 1.0 1.0))) (/ (* (- (* N N) (* 1.0 1.0)) N) (- (pow N 3) (pow 1.0 3))) (/ (* (- (* N N) (* 1.0 1.0)) N) (- (* N N) (* 1.0 1.0))) (* (- N 1.0) (+ (* (* N N) (* N N)) (+ (* (* 1.0 1.0) (* 1.0 1.0)) (* (* N N) (* 1.0 1.0))))) (* (- N 1.0) (+ (* N N) (* 1.0 1.0))) (* (- N 1.0) N) (* (- N 1.0) N) (* (- N 1.0) N) (* (- N 1.0) N) (* (- (pow (* N N) 3) (pow (* 1.0 1.0) 3)) N) (* (- (* (* N N) (* N N)) (* (* 1.0 1.0) (* 1.0 1.0))) N) (- (pow (* N N) 3) (pow (* 1.0 1.0) 3)) (+ (* (* N N) (* N N)) (+ (* (* 1.0 1.0) (* 1.0 1.0)) (* (* N N) (* 1.0 1.0)))) (- (* 1.0 1.0)) (- (* (* N N) (* N N)) (* (* 1.0 1.0) (* 1.0 1.0))) (+ (* N N) (* 1.0 1.0)) (+ N 1.0) (- N 1.0) (+ N 1.0) (- N 1.0) (+ N 1.0) (- N 1.0) (+ N 1.0) (- N 1.0) (- (* 1.0 1.0)) (+ (* 1.0 (pow N 2)) (* 1.0 N)) (+ (pow N 2) (* 1.0 N)) (+ (pow N 2) (* 1.0 N)) (atan2 1.0 (- (+ (/ (pow N 3) (- N 1.0)) 1) (* 1.0 (/ N (- N 1.0))))) (atan2 1.0 (- (+ (/ (pow N 3) (- N 1.0)) 1) (* 1.0 (/ N (- N 1.0))))) (atan2 1.0 (- (+ (* 1.0 (/ N (- 1.0 N))) 1) (/ (pow N 3) (- 1.0 N)))) (- (pow N 3) (* 1.0 N)) (- (pow N 3) (* 1.0 N)) (- (pow N 3) (* 1.0 N)) (- (pow N 2) 1.0) (- (pow N 2) 1.0) (- (pow N 2) 1.0) 0.676 * * [simplify]: iteration 0 : 176 enodes (cost 179 ) 0.679 * * [simplify]: iteration 1 : 549 enodes (cost 160 ) 0.689 * * [simplify]: iteration 2 : 2148 enodes (cost 143 ) 0.728 * * [simplify]: iteration 3 : 5001 enodes (cost 140 ) 0.729 * [simplify]: Simplified to: (* (- 1.0 N) (* N (+ N 1.0))) (- 1.0 N) (/ 1 (- N 1.0)) (/ (/ 1 N) (+ N 1.0)) (/ (- N 1.0) N) (/ 1 N) (/ 1 N) (/ 1 N) (/ 1 N) (/ 1 (+ N 1.0)) (/ (* (- (* N N) (* 1.0 1.0)) N) (- (pow N 3) (pow 1.0 3))) N (* (+ (+ (pow N 4) (* (* N N) (* 1.0 1.0))) (pow 1.0 4)) (+ N (- 1.0))) (* (- N 1.0) (+ (* N N) (* 1.0 1.0))) (* (- N 1.0) N) (* (- N 1.0) N) (* (- N 1.0) N) (* (- N 1.0) N) (+ (pow N 7) (- (* (pow 1.0 6) N))) (+ (- (* N (pow 1.0 4))) (pow N 5)) (- (pow (* N N) 3) (pow (* 1.0 1.0) 3)) (+ (+ (pow N 4) (* (* N N) (* 1.0 1.0))) (pow 1.0 4)) (- (* 1.0 1.0)) (+ (- (* (pow 1.0 3) 1.0)) (pow N 4)) (+ (* N N) (* 1.0 1.0)) (+ N 1.0) (- N 1.0) (+ N 1.0) (- N 1.0) (+ N 1.0) (- N 1.0) (+ N 1.0) (- N 1.0) (- (* 1.0 1.0)) (* 1.0 (+ (pow N 2) N)) (* N (+ N 1.0)) (* N (+ N 1.0)) (atan2 1.0 (- (+ (/ (pow N 3) (- N 1.0)) 1) (* 1.0 (/ N (- N 1.0))))) (atan2 1.0 (- (+ (/ (pow N 3) (- N 1.0)) 1) (* 1.0 (/ N (- N 1.0))))) (atan2 1.0 (- (+ (* 1.0 (/ N (- 1.0 N))) 1) (/ (pow N 3) (- 1.0 N)))) (- (pow N 3) (* 1.0 N)) (- (pow N 3) (* 1.0 N)) (- (pow N 3) (* 1.0 N)) (- (pow N 2) 1.0) (- (pow N 2) 1.0) (- (pow N 2) 1.0) 0.729 * * * [progress]: adding candidates to table 0.794 * * [progress]: iteration 4 / 4 0.794 * * * [progress]: picking best candidate 0.798 * * * * [pick]: Picked # 0.799 * * * [progress]: localizing error 0.810 * * * [progress]: generating rewritten candidates 0.810 * * * * [progress]: [ 1 / 3 ] rewriting at (2) 0.811 * * * * [progress]: [ 2 / 3 ] rewriting at (2 2 2) 0.816 * * * * [progress]: [ 3 / 3 ] rewriting at (2 2 2 2) 0.821 * * * [progress]: generating series expansions 0.821 * * * * [progress]: [ 1 / 3 ] generating series at (2) 0.822 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.822 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.822 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.822 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.822 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.823 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.823 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.823 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.824 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.824 * * * * [progress]: [ 2 / 3 ] generating series at (2 2 2) 0.824 * [approximate]: Taking taylor expansion of (* N (+ N 1.0)) in (N) around 0 0.824 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.824 * [taylor]: Taking taylor expansion of N in N 0.824 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.824 * [taylor]: Taking taylor expansion of N in N 0.824 * [taylor]: Taking taylor expansion of 1.0 in N 0.824 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.824 * [taylor]: Taking taylor expansion of N in N 0.824 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.824 * [taylor]: Taking taylor expansion of N in N 0.824 * [taylor]: Taking taylor expansion of 1.0 in N 0.834 * [approximate]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in (N) around 0 0.834 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.834 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.834 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.834 * [taylor]: Taking taylor expansion of N in N 0.834 * [taylor]: Taking taylor expansion of 1.0 in N 0.834 * [taylor]: Taking taylor expansion of N in N 0.835 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.835 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.835 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.835 * [taylor]: Taking taylor expansion of N in N 0.835 * [taylor]: Taking taylor expansion of 1.0 in N 0.835 * [taylor]: Taking taylor expansion of N in N 0.845 * [approximate]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in (N) around 0 0.845 * [taylor]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in N 0.845 * [taylor]: Taking taylor expansion of -1 in N 0.845 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.845 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.845 * [taylor]: Taking taylor expansion of 1.0 in N 0.845 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.845 * [taylor]: Taking taylor expansion of N in N 0.846 * [taylor]: Taking taylor expansion of N in N 0.846 * [taylor]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in N 0.846 * [taylor]: Taking taylor expansion of -1 in N 0.847 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.847 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.847 * [taylor]: Taking taylor expansion of 1.0 in N 0.847 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.847 * [taylor]: Taking taylor expansion of N in N 0.847 * [taylor]: Taking taylor expansion of N in N 0.865 * * * * [progress]: [ 3 / 3 ] generating series at (2 2 2 2) 0.865 * [approximate]: Taking taylor expansion of (/ 1 (* N (+ N 1.0))) in (N) around 0 0.865 * [taylor]: Taking taylor expansion of (/ 1 (* N (+ N 1.0))) in N 0.865 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.866 * [taylor]: Taking taylor expansion of N in N 0.866 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.866 * [taylor]: Taking taylor expansion of N in N 0.866 * [taylor]: Taking taylor expansion of 1.0 in N 0.867 * [taylor]: Taking taylor expansion of (/ 1 (* N (+ N 1.0))) in N 0.868 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.868 * [taylor]: Taking taylor expansion of N in N 0.868 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.868 * [taylor]: Taking taylor expansion of N in N 0.868 * [taylor]: Taking taylor expansion of 1.0 in N 0.875 * [approximate]: Taking taylor expansion of (/ N (+ (/ 1 N) 1.0)) in (N) around 0 0.875 * [taylor]: Taking taylor expansion of (/ N (+ (/ 1 N) 1.0)) in N 0.875 * [taylor]: Taking taylor expansion of N in N 0.875 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.875 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.875 * [taylor]: Taking taylor expansion of N in N 0.876 * [taylor]: Taking taylor expansion of 1.0 in N 0.876 * [taylor]: Taking taylor expansion of (/ N (+ (/ 1 N) 1.0)) in N 0.876 * [taylor]: Taking taylor expansion of N in N 0.876 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.876 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.876 * [taylor]: Taking taylor expansion of N in N 0.877 * [taylor]: Taking taylor expansion of 1.0 in N 0.884 * [approximate]: Taking taylor expansion of (* -1 (/ N (- 1.0 (/ 1 N)))) in (N) around 0 0.884 * [taylor]: Taking taylor expansion of (* -1 (/ N (- 1.0 (/ 1 N)))) in N 0.884 * [taylor]: Taking taylor expansion of -1 in N 0.884 * [taylor]: Taking taylor expansion of (/ N (- 1.0 (/ 1 N))) in N 0.884 * [taylor]: Taking taylor expansion of N in N 0.884 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.884 * [taylor]: Taking taylor expansion of 1.0 in N 0.884 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.884 * [taylor]: Taking taylor expansion of N in N 0.885 * [taylor]: Taking taylor expansion of (* -1 (/ N (- 1.0 (/ 1 N)))) in N 0.885 * [taylor]: Taking taylor expansion of -1 in N 0.885 * [taylor]: Taking taylor expansion of (/ N (- 1.0 (/ 1 N))) in N 0.885 * [taylor]: Taking taylor expansion of N in N 0.885 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.885 * [taylor]: Taking taylor expansion of 1.0 in N 0.885 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.885 * [taylor]: Taking taylor expansion of N in N 0.900 * * * [progress]: simplifying candidates 0.901 * [simplify]: Simplifying using # : (- 1) (- (/ (/ 1 N) (+ N 1.0))) (/ 1 (/ (/ 1 N) (+ N 1.0))) (/ (/ (/ 1 N) (+ N 1.0)) 1) (/ 1 (/ 1 N)) (/ 1 (/ (/ 1 N) (+ (pow N 3) (pow 1.0 3)))) (/ 1 (/ (/ 1 N) (- (* N N) (* 1.0 1.0)))) (/ 1 (/ 1 N)) (/ 1 (- (/ 1 N))) (/ 1 1) (/ 1 1) (/ 1 1) (/ 1 (- 1)) (/ 1 1) (- (/ 1 N)) (- (+ N 1.0)) (/ 1 (+ N 1.0)) (/ (+ N 1.0) (/ 1 N)) (/ (+ N 1.0) (/ 1 N)) (/ (/ 1 N) (+ (pow N 3) (pow 1.0 3))) (/ (/ 1 N) (- (* N N) (* 1.0 1.0))) (* (+ N 1.0) N) (* (+ N 1.0) (- N)) (* (+ N 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))) (+ (pow N 2) (* 1.0 N)) (+ (pow N 2) (* 1.0 N)) (+ (pow N 2) (* 1.0 N)) (- (+ (* 1.0 (/ 1 N)) (* 1.0 N)) 1.0) (- (+ (/ 1 (pow N 2)) (* 1.0 (/ 1 (pow N 4)))) (* 1.0 (/ 1 (pow N 3)))) (- (+ (/ 1 (pow N 2)) (* 1.0 (/ 1 (pow N 4)))) (* 1.0 (/ 1 (pow N 3)))) 0.904 * * [simplify]: iteration 0 : 118 enodes (cost 101 ) 0.907 * * [simplify]: iteration 1 : 463 enodes (cost 93 ) 0.918 * * [simplify]: iteration 2 : 2544 enodes (cost 92 ) 1.006 * * [simplify]: iteration 3 : 5002 enodes (cost 92 ) 1.007 * [simplify]: Simplified to: (- 1) (- (/ (/ 1 N) (+ N 1.0))) (* N (+ N 1.0)) (/ (/ 1 N) (+ N 1.0)) N (* N (+ (pow N 3) (pow 1.0 3))) (* N (- (* N N) (* 1.0 1.0))) N (/ N (- 1)) 1 1 1 (/ 1 (- 1)) 1 (- (/ 1 N)) (- (+ N 1.0)) (/ 1 (+ N 1.0)) (* N (+ N 1.0)) (* N (+ N 1.0)) (/ (/ 1 N) (+ (pow N 3) (pow 1.0 3))) (/ (/ 1 N) (- (* N N) (* 1.0 1.0))) (* N (+ N 1.0)) (* (+ N 1.0) (- N)) (* N (+ N 1.0)) (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))) (* N (+ N 1.0)) (* N (+ N 1.0)) (* N (+ N 1.0)) (+ (- (* 1.0 N) 1.0) (/ 1.0 N)) (+ (* 1.0 (- (/ 1 (pow N 4)) (/ 1 (pow N 3)))) (/ 1 (pow N 2))) (+ (* 1.0 (- (/ 1 (pow N 4)) (/ 1 (pow N 3)))) (/ 1 (pow N 2))) 1.008 * * * [progress]: adding candidates to table 1.063 * [progress]: [Phase 3 of 3] Extracting. 1.063 * * [regime]: Finding splitpoints for: (# # # # #) 1.064 * * * [regime-changes]: Trying 2 branch expressions: ((- (atan (+ N 1.0)) (atan N)) N) 1.064 * * * * [regimes]: Trying to branch on (- (atan (+ N 1.0)) (atan N)) from (# # # # #) 1.083 * * * * [regimes]: Trying to branch on N from (# # # # #) 1.103 * * * [regime]: Found split indices: #