8.449 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.027 * * * [progress]: [2/2] Setting up program. 0.030 * [progress]: [Phase 2 of 3] Improving. 0.030 * [simplify]: Simplifying using # : (- (atan (+ N 1.0)) (atan N)) 0.032 * * [simplify]: iteration 0 : 9 enodes (cost 4 ) 0.033 * * [simplify]: iteration 1 : 10 enodes (cost 4 ) 0.034 * * [simplify]: iteration 2 : 10 enodes (cost 4 ) 0.034 * [simplify]: Simplified to: (- (atan (+ N 1.0)) (atan N)) 0.034 * * [progress]: iteration 1 / 4 0.034 * * * [progress]: picking best candidate 0.036 * * * * [pick]: Picked # 0.036 * * * [progress]: localizing error 0.042 * * * [progress]: generating rewritten candidates 0.042 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.045 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 0.047 * * * [progress]: generating series expansions 0.047 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.047 * [approximate]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in (N) around 0 0.047 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.047 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.047 * [taylor]: Taking taylor expansion of (atan N) in N 0.047 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.047 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.047 * [taylor]: Taking taylor expansion of (atan N) in N 0.048 * [approximate]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in (N) around 0 0.048 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.048 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.048 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.048 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.048 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.048 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.049 * [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 0.049 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 0.049 * [approximate]: Taking taylor expansion of (atan (+ N 1.0)) in (N) around 0 0.049 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.049 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.049 * [approximate]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in (N) around 0 0.049 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.050 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.050 * [approximate]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in (N) around 0 0.050 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.050 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.050 * * * [progress]: simplifying candidates 0.051 * [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)) 0.053 * * [simplify]: iteration 0 : 75 enodes (cost 154 ) 0.055 * * [simplify]: iteration 1 : 145 enodes (cost 145 ) 0.058 * * [simplify]: iteration 2 : 289 enodes (cost 143 ) 0.062 * * [simplify]: iteration 3 : 681 enodes (cost 142 ) 0.075 * * [simplify]: iteration 4 : 2447 enodes (cost 142 ) 0.122 * * [simplify]: iteration 5 : 5001 enodes (cost 142 ) 0.123 * [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)) 0.123 * * * [progress]: adding candidates to table 0.160 * * [progress]: iteration 2 / 4 0.160 * * * [progress]: picking best candidate 0.165 * * * * [pick]: Picked # 0.165 * * * [progress]: localizing error 0.171 * * * [progress]: generating rewritten candidates 0.171 * * * * [progress]: [ 1 / 3 ] rewriting at (2) 0.172 * * * * [progress]: [ 2 / 3 ] rewriting at (2 2 2) 0.178 * * * * [progress]: [ 3 / 3 ] rewriting at (2 2) 0.181 * * * [progress]: generating series expansions 0.181 * * * * [progress]: [ 1 / 3 ] generating series at (2) 0.181 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.181 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.181 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.182 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.182 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.182 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.183 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.183 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.183 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.183 * * * * [progress]: [ 2 / 3 ] generating series at (2 2 2) 0.183 * [approximate]: Taking taylor expansion of (* N (+ N 1.0)) in (N) around 0 0.183 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.183 * [taylor]: Taking taylor expansion of N in N 0.183 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.183 * [taylor]: Taking taylor expansion of N in N 0.183 * [taylor]: Taking taylor expansion of 1.0 in N 0.183 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.183 * [taylor]: Taking taylor expansion of N in N 0.183 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.183 * [taylor]: Taking taylor expansion of N in N 0.184 * [taylor]: Taking taylor expansion of 1.0 in N 0.184 * [approximate]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in (N) around 0 0.184 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.184 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.184 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.184 * [taylor]: Taking taylor expansion of N in N 0.184 * [taylor]: Taking taylor expansion of 1.0 in N 0.184 * [taylor]: Taking taylor expansion of N in N 0.184 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.184 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.184 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.184 * [taylor]: Taking taylor expansion of N in N 0.184 * [taylor]: Taking taylor expansion of 1.0 in N 0.184 * [taylor]: Taking taylor expansion of N in N 0.186 * [approximate]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in (N) around 0 0.186 * [taylor]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in N 0.186 * [taylor]: Taking taylor expansion of -1 in N 0.186 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.186 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.186 * [taylor]: Taking taylor expansion of 1.0 in N 0.186 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.186 * [taylor]: Taking taylor expansion of N in N 0.186 * [taylor]: Taking taylor expansion of N in N 0.186 * [taylor]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in N 0.186 * [taylor]: Taking taylor expansion of -1 in N 0.186 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.186 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.186 * [taylor]: Taking taylor expansion of 1.0 in N 0.186 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.186 * [taylor]: Taking taylor expansion of N in N 0.186 * [taylor]: Taking taylor expansion of N in N 0.187 * * * * [progress]: [ 3 / 3 ] generating series at (2 2) 0.188 * [approximate]: Taking taylor expansion of (+ (pow N 2) (+ (* 1.0 N) 1)) in (N) around 0 0.188 * [taylor]: Taking taylor expansion of (+ (pow N 2) (+ (* 1.0 N) 1)) in N 0.188 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.188 * [taylor]: Taking taylor expansion of N in N 0.188 * [taylor]: Taking taylor expansion of (+ (* 1.0 N) 1) in N 0.188 * [taylor]: Taking taylor expansion of (* 1.0 N) in N 0.188 * [taylor]: Taking taylor expansion of 1.0 in N 0.188 * [taylor]: Taking taylor expansion of N in N 0.188 * [taylor]: Taking taylor expansion of 1 in N 0.188 * [taylor]: Taking taylor expansion of (+ (pow N 2) (+ (* 1.0 N) 1)) in N 0.188 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.188 * [taylor]: Taking taylor expansion of N in N 0.188 * [taylor]: Taking taylor expansion of (+ (* 1.0 N) 1) in N 0.188 * [taylor]: Taking taylor expansion of (* 1.0 N) in N 0.188 * [taylor]: Taking taylor expansion of 1.0 in N 0.188 * [taylor]: Taking taylor expansion of N in N 0.188 * [taylor]: Taking taylor expansion of 1 in N 0.188 * [approximate]: Taking taylor expansion of (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)) in (N) around 0 0.188 * [taylor]: Taking taylor expansion of (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)) in N 0.188 * [taylor]: Taking taylor expansion of (* 1.0 (/ 1 N)) in N 0.188 * [taylor]: Taking taylor expansion of 1.0 in N 0.188 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.188 * [taylor]: Taking taylor expansion of N in N 0.188 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow N 2)) 1) in N 0.188 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.188 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.188 * [taylor]: Taking taylor expansion of N in N 0.188 * [taylor]: Taking taylor expansion of 1 in N 0.188 * [taylor]: Taking taylor expansion of (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)) in N 0.188 * [taylor]: Taking taylor expansion of (* 1.0 (/ 1 N)) in N 0.188 * [taylor]: Taking taylor expansion of 1.0 in N 0.188 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.189 * [taylor]: Taking taylor expansion of N in N 0.189 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow N 2)) 1) in N 0.189 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.189 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.189 * [taylor]: Taking taylor expansion of N in N 0.189 * [taylor]: Taking taylor expansion of 1 in N 0.189 * [approximate]: Taking taylor expansion of (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))) in (N) around 0 0.189 * [taylor]: Taking taylor expansion of (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))) in N 0.189 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow N 2)) 1) in N 0.189 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.189 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.189 * [taylor]: Taking taylor expansion of N in N 0.189 * [taylor]: Taking taylor expansion of 1 in N 0.189 * [taylor]: Taking taylor expansion of (* 1.0 (/ 1 N)) in N 0.189 * [taylor]: Taking taylor expansion of 1.0 in N 0.189 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.189 * [taylor]: Taking taylor expansion of N in N 0.189 * [taylor]: Taking taylor expansion of (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))) in N 0.189 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow N 2)) 1) in N 0.189 * [taylor]: Taking taylor expansion of (/ 1 (pow N 2)) in N 0.189 * [taylor]: Taking taylor expansion of (pow N 2) in N 0.189 * [taylor]: Taking taylor expansion of N in N 0.189 * [taylor]: Taking taylor expansion of 1 in N 0.189 * [taylor]: Taking taylor expansion of (* 1.0 (/ 1 N)) in N 0.189 * [taylor]: Taking taylor expansion of 1.0 in N 0.189 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.189 * [taylor]: Taking taylor expansion of N in N 0.190 * * * [progress]: simplifying candidates 0.191 * [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) (* (exp 1) (exp (* (+ N 1.0) N))) (log (+ 1 (* (+ N 1.0) N))) (exp (+ 1 (* (+ N 1.0) N))) (* (cbrt (+ 1 (* (+ N 1.0) N))) (cbrt (+ 1 (* (+ N 1.0) N)))) (cbrt (+ 1 (* (+ N 1.0) N))) (* (* (+ 1 (* (+ N 1.0) N)) (+ 1 (* (+ N 1.0) N))) (+ 1 (* (+ N 1.0) N))) (sqrt (+ 1 (* (+ N 1.0) N))) (sqrt (+ 1 (* (+ N 1.0) N))) (+ (pow 1 3) (pow (* (+ N 1.0) N) 3)) (+ (* 1 1) (- (* (* (+ N 1.0) N) (* (+ N 1.0) N)) (* 1 (* (+ N 1.0) N)))) (- (* 1 1) (* (* (+ N 1.0) N) (* (+ N 1.0) N))) (- 1 (* (+ N 1.0) N)) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (+ (pow N 2) (* 1.0 N)) (+ (pow N 2) (* 1.0 N)) (+ (pow N 2) (* 1.0 N)) (+ (pow N 2) (+ (* 1.0 N) 1)) (+ (pow N 2) (+ (* 1.0 N) 1)) (+ (pow N 2) (+ (* 1.0 N) 1)) 0.194 * * [simplify]: iteration 0 : 177 enodes (cost 222 ) 0.198 * * [simplify]: iteration 1 : 766 enodes (cost 193 ) 0.216 * * [simplify]: iteration 2 : 4572 enodes (cost 193 ) 0.301 * * [simplify]: iteration 3 : 5001 enodes (cost 193 ) 0.305 * [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) (exp (+ 1 (* (+ N 1.0) N))) (log (+ 1 (* (+ N 1.0) N))) (exp (+ 1 (* (+ N 1.0) N))) (* (cbrt (+ 1 (* (+ N 1.0) N))) (cbrt (+ 1 (* (+ N 1.0) N)))) (cbrt (+ 1 (* (+ N 1.0) N))) (pow (+ 1 (* (+ N 1.0) N)) 3) (sqrt (+ 1 (* (+ N 1.0) N))) (sqrt (+ 1 (* (+ N 1.0) N))) (+ 1 (pow (* (+ N 1.0) N) 3)) (+ (* (* (+ N 1.0) N) (- (* (+ N 1.0) N) 1)) 1) (- 1 (* (* (+ N 1.0) N) (* (+ N 1.0) N))) (- 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))) (* (+ N 1.0) N) (* (+ N 1.0) N) (* (+ N 1.0) N) (+ 1 (* (+ N 1.0) N)) (+ 1 (* (+ N 1.0) N)) (+ 1 (* (+ N 1.0) N)) 0.305 * * * [progress]: adding candidates to table 0.361 * * [progress]: iteration 3 / 4 0.361 * * * [progress]: picking best candidate 0.377 * * * * [pick]: Picked # 0.377 * * * [progress]: localizing error 0.386 * * * [progress]: generating rewritten candidates 0.387 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 2) 0.391 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1 2) 0.395 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1 1) 0.400 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.401 * * * [progress]: generating series expansions 0.401 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 2) 0.401 * [approximate]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in (N) around 0 0.401 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.401 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.401 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.401 * [taylor]: Taking taylor expansion of 1/3 in N 0.401 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.401 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.401 * [taylor]: Taking taylor expansion of N in N 0.401 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.401 * [taylor]: Taking taylor expansion of N in N 0.401 * [taylor]: Taking taylor expansion of 1.0 in N 0.402 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.402 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.402 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.402 * [taylor]: Taking taylor expansion of 1/3 in N 0.402 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.402 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.402 * [taylor]: Taking taylor expansion of N in N 0.402 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.402 * [taylor]: Taking taylor expansion of N in N 0.402 * [taylor]: Taking taylor expansion of 1.0 in N 0.404 * [approximate]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in (N) around 0 0.404 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.404 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.404 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.404 * [taylor]: Taking taylor expansion of 1/3 in N 0.404 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.404 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.404 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.404 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.404 * [taylor]: Taking taylor expansion of N in N 0.404 * [taylor]: Taking taylor expansion of 1.0 in N 0.404 * [taylor]: Taking taylor expansion of N in N 0.404 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.404 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.404 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.404 * [taylor]: Taking taylor expansion of 1/3 in N 0.404 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.404 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.404 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.404 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.404 * [taylor]: Taking taylor expansion of N in N 0.404 * [taylor]: Taking taylor expansion of 1.0 in N 0.404 * [taylor]: Taking taylor expansion of N in N 0.406 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in (N) around 0 0.406 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.406 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.406 * [taylor]: Taking taylor expansion of -1 in N 0.406 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.406 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.406 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.406 * [taylor]: Taking taylor expansion of 1/3 in N 0.406 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.406 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.406 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.406 * [taylor]: Taking taylor expansion of 1.0 in N 0.406 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.406 * [taylor]: Taking taylor expansion of N in N 0.406 * [taylor]: Taking taylor expansion of N in N 0.407 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.407 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.407 * [taylor]: Taking taylor expansion of -1 in N 0.407 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.407 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.407 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.407 * [taylor]: Taking taylor expansion of 1/3 in N 0.407 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.407 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.407 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.407 * [taylor]: Taking taylor expansion of 1.0 in N 0.407 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.407 * [taylor]: Taking taylor expansion of N in N 0.407 * [taylor]: Taking taylor expansion of N in N 0.410 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1 2) 0.410 * [approximate]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in (N) around 0 0.410 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.410 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.410 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.410 * [taylor]: Taking taylor expansion of 1/3 in N 0.410 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.410 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.410 * [taylor]: Taking taylor expansion of N in N 0.410 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.410 * [taylor]: Taking taylor expansion of N in N 0.410 * [taylor]: Taking taylor expansion of 1.0 in N 0.410 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.410 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.410 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.411 * [taylor]: Taking taylor expansion of 1/3 in N 0.411 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.411 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.411 * [taylor]: Taking taylor expansion of N in N 0.411 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.411 * [taylor]: Taking taylor expansion of N in N 0.411 * [taylor]: Taking taylor expansion of 1.0 in N 0.412 * [approximate]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in (N) around 0 0.412 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.412 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.412 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.412 * [taylor]: Taking taylor expansion of 1/3 in N 0.412 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.413 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.413 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.413 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.413 * [taylor]: Taking taylor expansion of N in N 0.413 * [taylor]: Taking taylor expansion of 1.0 in N 0.413 * [taylor]: Taking taylor expansion of N in N 0.413 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.413 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.413 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.413 * [taylor]: Taking taylor expansion of 1/3 in N 0.413 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.413 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.413 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.413 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.413 * [taylor]: Taking taylor expansion of N in N 0.413 * [taylor]: Taking taylor expansion of 1.0 in N 0.413 * [taylor]: Taking taylor expansion of N in N 0.415 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in (N) around 0 0.415 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.415 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.415 * [taylor]: Taking taylor expansion of -1 in N 0.415 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.415 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.415 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.415 * [taylor]: Taking taylor expansion of 1/3 in N 0.415 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.415 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.415 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.415 * [taylor]: Taking taylor expansion of 1.0 in N 0.415 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.415 * [taylor]: Taking taylor expansion of N in N 0.415 * [taylor]: Taking taylor expansion of N in N 0.415 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.415 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.415 * [taylor]: Taking taylor expansion of -1 in N 0.415 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.416 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.416 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.416 * [taylor]: Taking taylor expansion of 1/3 in N 0.416 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.416 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.416 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.416 * [taylor]: Taking taylor expansion of 1.0 in N 0.416 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.416 * [taylor]: Taking taylor expansion of N in N 0.416 * [taylor]: Taking taylor expansion of N in N 0.419 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1 1) 0.419 * [approximate]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in (N) around 0 0.419 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.419 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.419 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.419 * [taylor]: Taking taylor expansion of 1/3 in N 0.419 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.419 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.419 * [taylor]: Taking taylor expansion of N in N 0.419 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.419 * [taylor]: Taking taylor expansion of N in N 0.419 * [taylor]: Taking taylor expansion of 1.0 in N 0.419 * [taylor]: Taking taylor expansion of (pow (* N (+ N 1.0)) 1/3) in N 0.419 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (* N (+ N 1.0))))) in N 0.419 * [taylor]: Taking taylor expansion of (* 1/3 (log (* N (+ N 1.0)))) in N 0.419 * [taylor]: Taking taylor expansion of 1/3 in N 0.419 * [taylor]: Taking taylor expansion of (log (* N (+ N 1.0))) in N 0.419 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.419 * [taylor]: Taking taylor expansion of N in N 0.419 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.419 * [taylor]: Taking taylor expansion of N in N 0.419 * [taylor]: Taking taylor expansion of 1.0 in N 0.421 * [approximate]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in (N) around 0 0.421 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.421 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.421 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.421 * [taylor]: Taking taylor expansion of 1/3 in N 0.421 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.421 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.421 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.421 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.421 * [taylor]: Taking taylor expansion of N in N 0.421 * [taylor]: Taking taylor expansion of 1.0 in N 0.421 * [taylor]: Taking taylor expansion of N in N 0.422 * [taylor]: Taking taylor expansion of (pow (/ (+ (/ 1 N) 1.0) N) 1/3) in N 0.422 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (+ (/ 1 N) 1.0) N)))) in N 0.422 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (+ (/ 1 N) 1.0) N))) in N 0.422 * [taylor]: Taking taylor expansion of 1/3 in N 0.422 * [taylor]: Taking taylor expansion of (log (/ (+ (/ 1 N) 1.0) N)) in N 0.422 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.422 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.422 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.422 * [taylor]: Taking taylor expansion of N in N 0.422 * [taylor]: Taking taylor expansion of 1.0 in N 0.422 * [taylor]: Taking taylor expansion of N in N 0.424 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in (N) around 0 0.424 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.424 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.424 * [taylor]: Taking taylor expansion of -1 in N 0.424 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.424 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.424 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.424 * [taylor]: Taking taylor expansion of 1/3 in N 0.424 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.424 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.424 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.424 * [taylor]: Taking taylor expansion of 1.0 in N 0.424 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.424 * [taylor]: Taking taylor expansion of N in N 0.424 * [taylor]: Taking taylor expansion of N in N 0.424 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ (- 1.0 (/ 1 N)) N) 1/3)) in N 0.424 * [taylor]: Taking taylor expansion of (cbrt -1) in N 0.424 * [taylor]: Taking taylor expansion of -1 in N 0.424 * [taylor]: Taking taylor expansion of (pow (/ (- 1.0 (/ 1 N)) N) 1/3) in N 0.424 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ (- 1.0 (/ 1 N)) N)))) in N 0.424 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ (- 1.0 (/ 1 N)) N))) in N 0.424 * [taylor]: Taking taylor expansion of 1/3 in N 0.424 * [taylor]: Taking taylor expansion of (log (/ (- 1.0 (/ 1 N)) N)) in N 0.424 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.424 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.424 * [taylor]: Taking taylor expansion of 1.0 in N 0.424 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.424 * [taylor]: Taking taylor expansion of N in N 0.424 * [taylor]: Taking taylor expansion of N in N 0.428 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.428 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.428 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.428 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.429 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.429 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.429 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.430 * [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 0.430 * [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 0.430 * [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 0.431 * * * [progress]: simplifying candidates 0.434 * [simplify]: Simplifying using # : (log (cbrt (* (+ N 1.0) N))) (exp (cbrt (* (+ N 1.0) N))) (cbrt (+ N 1.0)) (cbrt N) (cbrt (* (+ (pow N 3) (pow 1.0 3)) N)) (cbrt (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (cbrt (* (- (* N N) (* 1.0 1.0)) N)) (cbrt (- N 1.0)) (* (cbrt (cbrt (* (+ N 1.0) N))) (cbrt (cbrt (* (+ N 1.0) N)))) (cbrt (cbrt (* (+ N 1.0) N))) (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (log (cbrt (* (+ N 1.0) N))) (exp (cbrt (* (+ N 1.0) N))) (cbrt (+ N 1.0)) (cbrt N) (cbrt (* (+ (pow N 3) (pow 1.0 3)) N)) (cbrt (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (cbrt (* (- (* N N) (* 1.0 1.0)) N)) (cbrt (- N 1.0)) (* (cbrt (cbrt (* (+ N 1.0) N))) (cbrt (cbrt (* (+ N 1.0) N)))) (cbrt (cbrt (* (+ N 1.0) N))) (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (log (cbrt (* (+ N 1.0) N))) (exp (cbrt (* (+ N 1.0) N))) (cbrt (+ N 1.0)) (cbrt N) (cbrt (* (+ (pow N 3) (pow 1.0 3)) N)) (cbrt (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (cbrt (* (- (* N N) (* 1.0 1.0)) N)) (cbrt (- N 1.0)) (* (cbrt (cbrt (* (+ N 1.0) N))) (cbrt (cbrt (* (+ N 1.0) N)))) (cbrt (cbrt (* (+ N 1.0) N))) (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (log (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (exp (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (* (cbrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (cbrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N))))))) (cbrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (* (* (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N))))) (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (sqrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (sqrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (- (+ (exp (* 1/3 (+ (log 1.0) (log N)))) (+ (* 0.05555555555555555 (* (exp (* 1/3 (+ (log 1.0) (log N)))) (pow N 2))) (* 0.3333333333333333 (* (exp (* 1/3 (+ (log 1.0) (log N)))) N)))) (* 1/6 (/ (* (exp (* 1/3 (+ (log 1.0) (log N)))) (pow N 2)) (pow 1.0 2)))) (- (+ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) (* 0.3333333333333333 (/ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) N))) (* 0.1111111111111111 (/ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) (pow N 2)))) (- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 0.3333333333333333 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 0.1111111111111111 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2)))) (- (+ (exp (* 1/3 (+ (log 1.0) (log N)))) (+ (* 0.05555555555555555 (* (exp (* 1/3 (+ (log 1.0) (log N)))) (pow N 2))) (* 0.3333333333333333 (* (exp (* 1/3 (+ (log 1.0) (log N)))) N)))) (* 1/6 (/ (* (exp (* 1/3 (+ (log 1.0) (log N)))) (pow N 2)) (pow 1.0 2)))) (- (+ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) (* 0.3333333333333333 (/ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) N))) (* 0.1111111111111111 (/ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) (pow N 2)))) (- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 0.3333333333333333 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 0.1111111111111111 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2)))) (- (+ (exp (* 1/3 (+ (log 1.0) (log N)))) (+ (* 0.05555555555555555 (* (exp (* 1/3 (+ (log 1.0) (log N)))) (pow N 2))) (* 0.3333333333333333 (* (exp (* 1/3 (+ (log 1.0) (log N)))) N)))) (* 1/6 (/ (* (exp (* 1/3 (+ (log 1.0) (log N)))) (pow N 2)) (pow 1.0 2)))) (- (+ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) (* 0.3333333333333333 (/ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) N))) (* 0.1111111111111111 (/ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) (pow N 2)))) (- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 0.3333333333333333 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 0.1111111111111111 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2)))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.438 * * [simplify]: iteration 0 : 207 enodes (cost 623 ) 0.441 * * [simplify]: iteration 1 : 572 enodes (cost 575 ) 0.450 * * [simplify]: iteration 2 : 1929 enodes (cost 533 ) 0.484 * * [simplify]: iteration 3 : 5001 enodes (cost 525 ) 0.487 * [simplify]: Simplified to: (log (cbrt (* (+ N 1.0) N))) (exp (cbrt (* (+ N 1.0) N))) (cbrt (+ N 1.0)) (pow N 1/3) (cbrt (* (+ (pow N 3) (pow 1.0 3)) N)) (cbrt (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (cbrt (* (- (* N N) (* 1.0 1.0)) N)) (cbrt (- N 1.0)) (* (cbrt (cbrt (* (+ N 1.0) N))) (cbrt (cbrt (* (+ N 1.0) N)))) (cbrt (cbrt (* (+ N 1.0) N))) (* (+ N 1.0) N) (sqrt (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (log (cbrt (* (+ N 1.0) N))) (exp (cbrt (* (+ N 1.0) N))) (cbrt (+ N 1.0)) (pow N 1/3) (cbrt (* (+ (pow N 3) (pow 1.0 3)) N)) (cbrt (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (cbrt (* (- (* N N) (* 1.0 1.0)) N)) (cbrt (- N 1.0)) (* (cbrt (cbrt (* (+ N 1.0) N))) (cbrt (cbrt (* (+ N 1.0) N)))) (cbrt (cbrt (* (+ N 1.0) N))) (* (+ N 1.0) N) (sqrt (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (log (cbrt (* (+ N 1.0) N))) (exp (cbrt (* (+ N 1.0) N))) (cbrt (+ N 1.0)) (pow N 1/3) (cbrt (* (+ (pow N 3) (pow 1.0 3)) N)) (cbrt (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (cbrt (* (- (* N N) (* 1.0 1.0)) N)) (cbrt (- N 1.0)) (* (cbrt (cbrt (* (+ N 1.0) N))) (cbrt (cbrt (* (+ N 1.0) N)))) (cbrt (cbrt (* (+ N 1.0) N))) (* (+ N 1.0) N) (sqrt (cbrt (* (+ N 1.0) N))) (sqrt (cbrt (* (+ N 1.0) N))) (log (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (exp (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (* (cbrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (cbrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N))))))) (cbrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 3) (sqrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (sqrt (atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))) (+ (+ (/ -1/6 (* (/ 1.0 (pow N 2)) (/ 1.0 (* (pow N 1/3) (pow 1.0 1/3))))) (* (pow N 1/3) (pow 1.0 1/3))) (* (* (pow N 1/3) (pow 1.0 1/3)) (+ (* N 0.3333333333333333) (* (pow N 2) 0.05555555555555555)))) (- (+ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) (* 0.3333333333333333 (/ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) N))) (* 0.1111111111111111 (/ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) (pow N 2)))) (- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 0.3333333333333333 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 0.1111111111111111 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2)))) (+ (+ (/ -1/6 (* (/ 1.0 (pow N 2)) (/ 1.0 (* (pow N 1/3) (pow 1.0 1/3))))) (* (pow N 1/3) (pow 1.0 1/3))) (* (* (pow N 1/3) (pow 1.0 1/3)) (+ (* N 0.3333333333333333) (* (pow N 2) 0.05555555555555555)))) (- (+ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) (* 0.3333333333333333 (/ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) N))) (* 0.1111111111111111 (/ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) (pow N 2)))) (- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 0.3333333333333333 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 0.1111111111111111 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2)))) (+ (+ (/ -1/6 (* (/ 1.0 (pow N 2)) (/ 1.0 (* (pow N 1/3) (pow 1.0 1/3))))) (* (pow N 1/3) (pow 1.0 1/3))) (* (* (pow N 1/3) (pow 1.0 1/3)) (+ (* N 0.3333333333333333) (* (pow N 2) 0.05555555555555555)))) (- (+ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) (* 0.3333333333333333 (/ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) N))) (* 0.1111111111111111 (/ (exp (* 1/3 (- (log 1) (* 2 (log (/ 1 N)))))) (pow N 2)))) (- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 0.3333333333333333 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 0.1111111111111111 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2)))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.488 * * * [progress]: adding candidates to table 0.631 * * [progress]: iteration 4 / 4 0.631 * * * [progress]: picking best candidate 0.644 * * * * [pick]: Picked # 0.644 * * * [progress]: localizing error 0.654 * * * [progress]: generating rewritten candidates 0.654 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.655 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 0.656 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 0.657 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 0.658 * * * [progress]: generating series expansions 0.658 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.658 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 0.658 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.658 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 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 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 0.660 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.660 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 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 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 0.662 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.662 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 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 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 0.665 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 0.665 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.665 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.665 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.665 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.666 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 0.666 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.666 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.667 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.667 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.669 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 0.669 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.669 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.669 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.669 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.671 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 0.671 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.671 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.671 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.671 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.671 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.671 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.672 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.672 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.672 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.673 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 0.673 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.673 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.673 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.673 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.673 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.673 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.674 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.674 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.674 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.675 * * * [progress]: simplifying candidates 0.675 * [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))) 0.679 * * [simplify]: iteration 0 : 49 enodes (cost 332 ) 0.680 * * [simplify]: iteration 1 : 79 enodes (cost 294 ) 0.682 * * [simplify]: iteration 2 : 159 enodes (cost 294 ) 0.685 * * [simplify]: iteration 3 : 330 enodes (cost 292 ) 0.695 * * [simplify]: iteration 4 : 1184 enodes (cost 292 ) 0.747 * * [simplify]: iteration 5 : 5001 enodes (cost 292 ) 0.749 * [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))) 0.749 * * * [progress]: adding candidates to table 0.836 * [progress]: [Phase 3 of 3] Extracting. 0.836 * * [regime]: Finding splitpoints for: (# # # # # # # #) 0.837 * * * [regime-changes]: Trying 2 branch expressions: ((- (atan (+ N 1.0)) (atan N)) N) 0.837 * * * * [regimes]: Trying to branch on (- (atan (+ N 1.0)) (atan N)) from (# # # # # # # #) 0.879 * * * * [regimes]: Trying to branch on N from (# # # # # # # #) 0.921 * * * [regime]: Found split indices: #