11.253 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.026 * * * [progress]: [2/2] Setting up program. 0.028 * [progress]: [Phase 2 of 3] Improving. 0.028 * [simplify]: Simplifying using # : (- (atan (+ N 1.0)) (atan N)) 0.029 * * [simplify]: iteration 0 : 6 enodes (cost 7 ) 0.030 * * [simplify]: iteration 1 : 9 enodes (cost 7 ) 0.031 * * [simplify]: iteration 2 : 10 enodes (cost 7 ) 0.032 * * [simplify]: iteration done : 10 enodes (cost 7 ) 0.032 * [simplify]: Simplified to: (- (atan (+ N 1.0)) (atan N)) 0.032 * * [progress]: iteration 1 / 4 0.032 * * * [progress]: picking best candidate 0.034 * * * * [pick]: Picked # 0.034 * * * [progress]: localizing error 0.043 * * * [progress]: generating rewritten candidates 0.043 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.046 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 0.047 * * * [progress]: generating series expansions 0.047 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.048 * [approximate]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in (N) around 0 0.048 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.048 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.048 * [taylor]: Taking taylor expansion of (atan N) in N 0.048 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.048 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.048 * [taylor]: Taking taylor expansion of (atan N) in N 0.051 * [approximate]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in (N) around 0 0.051 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.051 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.051 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.051 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.051 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.051 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.054 * [approximate]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in (N) around 0 0.055 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.055 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.055 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.055 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.055 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.055 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.058 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 0.058 * [approximate]: Taking taylor expansion of (atan (+ N 1.0)) in (N) around 0 0.058 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.058 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.058 * [approximate]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in (N) around 0 0.058 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.058 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.059 * [approximate]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in (N) around 0 0.059 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.059 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.059 * * * [progress]: simplifying candidates 0.059 * [simplify]: Simplifying using # : (fma (* (cbrt (atan (+ N 1.0))) (cbrt (atan (+ N 1.0)))) (cbrt (atan (+ N 1.0))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))) (fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))) (fma (* (cbrt (atan (+ N 1.0))) (cbrt (atan (+ N 1.0)))) (cbrt (atan (+ N 1.0))) (- (* (sqrt (atan N)) (sqrt (atan N))))) (fma (- (sqrt (atan N))) (sqrt (atan N)) (* (sqrt (atan N)) (sqrt (atan N)))) (fma (* (cbrt (atan (+ N 1.0))) (cbrt (atan (+ N 1.0)))) (cbrt (atan (+ N 1.0))) (- (* (atan N) 1))) (fma (- (atan N)) 1 (* (atan N) 1)) (fma (sqrt (atan (+ N 1.0))) (sqrt (atan (+ N 1.0))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))) (fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))) (fma (sqrt (atan (+ N 1.0))) (sqrt (atan (+ N 1.0))) (- (* (sqrt (atan N)) (sqrt (atan N))))) (fma (- (sqrt (atan N))) (sqrt (atan N)) (* (sqrt (atan N)) (sqrt (atan N)))) (fma (sqrt (atan (+ N 1.0))) (sqrt (atan (+ N 1.0))) (- (* (atan N) 1))) (fma (- (atan N)) 1 (* (atan N) 1)) (fma 1 (atan (+ N 1.0)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))) (fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))) (fma 1 (atan (+ N 1.0)) (- (* (sqrt (atan N)) (sqrt (atan N))))) (fma (- (sqrt (atan N))) (sqrt (atan N)) (* (sqrt (atan N)) (sqrt (atan N)))) (fma 1 (atan (+ N 1.0)) (- (* (atan N) 1))) (fma (- (atan N)) 1 (* (atan N) 1)) (expm1 (- (atan (+ N 1.0)) (atan N))) (log1p (- (atan (+ N 1.0)) (atan N))) (- (atan N)) (- (atan N)) (- (atan N)) (- (+ N 1.0) N) (+ 1 (* (+ N 1.0) N)) (/ (exp (atan (+ N 1.0))) (exp (atan N))) (log (- (atan (+ N 1.0)) (atan N))) (exp (- (atan (+ N 1.0)) (atan N))) (* (cbrt (- (atan (+ N 1.0)) (atan N))) (cbrt (- (atan (+ N 1.0)) (atan N)))) (cbrt (- (atan (+ N 1.0)) (atan N))) (* (* (- (atan (+ N 1.0)) (atan N)) (- (atan (+ N 1.0)) (atan N))) (- (atan (+ N 1.0)) (atan N))) (sqrt (- (atan (+ N 1.0)) (atan N))) (sqrt (- (atan (+ N 1.0)) (atan N))) (- (pow (atan (+ N 1.0)) 3) (pow (atan N) 3)) (+ (* (atan (+ N 1.0)) (atan (+ N 1.0))) (+ (* (atan N) (atan N)) (* (atan (+ N 1.0)) (atan N)))) (- (atan N)) (- (* (atan (+ N 1.0)) (atan (+ N 1.0))) (* (atan N) (atan N))) (+ (atan (+ N 1.0)) (atan N)) (+ (sqrt (atan (+ N 1.0))) (sqrt (atan N))) (- (sqrt (atan (+ N 1.0))) (sqrt (atan N))) (- (atan (+ N 1.0)) (atan N)) (- (atan N)) (expm1 (atan (+ N 1.0))) (log1p (atan (+ N 1.0))) (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)) 0.062 * * [simplify]: iteration 0 : 66 enodes (cost 624 ) 0.071 * * [simplify]: iteration 1 : 127 enodes (cost 503 ) 0.104 * * [simplify]: iteration 2 : 301 enodes (cost 416 ) 0.234 * * [simplify]: iteration 3 : 1115 enodes (cost 355 ) 1.850 * * [simplify]: iteration 4 : 4770 enodes (cost 346 ) 2.830 * * [simplify]: iteration done : 5000 enodes (cost 346 ) 2.831 * [simplify]: Simplified to: (- (atan (+ N 1.0)) (atan N)) 0 (- (atan (+ N 1.0)) (atan N)) 0 (- (atan (+ N 1.0)) (atan N)) 0 (- (atan (+ N 1.0)) (atan N)) 0 (- (atan (+ N 1.0)) (atan N)) 0 (- (atan (+ N 1.0)) (atan N)) 0 (- (atan (+ N 1.0)) (atan N)) 0 (- (atan (+ N 1.0)) (atan N)) 0 (- (atan (+ N 1.0)) (atan N)) 0 (expm1 (- (atan (+ N 1.0)) (atan N))) (log1p (- (atan (+ N 1.0)) (atan N))) (- (atan N)) (- (atan N)) (- (atan N)) (+ 0 1.0) (fma N (+ N 1.0) 1) (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)) (fma (atan N) (atan N) (* (+ (atan (+ N 1.0)) (atan N)) (atan (+ N 1.0)))) (- (atan N)) (- (* (atan (+ N 1.0)) (atan (+ N 1.0))) (* (atan N) (atan N))) (+ (atan N) (atan (+ N 1.0))) (+ (sqrt (atan (+ N 1.0))) (sqrt (atan N))) (- (sqrt (atan (+ N 1.0))) (sqrt (atan N))) (- (atan (+ N 1.0)) (atan N)) (- (atan N)) (expm1 (atan (+ N 1.0))) (log1p (atan (+ N 1.0))) (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)) 2.836 * * * [progress]: adding candidates to table 2.901 * * [progress]: iteration 2 / 4 2.901 * * * [progress]: picking best candidate 2.902 * * * * [pick]: Picked # 2.902 * * * [progress]: localizing error 2.909 * * * [progress]: generating rewritten candidates 2.909 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 2.909 * * * [progress]: generating series expansions 2.909 * * * * [progress]: [ 1 / 1 ] generating series at (2) 2.910 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 2.910 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 2.910 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 2.911 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 2.911 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 2.911 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 2.911 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 2.911 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 2.911 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 2.912 * * * [progress]: simplifying candidates 2.912 * [simplify]: Simplifying using # : (expm1 (atan2 (+ 0 1.0) (fma N (+ N 1.0) 1))) (log1p (atan2 (+ 0 1.0) (fma N (+ N 1.0) 1))) (log (atan2 (+ 0 1.0) (fma N (+ N 1.0) 1))) (exp (atan2 (+ 0 1.0) (fma N (+ N 1.0) 1))) (* (cbrt (atan2 (+ 0 1.0) (fma N (+ N 1.0) 1))) (cbrt (atan2 (+ 0 1.0) (fma N (+ N 1.0) 1)))) (cbrt (atan2 (+ 0 1.0) (fma N (+ N 1.0) 1))) (* (* (atan2 (+ 0 1.0) (fma N (+ N 1.0) 1)) (atan2 (+ 0 1.0) (fma N (+ N 1.0) 1))) (atan2 (+ 0 1.0) (fma N (+ N 1.0) 1))) (sqrt (atan2 (+ 0 1.0) (fma N (+ N 1.0) 1))) (sqrt (atan2 (+ 0 1.0) (fma N (+ N 1.0) 1))) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) 2.913 * * [simplify]: iteration 0 : 18 enodes (cost 156 ) 2.915 * * [simplify]: iteration 1 : 24 enodes (cost 132 ) 2.918 * * [simplify]: iteration 2 : 35 enodes (cost 116 ) 2.922 * * [simplify]: iteration 3 : 52 enodes (cost 116 ) 2.928 * * [simplify]: iteration 4 : 64 enodes (cost 116 ) 2.935 * * [simplify]: iteration 5 : 74 enodes (cost 116 ) 2.945 * * [simplify]: iteration 6 : 97 enodes (cost 116 ) 2.959 * * [simplify]: iteration 7 : 159 enodes (cost 116 ) 3.002 * * [simplify]: iteration 8 : 360 enodes (cost 116 ) 3.350 * * [simplify]: iteration 9 : 1280 enodes (cost 116 ) 5.039 * * [simplify]: iteration done : 5000 enodes (cost 116 ) 5.039 * [simplify]: Simplified to: (expm1 (atan2 1.0 (fma N (+ N 1.0) 1))) (log1p (atan2 1.0 (fma N (+ N 1.0) 1))) (log (atan2 1.0 (fma N (+ N 1.0) 1))) (exp (atan2 1.0 (fma N (+ N 1.0) 1))) (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) 5.040 * * * [progress]: adding candidates to table 5.063 * * [progress]: iteration 3 / 4 5.063 * * * [progress]: picking best candidate 5.067 * * * * [pick]: Picked # 5.067 * * * [progress]: localizing error 5.078 * * * [progress]: generating rewritten candidates 5.078 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 5.079 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 5.079 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 5.086 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 5.088 * * * [progress]: generating series expansions 5.088 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 5.088 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 5.088 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 5.088 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 5.088 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 5.088 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 5.092 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 5.092 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 5.092 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 5.092 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 5.092 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 5.095 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 5.095 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 5.095 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 5.096 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 5.096 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 5.099 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 5.099 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 5.099 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 5.099 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 5.099 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 5.099 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 5.102 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 5.102 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 5.102 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 5.103 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 5.103 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 5.106 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 5.106 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 5.106 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 5.107 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 5.107 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 5.110 * * * * [progress]: [ 3 / 4 ] generating series at (2) 5.110 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 5.110 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 5.110 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 5.111 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 5.111 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 5.111 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 5.111 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 5.111 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 5.111 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 5.112 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 5.112 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 5.112 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 5.112 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 5.112 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 5.112 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 5.112 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 5.113 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 5.113 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 5.113 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 5.113 * * * [progress]: simplifying candidates 5.115 * [simplify]: Simplifying using # : (expm1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt 1) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (/ 1 2) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (expm1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt 1) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (/ 1 2) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (expm1 (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (log1p (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (+ 1/2 1/2) (+ 1/2 (/ 1 2)) (+ 1 1) (+ (/ 1 2) 1/2) (+ (/ 1 2) (/ 1 2)) (* (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1))) (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1))) (+ 1 1) (+ (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (log (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (exp (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (* (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (cbrt (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))))) (cbrt (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (* (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))))) (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))))) (* (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt 1) (sqrt 1)) (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* 1 1) (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* 2 1/2) (* 2 1) (* 2 (/ 1 2)) (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))))) (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))))) (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt 1)) (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1) (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (expm1 (atan2 1.0 (fma N (+ N 1.0) 1))) (log1p (atan2 1.0 (fma N (+ N 1.0) 1))) (log (atan2 1.0 (fma N (+ N 1.0) 1))) (exp (atan2 1.0 (fma N (+ N 1.0) 1))) (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (* (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1))) (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) 5.118 * * [simplify]: iteration 0 : 63 enodes (cost 1755 ) 5.133 * * [simplify]: iteration 1 : 97 enodes (cost 1200 ) 5.149 * * [simplify]: iteration 2 : 214 enodes (cost 1086 ) 5.240 * * [simplify]: iteration 3 : 511 enodes (cost 1041 ) 5.398 * * [simplify]: iteration 4 : 1003 enodes (cost 1009 ) 6.911 * * [simplify]: iteration 5 : 4642 enodes (cost 982 ) 8.722 * * [simplify]: iteration done : 5001 enodes (cost 982 ) 8.722 * [simplify]: Simplified to: (expm1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 2) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 3) (fabs (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2 (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (expm1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 2) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 3) (fabs (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2 (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (expm1 (atan2 1.0 (fma N (+ N 1.0) 1))) (log1p (atan2 1.0 (fma N (+ N 1.0) 1))) 1 1 2 1 1 (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 4) (atan2 1.0 (fma N (+ N 1.0) 1)) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 4) 2 (log (atan2 1.0 (fma N (+ N 1.0) 1))) (log (atan2 1.0 (fma N (+ N 1.0) 1))) (exp (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) (pow (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 4) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 4) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 4) (pow (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 2) (pow (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 4) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1 (atan2 1.0 (fma N (+ N 1.0) 1)) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1 (atan2 1.0 (fma N (+ N 1.0) 1)) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1 2 1 (pow (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 5) (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (fabs (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 4) (* (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (atan2 1.0 (fma N (+ N 1.0) 1)) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (atan2 1.0 (fma N (+ N 1.0) 1)) (expm1 (atan2 1.0 (fma N (+ N 1.0) 1))) (log1p (atan2 1.0 (fma N (+ N 1.0) 1))) (log (atan2 1.0 (fma N (+ N 1.0) 1))) (exp (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 4) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) 8.723 * * * [progress]: adding candidates to table 8.866 * * [progress]: iteration 4 / 4 8.866 * * * [progress]: picking best candidate 8.876 * * * * [pick]: Picked # 8.876 * * * [progress]: localizing error 8.886 * * * [progress]: generating rewritten candidates 8.886 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1) 8.887 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1) 8.887 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 8.890 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1) 8.892 * * * [progress]: generating series expansions 8.892 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1) 8.892 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 8.892 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 8.892 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 8.892 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 8.892 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 8.896 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 8.896 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 8.896 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 8.896 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 8.896 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 8.899 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 8.899 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 8.899 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 8.900 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 8.900 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 8.903 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1) 8.903 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 8.903 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 8.903 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 8.903 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 8.903 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 8.906 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 8.906 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 8.906 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 8.906 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 8.906 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 8.910 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 8.910 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 8.910 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 8.910 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 8.910 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 8.913 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 8.913 * [approximate]: Taking taylor expansion of (pow (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/4) 3) in (N) around 0 8.913 * [taylor]: Taking taylor expansion of (pow (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/4) 3) in N 8.913 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/4) in N 8.914 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (atan2 1.0 (fma N (+ N 1.0) 1))))) in N 8.914 * [taylor]: Taking taylor expansion of (* 1/4 (log (atan2 1.0 (fma N (+ N 1.0) 1)))) in N 8.914 * [taylor]: Taking taylor expansion of 1/4 in N 8.914 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma N (+ N 1.0) 1))) in N 8.914 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 8.914 * [taylor]: Taking taylor expansion of (pow (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/4) 3) in N 8.914 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/4) in N 8.914 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (atan2 1.0 (fma N (+ N 1.0) 1))))) in N 8.914 * [taylor]: Taking taylor expansion of (* 1/4 (log (atan2 1.0 (fma N (+ N 1.0) 1)))) in N 8.914 * [taylor]: Taking taylor expansion of 1/4 in N 8.914 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma N (+ N 1.0) 1))) in N 8.914 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 8.957 * [approximate]: Taking taylor expansion of (pow (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/4) 3) in (N) around 0 8.958 * [taylor]: Taking taylor expansion of (pow (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/4) 3) in N 8.958 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/4) in N 8.958 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))))) in N 8.958 * [taylor]: Taking taylor expansion of (* 1/4 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)))) in N 8.958 * [taylor]: Taking taylor expansion of 1/4 in N 8.958 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 8.958 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 8.958 * [taylor]: Taking taylor expansion of (pow (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/4) 3) in N 8.958 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/4) in N 8.958 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))))) in N 8.958 * [taylor]: Taking taylor expansion of (* 1/4 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)))) in N 8.958 * [taylor]: Taking taylor expansion of 1/4 in N 8.958 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 8.958 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 9.001 * [approximate]: Taking taylor expansion of (pow (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/4) 3) in (N) around 0 9.001 * [taylor]: Taking taylor expansion of (pow (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/4) 3) in N 9.001 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/4) in N 9.001 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))))) in N 9.001 * [taylor]: Taking taylor expansion of (* 1/4 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)))) in N 9.001 * [taylor]: Taking taylor expansion of 1/4 in N 9.001 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 9.001 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 9.002 * [taylor]: Taking taylor expansion of (pow (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/4) 3) in N 9.002 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/4) in N 9.002 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))))) in N 9.002 * [taylor]: Taking taylor expansion of (* 1/4 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)))) in N 9.002 * [taylor]: Taking taylor expansion of 1/4 in N 9.002 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 9.002 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 9.049 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1) 9.049 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 9.049 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 9.049 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 9.049 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 9.049 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 9.049 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 9.050 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 9.050 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 9.050 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 9.050 * * * [progress]: simplifying candidates 9.051 * [simplify]: Simplifying using # : (expm1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt 1) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (/ 1 2) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (expm1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt 1) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (/ 1 2) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (expm1 (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) (log1p (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) (* (log (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (* (log (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (* 1/2 3) (* 1 3) (* (/ 1/2 2) 3) (* (/ 1 2) 3) (* (/ (/ 1 2) 2) 3) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (cbrt 3) (cbrt 3))) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt 3)) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 1) (pow (* (cbrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))))) 3) (pow (cbrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))))) 3) (pow (sqrt (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))))) 3) (pow (sqrt (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt 1)) 3) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt 1) 3) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow 1 3) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (log (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) (exp (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) (* (cbrt (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) (cbrt (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3))) (cbrt (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) (* (* (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) (pow (* (cbrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))))) 3) (pow (cbrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))))) 3) (pow (sqrt (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))))) 3) (pow (sqrt (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt 1)) 3) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt 1) 3) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow 1 3) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (/ 3 2) (sqrt (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) (sqrt (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (/ 3 2)) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (/ 3 2)) (expm1 (atan2 1.0 (fma N (+ N 1.0) 1))) (log1p (atan2 1.0 (fma N (+ N 1.0) 1))) (log (atan2 1.0 (fma N (+ N 1.0) 1))) (exp (atan2 1.0 (fma N (+ N 1.0) 1))) (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (* (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1))) (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) 1/4) (pow (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) 1/4) (pow (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) 1/4) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) 9.054 * * [simplify]: iteration 0 : 80 enodes (cost 1383 ) 9.076 * * [simplify]: iteration 1 : 176 enodes (cost 1137 ) 9.115 * * [simplify]: iteration 2 : 427 enodes (cost 1112 ) 9.432 * * [simplify]: iteration 3 : 2588 enodes (cost 1096 ) 10.871 * * [simplify]: iteration done : 5000 enodes (cost 1096 ) 10.871 * [simplify]: Simplified to: (expm1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (cbrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 4) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 3) (fabs (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2 (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (expm1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (cbrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 4) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 3) (fabs (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2 (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (expm1 (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) (log1p (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) (log (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) (log (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) 3/2 3 3/4 3/2 3/4 (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (cbrt 3) (cbrt 3))) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt 3)) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (fabs (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (fabs (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) 1 (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) 1 (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) 1 (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (log (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) (exp (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) 3) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (fabs (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (fabs (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) 1 (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) 1 (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) (pow (sqrt (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) 3) 1 (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 3/2 (sqrt (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) (sqrt (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3/2) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3/2) (expm1 (atan2 1.0 (fma N (+ N 1.0) 1))) (log1p (atan2 1.0 (fma N (+ N 1.0) 1))) (log (atan2 1.0 (fma N (+ N 1.0) 1))) (exp (atan2 1.0 (fma N (+ N 1.0) 1))) (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) 1/4) (pow (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) 1/4) (pow (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) 1/4) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) 10.872 * * * [progress]: adding candidates to table 11.057 * [progress]: [Phase 3 of 3] Extracting. 11.057 * * [regime]: Finding splitpoints for: (# # # # # # #) 11.059 * * * [regime-changes]: Trying 1 branch expressions: (N) 11.059 * * * * [regimes]: Trying to branch on N from (# # # # # # #) 11.085 * * * [regime]: Found split indices: #