10.134 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.026 * * * [progress]: [2/2] Setting up program. 0.029 * [progress]: [Phase 2 of 3] Improving. 0.029 * [simplify]: Simplifying using # : (- (atan (+ N 1.0)) (atan N)) 0.030 * * [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 0.042 * * * [progress]: generating rewritten candidates 0.042 * * * * [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) 0.047 * [approximate]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in (N) around 0 0.047 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.047 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.047 * [taylor]: Taking taylor expansion of (atan N) in N 0.047 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.048 * [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 0.055 * [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 0.060 * [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 ) 0.103 * * [simplify]: iteration 2 : 301 enodes (cost 416 ) 0.216 * * [simplify]: iteration 3 : 1137 enodes (cost 355 ) 0.947 * * [simplify]: iteration done : 5002 enodes (cost 355 ) 0.947 * [simplify]: Simplified to: (- (pow (cbrt (atan (+ N 1.0))) 3) (atan N)) 0 (- (pow (cbrt (atan (+ N 1.0))) 3) (atan N)) 0 (- (pow (cbrt (atan (+ N 1.0))) 3) (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)) 0.948 * * * [progress]: adding candidates to table 1.015 * * [progress]: iteration 2 / 4 1.015 * * * [progress]: picking best candidate 1.017 * * * * [pick]: Picked # 1.017 * * * [progress]: localizing error 1.024 * * * [progress]: generating rewritten candidates 1.024 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 1.024 * * * [progress]: generating series expansions 1.024 * * * * [progress]: [ 1 / 1 ] generating series at (2) 1.025 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 1.025 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 1.025 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 1.026 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 1.026 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 1.026 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 1.026 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 1.027 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 1.027 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 1.027 * * * [progress]: simplifying candidates 1.027 * [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)) 1.028 * * [simplify]: iteration 0 : 18 enodes (cost 156 ) 1.031 * * [simplify]: iteration 1 : 24 enodes (cost 132 ) 1.034 * * [simplify]: iteration 2 : 44 enodes (cost 116 ) 1.041 * * [simplify]: iteration 3 : 82 enodes (cost 116 ) 1.063 * * [simplify]: iteration 4 : 165 enodes (cost 116 ) 1.192 * * [simplify]: iteration 5 : 524 enodes (cost 116 ) 2.266 * * [simplify]: iteration done : 5000 enodes (cost 116 ) 2.266 * [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)) 2.266 * * * [progress]: adding candidates to table 2.289 * * [progress]: iteration 3 / 4 2.289 * * * [progress]: picking best candidate 2.293 * * * * [pick]: Picked # 2.293 * * * [progress]: localizing error 2.303 * * * [progress]: generating rewritten candidates 2.303 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 2.304 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 2.305 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 2.311 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 2.313 * * * [progress]: generating series expansions 2.313 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 2.313 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 2.313 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 2.313 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 2.314 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 2.314 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 2.317 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 2.317 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 2.317 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 2.317 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 2.317 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 2.321 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 2.321 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 2.321 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 2.321 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 2.321 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 2.325 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 2.325 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 2.325 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 2.325 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 2.325 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 2.325 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 2.328 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 2.328 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 2.328 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 2.328 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 2.328 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 2.332 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 2.332 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 2.332 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 2.333 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 2.333 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 2.336 * * * * [progress]: [ 3 / 4 ] generating series at (2) 2.336 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 2.336 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 2.336 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 2.337 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 2.337 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 2.337 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 2.337 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 2.337 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 2.337 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 2.338 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 2.338 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 2.338 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 2.338 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 2.338 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 2.338 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 2.338 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 2.339 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 2.339 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 2.339 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 2.339 * * * [progress]: simplifying candidates 2.340 * [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)) 2.344 * * [simplify]: iteration 0 : 63 enodes (cost 1755 ) 2.358 * * [simplify]: iteration 1 : 97 enodes (cost 1200 ) 2.384 * * [simplify]: iteration 2 : 278 enodes (cost 1086 ) 2.606 * * [simplify]: iteration 3 : 1555 enodes (cost 1059 ) 3.776 * * [simplify]: iteration done : 5000 enodes (cost 1059 ) 3.776 * [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)))) (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)))) (* (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)))) (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 (* (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))) 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) (* (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) (* (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 (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 4) (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (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 (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)))) 4) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* (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))) (* (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)) 3.777 * * * [progress]: adding candidates to table 3.930 * * [progress]: iteration 4 / 4 3.930 * * * [progress]: picking best candidate 3.938 * * * * [pick]: Picked # 3.938 * * * [progress]: localizing error 3.948 * * * [progress]: generating rewritten candidates 3.948 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1) 3.949 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1) 3.949 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 3.952 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 1) 3.954 * * * [progress]: generating series expansions 3.954 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1) 3.954 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 3.954 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 3.954 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 3.955 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 3.955 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 3.958 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 3.958 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 3.958 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 3.959 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 3.959 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 3.962 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 3.962 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 3.962 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 3.963 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 3.963 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 3.966 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1) 3.967 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 3.967 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 3.967 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 3.967 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 3.967 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 3.970 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 3.970 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 3.970 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 3.971 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 3.971 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 3.974 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 3.974 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 3.974 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 3.975 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 3.975 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 3.978 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 3.978 * [approximate]: Taking taylor expansion of (pow (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/4) 3) in (N) around 0 3.978 * [taylor]: Taking taylor expansion of (pow (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/4) 3) in N 3.978 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/4) in N 3.978 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (atan2 1.0 (fma N (+ N 1.0) 1))))) in N 3.978 * [taylor]: Taking taylor expansion of (* 1/4 (log (atan2 1.0 (fma N (+ N 1.0) 1)))) in N 3.979 * [taylor]: Taking taylor expansion of 1/4 in N 3.979 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma N (+ N 1.0) 1))) in N 3.979 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 3.979 * [taylor]: Taking taylor expansion of (pow (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/4) 3) in N 3.979 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/4) in N 3.979 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (atan2 1.0 (fma N (+ N 1.0) 1))))) in N 3.979 * [taylor]: Taking taylor expansion of (* 1/4 (log (atan2 1.0 (fma N (+ N 1.0) 1)))) in N 3.979 * [taylor]: Taking taylor expansion of 1/4 in N 3.979 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma N (+ N 1.0) 1))) in N 3.979 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 4.026 * [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 4.026 * [taylor]: Taking taylor expansion of (pow (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/4) 3) in N 4.026 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/4) in N 4.026 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))))) in N 4.026 * [taylor]: Taking taylor expansion of (* 1/4 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)))) in N 4.026 * [taylor]: Taking taylor expansion of 1/4 in N 4.026 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 4.026 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 4.026 * [taylor]: Taking taylor expansion of (pow (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/4) 3) in N 4.026 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/4) in N 4.026 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))))) in N 4.026 * [taylor]: Taking taylor expansion of (* 1/4 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)))) in N 4.026 * [taylor]: Taking taylor expansion of 1/4 in N 4.026 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 4.026 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 4.076 * [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 4.076 * [taylor]: Taking taylor expansion of (pow (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/4) 3) in N 4.076 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/4) in N 4.076 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))))) in N 4.076 * [taylor]: Taking taylor expansion of (* 1/4 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)))) in N 4.076 * [taylor]: Taking taylor expansion of 1/4 in N 4.076 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 4.076 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 4.076 * [taylor]: Taking taylor expansion of (pow (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/4) 3) in N 4.076 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/4) in N 4.076 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))))) in N 4.076 * [taylor]: Taking taylor expansion of (* 1/4 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)))) in N 4.076 * [taylor]: Taking taylor expansion of 1/4 in N 4.076 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 4.076 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 4.122 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 1) 4.122 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 4.123 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 4.123 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 4.123 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 4.123 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 4.123 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 4.123 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 4.123 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 4.124 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 4.124 * * * [progress]: simplifying candidates 4.125 * [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)) 4.128 * * [simplify]: iteration 0 : 80 enodes (cost 1383 ) 4.153 * * [simplify]: iteration 1 : 176 enodes (cost 1137 ) 4.200 * * [simplify]: iteration 2 : 490 enodes (cost 1112 ) 4.474 * * [simplify]: iteration 3 : 2873 enodes (cost 1093 ) 6.290 * * [simplify]: iteration done : 5000 enodes (cost 1090 ) 6.291 * [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 (atan2 1.0 (fma N (+ N 1.0) 1))) 4/3) (/ (log (atan2 1.0 (fma N (+ N 1.0) 1))) 4/3) 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 (atan2 1.0 (fma N (+ N 1.0) 1))) 4/3) (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)) 6.291 * * * [progress]: adding candidates to table 6.481 * [progress]: [Phase 3 of 3] Extracting. 6.481 * * [regime]: Finding splitpoints for: (# # # # # # #) 6.482 * * * [regime-changes]: Trying 1 branch expressions: (N) 6.482 * * * * [regimes]: Trying to branch on N from (# # # # # # #) 6.509 * * * [regime]: Found split indices: #