5.793 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.028 * * * [progress]: [2/2] Setting up program. 0.030 * [progress]: [Phase 2 of 3] Improving. 0.031 * [simplify]: Simplifying using # : (- (atan (+ N 1.0)) (atan N)) 0.035 * * [simplify]: iteration 0 : 71 enodes (cost 7 ) 0.035 * * [simplify]: iteration 1 : 71 enodes (cost 7 ) 0.035 * [simplify]: Simplified to: (- (atan (+ N 1.0)) (atan N)) 0.035 * * [progress]: iteration 1 / 4 0.035 * * * [progress]: picking best candidate 0.037 * * * * [pick]: Picked # 0.038 * * * [progress]: localizing error 0.043 * * * [progress]: generating rewritten candidates 0.043 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.047 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 0.048 * * * [progress]: generating series expansions 0.048 * * * * [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 0.049 * [taylor]: Taking taylor expansion of (atan N) in N 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 0.049 * [taylor]: Taking taylor expansion of (atan N) in N 0.049 * [approximate]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in (N) around 0 0.049 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.049 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.049 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.049 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.049 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.049 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.050 * [approximate]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in (N) around 0 0.050 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.050 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.050 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.050 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.050 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.050 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.051 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 0.051 * [approximate]: Taking taylor expansion of (atan (+ N 1.0)) in (N) around 0 0.051 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.051 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.051 * [approximate]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in (N) around 0 0.051 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.051 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.051 * [approximate]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in (N) around 0 0.051 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.051 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.052 * * * [progress]: simplifying candidates 0.052 * [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)) (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)) 0.117 * * [simplify]: iteration 0 : 5349 enodes (cost 236 ) 0.118 * [simplify]: Simplified to: 1.0 (+ 1 (* N (+ N 1.0))) (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) (atan N)) (* (atan (+ N 1.0)) (+ (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)) (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)) 0.119 * * * [progress]: adding candidates to table 0.156 * * [progress]: iteration 2 / 4 0.156 * * * [progress]: picking best candidate 0.158 * * * * [pick]: Picked # 0.158 * * * [progress]: localizing error 0.164 * * * [progress]: generating rewritten candidates 0.164 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.164 * * * [progress]: generating series expansions 0.164 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.165 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.165 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.165 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.165 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.165 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.165 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.166 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.166 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.166 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.167 * * * [progress]: simplifying candidates 0.167 * [simplify]: Simplifying using # : (log (atan2 1.0 (+ 1 (* N (+ N 1.0))))) (exp (atan2 1.0 (+ 1 (* N (+ N 1.0))))) (* (cbrt (atan2 1.0 (+ 1 (* N (+ N 1.0))))) (cbrt (atan2 1.0 (+ 1 (* N (+ N 1.0)))))) (cbrt (atan2 1.0 (+ 1 (* N (+ N 1.0))))) (* (* (atan2 1.0 (+ 1 (* N (+ N 1.0)))) (atan2 1.0 (+ 1 (* N (+ N 1.0))))) (atan2 1.0 (+ 1 (* N (+ N 1.0))))) (sqrt (atan2 1.0 (+ 1 (* N (+ N 1.0))))) (sqrt (atan2 1.0 (+ 1 (* 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))) 0.290 * * [simplify]: iteration 0 : 4712 enodes (cost 109 ) 0.290 * * [simplify]: iteration 1 : 4712 enodes (cost 109 ) 0.291 * [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))))) (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) 0.291 * * * [progress]: adding candidates to table 0.307 * * [progress]: iteration 3 / 4 0.307 * * * [progress]: picking best candidate 0.319 * * * * [pick]: Picked # 0.319 * * * [progress]: localizing error 0.327 * * * [progress]: generating rewritten candidates 0.327 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.328 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 0.329 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 0.335 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 0.338 * * * [progress]: generating series expansions 0.338 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.338 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 0.338 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.338 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.338 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.338 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.340 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 0.340 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.340 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.340 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.340 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.342 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 0.342 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.342 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.342 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.342 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.344 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 0.344 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 0.344 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.344 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.344 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.345 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.346 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 0.346 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.346 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.346 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.346 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.348 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 0.348 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.348 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.348 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.348 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.350 * * * * [progress]: [ 3 / 4 ] generating series at (2) 0.350 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.350 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.350 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.351 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.351 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.351 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.352 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.352 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.352 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.352 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 0.352 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.352 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.353 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.353 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.353 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.353 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.354 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.354 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.354 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.354 * * * [progress]: simplifying candidates 0.355 * [simplify]: Simplifying using # : (log (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (exp (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (* (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (* (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt 1) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (/ 1 2) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (log (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (exp (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (* (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (* (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt 1) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (/ 1 2) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (+ 1/2 1/2) (+ 1/2 (/ 1 2)) (+ 1 1) (+ (/ 1 2) 1/2) (+ (/ 1 2) (/ 1 2)) (* (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (* (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (+ 1 1) (+ (log (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (log (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (log (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (exp (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (* (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (* (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (cbrt (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (cbrt (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))))) (cbrt (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (* (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (sqrt (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (* (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (* (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (sqrt (* (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))))) (* (sqrt (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt 1) (sqrt 1)) (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* 1 1) (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* 2 1/2) (* 2 1) (* 2 (/ 1 2)) (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))))) (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (* (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))))) (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt 1)) (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) 1) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (* (sqrt (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (log (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (exp (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (* (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (* (* (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.395 * * [simplify]: iteration 0 : 5253 enodes (cost 989 ) 0.399 * [simplify]: Simplified to: (log (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (exp (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (cbrt (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 (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (pow (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) 3) (fabs (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 1 (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) 1/2 (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 1 1 2 1 1 (pow (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) 4) (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) (pow (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) 4) 2 (log (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (log (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (exp (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (pow (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) 3) (pow (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 4) (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (pow (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) 3) (pow (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) 4) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (pow (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 4) (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (pow (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 4) (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) 1 (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) 1 (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) 1 2 1 (pow (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 5) (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (fabs (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (pow (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 3) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (pow (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 3) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (pow (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 4) (* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))) (pow (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 3) (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) (pow (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 3) (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) (log (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (exp (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (pow (cbrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 4) (cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (pow (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) 3) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) (atan2 1.0 (+ 1 (* N (+ 1.0 N)))) 0.399 * * * [progress]: adding candidates to table 0.516 * * [progress]: iteration 4 / 4 0.516 * * * [progress]: picking best candidate 0.530 * * * * [pick]: Picked # 0.530 * * * [progress]: localizing error 0.544 * * * [progress]: generating rewritten candidates 0.544 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1) 0.545 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1) 0.547 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1) 0.547 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1 1) 0.548 * * * [progress]: generating series expansions 0.548 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1) 0.549 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 0.549 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.549 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.549 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.549 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.550 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 0.550 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.550 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.551 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.551 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.553 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 0.553 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.553 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.553 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.553 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.555 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1) 0.555 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 0.555 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.555 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.555 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.555 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.556 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 0.556 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.556 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.557 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.557 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.559 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 0.559 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.559 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.559 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.559 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.561 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1) 0.561 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.561 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.561 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.561 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.561 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.561 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.562 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.562 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.562 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.563 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1 1) 0.563 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.563 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.563 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.563 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.563 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.563 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.564 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.564 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.564 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.565 * * * [progress]: simplifying candidates 0.565 * [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))) 0.619 * * [simplify]: iteration 0 : 4899 enodes (cost 570 ) 0.619 * * [simplify]: iteration 1 : 4899 enodes (cost 570 ) 0.621 * [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)))) 0.622 * * * [progress]: adding candidates to table 0.739 * [progress]: [Phase 3 of 3] Extracting. 0.739 * * [regime]: Finding splitpoints for: (# # # # # # #) 0.741 * * * [regime-changes]: Trying 1 branch expressions: (N) 0.741 * * * * [regimes]: Trying to branch on N from (# # # # # # #) 0.792 * * * [regime]: Found split indices: #