7.988 * [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)) 0.031 * * [simplify]: iteration 0 : 9 enodes (cost 4 ) 0.032 * * [simplify]: iteration 1 : 10 enodes (cost 4 ) 0.033 * * [simplify]: iteration 2 : 10 enodes (cost 4 ) 0.033 * [simplify]: Simplified to: (- (atan (+ N 1.0)) (atan N)) 0.034 * * [progress]: iteration 1 / 4 0.034 * * * [progress]: picking best candidate 0.035 * * * * [pick]: Picked # 0.035 * * * [progress]: localizing error 0.041 * * * [progress]: generating rewritten candidates 0.041 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.045 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 0.046 * * * [progress]: generating series expansions 0.046 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.046 * [approximate]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in (N) around 0 0.046 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.046 * [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 0.050 * [approximate]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in (N) around 0 0.050 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.050 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.050 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.050 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.050 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.050 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.053 * [approximate]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in (N) around 0 0.053 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.053 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.053 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.053 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.053 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.054 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.057 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 0.057 * [approximate]: Taking taylor expansion of (atan (+ N 1.0)) in (N) around 0 0.057 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.057 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.057 * [approximate]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in (N) around 0 0.057 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.057 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.057 * [approximate]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in (N) around 0 0.057 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.057 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.058 * * * [progress]: simplifying candidates 0.058 * [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 : 129 enodes (cost 365 ) 0.065 * * [simplify]: iteration 1 : 345 enodes (cost 264 ) 0.074 * * [simplify]: iteration 2 : 1480 enodes (cost 254 ) 0.107 * * [simplify]: iteration 3 : 5001 enodes (cost 198 ) 0.109 * [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)) 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 1.0)) (+ (atan (+ N 1.0)) (atan N)) (* (atan N) (atan N))) (- (atan N)) (- (* (atan (+ N 1.0)) (atan (+ N 1.0))) (* (atan N) (atan N))) (+ (atan (+ N 1.0)) (atan N)) (+ (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)) 0.109 * * * [progress]: adding candidates to table 0.180 * * [progress]: iteration 2 / 4 0.180 * * * [progress]: picking best candidate 0.181 * * * * [pick]: Picked # 0.181 * * * [progress]: localizing error 0.190 * * * [progress]: generating rewritten candidates 0.190 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.190 * * * * [progress]: [ 2 / 2 ] rewriting at (2 2) 0.191 * * * [progress]: generating series expansions 0.191 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.191 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 0.191 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.191 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.191 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 0.191 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.192 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.192 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 0.192 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.192 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.192 * * * * [progress]: [ 2 / 2 ] generating series at (2 2) 0.193 * [approximate]: Taking taylor expansion of (fma N (+ N 1.0) 1) in (N) around 0 0.193 * [taylor]: Taking taylor expansion of (fma N (+ N 1.0) 1) in N 0.193 * [taylor]: Rewrote expression to (+ (* N (+ N 1.0)) 1) 0.193 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.193 * [taylor]: Taking taylor expansion of N in N 0.193 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.193 * [taylor]: Taking taylor expansion of N in N 0.193 * [taylor]: Taking taylor expansion of 1.0 in N 0.193 * [taylor]: Taking taylor expansion of 1 in N 0.193 * [taylor]: Taking taylor expansion of (fma N (+ N 1.0) 1) in N 0.193 * [taylor]: Rewrote expression to (+ (* N (+ N 1.0)) 1) 0.193 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.193 * [taylor]: Taking taylor expansion of N in N 0.193 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.193 * [taylor]: Taking taylor expansion of N in N 0.193 * [taylor]: Taking taylor expansion of 1.0 in N 0.193 * [taylor]: Taking taylor expansion of 1 in N 0.197 * [approximate]: Taking taylor expansion of (fma (/ 1 N) (+ (/ 1 N) 1.0) 1) in (N) around 0 0.197 * [taylor]: Taking taylor expansion of (fma (/ 1 N) (+ (/ 1 N) 1.0) 1) in N 0.197 * [taylor]: Rewrote expression to (+ (* (/ 1 N) (+ (/ 1 N) 1.0)) 1) 0.197 * [taylor]: Taking taylor expansion of (* (/ 1 N) (+ (/ 1 N) 1.0)) in N 0.197 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.197 * [taylor]: Taking taylor expansion of N in N 0.197 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.197 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.197 * [taylor]: Taking taylor expansion of N in N 0.197 * [taylor]: Taking taylor expansion of 1.0 in N 0.198 * [taylor]: Taking taylor expansion of 1 in N 0.198 * [taylor]: Taking taylor expansion of (fma (/ 1 N) (+ (/ 1 N) 1.0) 1) in N 0.198 * [taylor]: Rewrote expression to (+ (* (/ 1 N) (+ (/ 1 N) 1.0)) 1) 0.198 * [taylor]: Taking taylor expansion of (* (/ 1 N) (+ (/ 1 N) 1.0)) in N 0.198 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.198 * [taylor]: Taking taylor expansion of N in N 0.198 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.198 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.198 * [taylor]: Taking taylor expansion of N in N 0.198 * [taylor]: Taking taylor expansion of 1.0 in N 0.198 * [taylor]: Taking taylor expansion of 1 in N 0.203 * [approximate]: Taking taylor expansion of (fma (/ -1 N) (- 1.0 (/ 1 N)) 1) in (N) around 0 0.203 * [taylor]: Taking taylor expansion of (fma (/ -1 N) (- 1.0 (/ 1 N)) 1) in N 0.203 * [taylor]: Rewrote expression to (+ (* (/ -1 N) (- 1.0 (/ 1 N))) 1) 0.204 * [taylor]: Taking taylor expansion of (* (/ -1 N) (- 1.0 (/ 1 N))) in N 0.204 * [taylor]: Taking taylor expansion of (/ -1 N) in N 0.204 * [taylor]: Taking taylor expansion of -1 in N 0.204 * [taylor]: Taking taylor expansion of N in N 0.204 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.204 * [taylor]: Taking taylor expansion of 1.0 in N 0.204 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.204 * [taylor]: Taking taylor expansion of N in N 0.204 * [taylor]: Taking taylor expansion of 1 in N 0.204 * [taylor]: Taking taylor expansion of (fma (/ -1 N) (- 1.0 (/ 1 N)) 1) in N 0.204 * [taylor]: Rewrote expression to (+ (* (/ -1 N) (- 1.0 (/ 1 N))) 1) 0.204 * [taylor]: Taking taylor expansion of (* (/ -1 N) (- 1.0 (/ 1 N))) in N 0.204 * [taylor]: Taking taylor expansion of (/ -1 N) in N 0.204 * [taylor]: Taking taylor expansion of -1 in N 0.204 * [taylor]: Taking taylor expansion of N in N 0.205 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.205 * [taylor]: Taking taylor expansion of 1.0 in N 0.205 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.205 * [taylor]: Taking taylor expansion of N in N 0.205 * [taylor]: Taking taylor expansion of 1 in N 0.211 * * * [progress]: simplifying candidates 0.212 * [simplify]: Simplifying using # : (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))) (expm1 (fma N (+ N 1.0) 1)) (log1p (fma N (+ N 1.0) 1)) (* N (+ N 1.0)) (log (fma N (+ N 1.0) 1)) (exp (fma N (+ N 1.0) 1)) (* (cbrt (fma N (+ N 1.0) 1)) (cbrt (fma N (+ N 1.0) 1))) (cbrt (fma N (+ N 1.0) 1)) (* (* (fma N (+ N 1.0) 1) (fma N (+ N 1.0) 1)) (fma N (+ N 1.0) 1)) (sqrt (fma N (+ N 1.0) 1)) (sqrt (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)) (+ (pow N 2) (+ (* 1.0 N) 1)) (+ (pow N 2) (+ (* 1.0 N) 1)) (+ (pow N 2) (+ (* 1.0 N) 1)) 0.215 * * [simplify]: iteration 0 : 47 enodes (cost 101 ) 0.217 * * [simplify]: iteration 1 : 104 enodes (cost 89 ) 0.220 * * [simplify]: iteration 2 : 513 enodes (cost 89 ) 0.235 * * [simplify]: iteration 3 : 4531 enodes (cost 89 ) 0.352 * * [simplify]: iteration 4 : 5001 enodes (cost 89 ) 0.353 * [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))) (expm1 (fma N (+ N 1.0) 1)) (log1p (fma N (+ N 1.0) 1)) (* N (+ N 1.0)) (log (fma N (+ N 1.0) 1)) (exp (fma N (+ N 1.0) 1)) (* (cbrt (fma N (+ N 1.0) 1)) (cbrt (fma N (+ N 1.0) 1))) (cbrt (fma N (+ N 1.0) 1)) (pow (fma N (+ N 1.0) 1) 3) (sqrt (fma N (+ N 1.0) 1)) (sqrt (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)) (fma N (+ N 1.0) 1) (fma N (+ N 1.0) 1) (fma N (+ N 1.0) 1) 0.353 * * * [progress]: adding candidates to table 0.403 * * [progress]: iteration 3 / 4 0.403 * * * [progress]: picking best candidate 0.411 * * * * [pick]: Picked # 0.411 * * * [progress]: localizing error 0.419 * * * [progress]: generating rewritten candidates 0.419 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.420 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 0.421 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 0.421 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 0.422 * * * [progress]: generating series expansions 0.422 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.422 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 0.422 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.422 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.423 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.423 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.426 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 0.426 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.426 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.426 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.426 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.430 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 0.430 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.430 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.430 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.430 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.433 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 0.433 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 0.434 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.434 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.434 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.434 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.437 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 0.437 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.437 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.437 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.437 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.441 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 0.441 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.441 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.441 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.441 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.444 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 0.445 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 0.445 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.445 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.445 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 0.445 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.445 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.445 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 0.446 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.446 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.446 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 0.446 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 0.446 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.446 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.446 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 0.446 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.447 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.447 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 0.447 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.447 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.447 * * * [progress]: simplifying candidates 0.448 * [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 (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))) (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)) 0.451 * * [simplify]: iteration 0 : 37 enodes (cost 296 ) 0.453 * * [simplify]: iteration 1 : 62 enodes (cost 276 ) 0.455 * * [simplify]: iteration 2 : 100 enodes (cost 276 ) 0.459 * * [simplify]: iteration 3 : 148 enodes (cost 276 ) 0.462 * * [simplify]: iteration 4 : 341 enodes (cost 276 ) 0.468 * * [simplify]: iteration 5 : 975 enodes (cost 276 ) 0.496 * * [simplify]: iteration 6 : 3911 enodes (cost 274 ) 0.625 * * [simplify]: iteration 7 : 5001 enodes (cost 274 ) 0.628 * [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)))) (* (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)))) (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)))) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2) 1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2 (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2) (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)))) (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)))) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2) 1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2 (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2) (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))) (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))) (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)) 0.628 * * * [progress]: adding candidates to table 0.755 * * [progress]: iteration 4 / 4 0.755 * * * [progress]: picking best candidate 0.761 * * * * [pick]: Picked # 0.762 * * * [progress]: localizing error 0.775 * * * [progress]: generating rewritten candidates 0.775 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 2 1) 0.775 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1) 0.776 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 0.777 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 0.778 * * * [progress]: generating series expansions 0.778 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 2 1) 0.778 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) in (N) around 0 0.778 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) in N 0.778 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma N (+ N 1.0) 1))))) in N 0.778 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma N (+ N 1.0) 1)))) in N 0.778 * [taylor]: Taking taylor expansion of 1/3 in N 0.778 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.778 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.778 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) in N 0.778 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma N (+ N 1.0) 1))))) in N 0.778 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma N (+ N 1.0) 1)))) in N 0.778 * [taylor]: Taking taylor expansion of 1/3 in N 0.778 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.778 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.814 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/3) in (N) around 0 0.815 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/3) in N 0.815 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))))) in N 0.815 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)))) in N 0.815 * [taylor]: Taking taylor expansion of 1/3 in N 0.815 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.815 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.815 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/3) in N 0.815 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))))) in N 0.815 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)))) in N 0.815 * [taylor]: Taking taylor expansion of 1/3 in N 0.815 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.815 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.849 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/3) in (N) around 0 0.849 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/3) in N 0.850 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))))) in N 0.850 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)))) in N 0.850 * [taylor]: Taking taylor expansion of 1/3 in N 0.850 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.850 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.850 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/3) in N 0.850 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))))) in N 0.850 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)))) in N 0.850 * [taylor]: Taking taylor expansion of 1/3 in N 0.850 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.850 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.884 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1) 0.885 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) in (N) around 0 0.885 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) in N 0.885 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma N (+ N 1.0) 1))))) in N 0.885 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma N (+ N 1.0) 1)))) in N 0.885 * [taylor]: Taking taylor expansion of 1/3 in N 0.885 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.885 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.885 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) in N 0.885 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma N (+ N 1.0) 1))))) in N 0.885 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma N (+ N 1.0) 1)))) in N 0.885 * [taylor]: Taking taylor expansion of 1/3 in N 0.885 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.885 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.921 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/3) in (N) around 0 0.921 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/3) in N 0.921 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))))) in N 0.921 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)))) in N 0.922 * [taylor]: Taking taylor expansion of 1/3 in N 0.922 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.922 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.922 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/3) in N 0.922 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))))) in N 0.922 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)))) in N 0.922 * [taylor]: Taking taylor expansion of 1/3 in N 0.922 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.922 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.956 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/3) in (N) around 0 0.956 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/3) in N 0.956 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))))) in N 0.956 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)))) in N 0.956 * [taylor]: Taking taylor expansion of 1/3 in N 0.956 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.956 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.957 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/3) in N 0.957 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))))) in N 0.957 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)))) in N 0.957 * [taylor]: Taking taylor expansion of 1/3 in N 0.957 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.957 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.994 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 0.995 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 0.995 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.995 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.995 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.995 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.998 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 0.998 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.998 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.998 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.999 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 1.002 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 1.002 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 1.002 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 1.002 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 1.002 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 1.006 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 1.006 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 1.006 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 1.006 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 1.006 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 1.006 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 1.006 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 1.007 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 1.007 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 1.007 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 1.007 * * * [progress]: simplifying candidates 1.008 * [simplify]: Simplifying using # : (expm1 (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (cbrt (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 1) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (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)))) (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)))) (expm1 (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (cbrt (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 1) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (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)))) (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)))) (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 (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))) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 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))) (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)) 1.012 * * [simplify]: iteration 0 : 52 enodes (cost 352 ) 1.014 * * [simplify]: iteration 1 : 109 enodes (cost 319 ) 1.016 * * [simplify]: iteration 2 : 235 enodes (cost 315 ) 1.021 * * [simplify]: iteration 3 : 808 enodes (cost 315 ) 1.060 * * [simplify]: iteration 4 : 5002 enodes (cost 315 ) 1.062 * [simplify]: Simplified to: (expm1 (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (cbrt (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 1) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (* (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (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)))) (expm1 (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (cbrt (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 1) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (* (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (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)))) (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)))) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 3) (fabs (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3)) (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 (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 (atan2 1.0 (fma N (+ N 1.0) 1)) 2/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (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))) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 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))) (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)) 1.062 * * * [progress]: adding candidates to table 1.239 * [progress]: [Phase 3 of 3] Extracting. 1.239 * * [regime]: Finding splitpoints for: (# # # # #) 1.240 * * * [regime-changes]: Trying 1 branch expressions: (N) 1.240 * * * * [regimes]: Trying to branch on N from (# # # # #) 1.259 * * * [regime]: Found split indices: #