10.112 * [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 ) 0.033 * * [simplify]: iteration 1 : 10 enodes (cost 4 ) 0.034 * * [simplify]: iteration 2 : 10 enodes (cost 4 ) 0.034 * [simplify]: Simplified to: (- (atan (+ N 1.0)) (atan N)) 0.035 * * [progress]: iteration 1 / 4 0.035 * * * [progress]: picking best candidate 0.036 * * * * [pick]: Picked # 0.036 * * * [progress]: localizing error 0.042 * * * [progress]: generating rewritten candidates 0.042 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.046 * * * * [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 0.048 * [taylor]: Taking taylor expansion of (atan N) in N 0.048 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.048 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.048 * [taylor]: Taking taylor expansion of (atan N) in N 0.051 * [approximate]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in (N) around 0 0.051 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.051 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.051 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.051 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.051 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.051 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.054 * [approximate]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in (N) around 0 0.054 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.054 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.054 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.055 * [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 0.058 * [approximate]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in (N) around 0 0.058 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.058 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.059 * * * [progress]: simplifying candidates 0.059 * [simplify]: Simplifying using # : (fma (* (cbrt (atan (+ N 1.0))) (cbrt (atan (+ N 1.0)))) (cbrt (atan (+ N 1.0))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))) (fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))) (fma (* (cbrt (atan (+ N 1.0))) (cbrt (atan (+ N 1.0)))) (cbrt (atan (+ N 1.0))) (- (* (sqrt (atan N)) (sqrt (atan N))))) (fma (- (sqrt (atan N))) (sqrt (atan N)) (* (sqrt (atan N)) (sqrt (atan N)))) (fma (* (cbrt (atan (+ N 1.0))) (cbrt (atan (+ N 1.0)))) (cbrt (atan (+ N 1.0))) (- (* (atan N) 1))) (fma (- (atan N)) 1 (* (atan N) 1)) (fma (sqrt (atan (+ N 1.0))) (sqrt (atan (+ N 1.0))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))) (fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))) (fma (sqrt (atan (+ N 1.0))) (sqrt (atan (+ N 1.0))) (- (* (sqrt (atan N)) (sqrt (atan N))))) (fma (- (sqrt (atan N))) (sqrt (atan N)) (* (sqrt (atan N)) (sqrt (atan N)))) (fma (sqrt (atan (+ N 1.0))) (sqrt (atan (+ N 1.0))) (- (* (atan N) 1))) (fma (- (atan N)) 1 (* (atan N) 1)) (fma 1 (atan (+ N 1.0)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))) (fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))) (fma 1 (atan (+ N 1.0)) (- (* (sqrt (atan N)) (sqrt (atan N))))) (fma (- (sqrt (atan N))) (sqrt (atan N)) (* (sqrt (atan N)) (sqrt (atan N)))) (fma 1 (atan (+ N 1.0)) (- (* (atan N) 1))) (fma (- (atan N)) 1 (* (atan N) 1)) (expm1 (- (atan (+ N 1.0)) (atan N))) (log1p (- (atan (+ N 1.0)) (atan N))) (- (atan N)) (- (atan N)) (- (atan N)) (- (+ N 1.0) N) (+ 1 (* (+ N 1.0) N)) (/ (exp (atan (+ N 1.0))) (exp (atan N))) (log (- (atan (+ N 1.0)) (atan N))) (exp (- (atan (+ N 1.0)) (atan N))) (* (cbrt (- (atan (+ N 1.0)) (atan N))) (cbrt (- (atan (+ N 1.0)) (atan N)))) (cbrt (- (atan (+ N 1.0)) (atan N))) (* (* (- (atan (+ N 1.0)) (atan N)) (- (atan (+ N 1.0)) (atan N))) (- (atan (+ N 1.0)) (atan N))) (sqrt (- (atan (+ N 1.0)) (atan N))) (sqrt (- (atan (+ N 1.0)) (atan N))) (- (pow (atan (+ N 1.0)) 3) (pow (atan N) 3)) (+ (* (atan (+ N 1.0)) (atan (+ N 1.0))) (+ (* (atan N) (atan N)) (* (atan (+ N 1.0)) (atan N)))) (- (atan N)) (- (* (atan (+ N 1.0)) (atan (+ N 1.0))) (* (atan N) (atan N))) (+ (atan (+ N 1.0)) (atan N)) (+ (sqrt (atan (+ N 1.0))) (sqrt (atan N))) (- (sqrt (atan (+ N 1.0))) (sqrt (atan N))) (- (atan (+ N 1.0)) (atan N)) (- (atan N)) (expm1 (atan (+ N 1.0))) (log1p (atan (+ N 1.0))) (log (atan (+ N 1.0))) (exp (atan (+ N 1.0))) (* (cbrt (atan (+ N 1.0))) (cbrt (atan (+ N 1.0)))) (cbrt (atan (+ N 1.0))) (* (* (atan (+ N 1.0)) (atan (+ N 1.0))) (atan (+ N 1.0))) (sqrt (atan (+ N 1.0))) (sqrt (atan (+ N 1.0))) (- (atan (+ N 1.0)) (atan N)) (- (atan (+ N 1.0)) (atan N)) (- (atan (+ N 1.0)) (atan N)) (atan (+ N 1.0)) (atan (+ N 1.0)) (atan (+ N 1.0)) 0.068 * * [simplify]: iteration 0 : 129 enodes (cost 365 ) 0.071 * * [simplify]: iteration 1 : 345 enodes (cost 264 ) 0.079 * * [simplify]: iteration 2 : 1480 enodes (cost 254 ) 0.112 * * [simplify]: iteration 3 : 5001 enodes (cost 198 ) 0.113 * [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)) 0.113 * * * [progress]: adding candidates to table 0.183 * * [progress]: iteration 2 / 4 0.183 * * * [progress]: picking best candidate 0.185 * * * * [pick]: Picked # 0.185 * * * [progress]: localizing error 0.190 * * * [progress]: generating rewritten candidates 0.190 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.191 * * * [progress]: generating series expansions 0.191 * * * * [progress]: [ 1 / 1 ] 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 0.191 * [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]: simplifying candidates 0.193 * [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))) (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)) 0.195 * * [simplify]: iteration 0 : 21 enodes (cost 57 ) 0.197 * * [simplify]: iteration 1 : 32 enodes (cost 50 ) 0.198 * * [simplify]: iteration 2 : 55 enodes (cost 50 ) 0.200 * * [simplify]: iteration 3 : 70 enodes (cost 50 ) 0.201 * * [simplify]: iteration 4 : 89 enodes (cost 50 ) 0.203 * * [simplify]: iteration 5 : 143 enodes (cost 50 ) 0.208 * * [simplify]: iteration 6 : 567 enodes (cost 50 ) 0.224 * * [simplify]: iteration 7 : 1779 enodes (cost 50 ) 0.290 * * [simplify]: iteration 8 : 5001 enodes (cost 50 ) 0.291 * [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)) 0.291 * * * [progress]: adding candidates to table 0.313 * * [progress]: iteration 3 / 4 0.313 * * * [progress]: picking best candidate 0.322 * * * * [pick]: Picked # 0.322 * * * [progress]: localizing error 0.330 * * * [progress]: generating rewritten candidates 0.330 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.331 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 0.332 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 0.338 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 0.341 * * * [progress]: generating series expansions 0.341 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.341 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 0.341 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.341 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.342 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.342 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.345 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 0.345 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.345 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.345 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.345 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.349 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 0.349 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.349 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.349 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.349 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.353 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 0.353 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 0.353 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.353 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.353 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.353 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.356 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 0.356 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.356 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.356 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.356 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.360 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 0.360 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.360 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.360 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.360 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.364 * * * * [progress]: [ 3 / 4 ] generating series at (2) 0.364 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 0.364 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.364 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.364 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 0.364 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.364 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.365 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 0.365 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.365 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.365 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 0.365 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 0.365 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.366 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.366 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 0.366 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.366 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.366 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 0.366 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.366 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.367 * * * [progress]: simplifying candidates 0.368 * [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)) 0.374 * * [simplify]: iteration 0 : 100 enodes (cost 554 ) 0.377 * * [simplify]: iteration 1 : 375 enodes (cost 496 ) 0.388 * * [simplify]: iteration 2 : 2244 enodes (cost 476 ) 0.473 * * [simplify]: iteration 3 : 5001 enodes (cost 461 ) 0.476 * [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 (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 4) (atan2 1.0 (fma N (+ N 1.0) 1)) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 4) 2 (log (atan2 1.0 (fma N (+ N 1.0) 1))) (log (atan2 1.0 (fma N (+ N 1.0) 1))) (exp (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) (pow (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 4) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 4) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 4) (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (pow (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 4) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1 (atan2 1.0 (fma N (+ N 1.0) 1)) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1 (atan2 1.0 (fma N (+ N 1.0) 1)) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1 2 1 (pow (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 5) (* (fabs (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) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 4) (* (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (atan2 1.0 (fma N (+ N 1.0) 1)) (pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3) (atan2 1.0 (fma N (+ N 1.0) 1)) (expm1 (atan2 1.0 (fma N (+ N 1.0) 1))) (log1p (atan2 1.0 (fma N (+ N 1.0) 1))) (log (atan2 1.0 (fma N (+ N 1.0) 1))) (exp (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 4) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) 0.477 * * * [progress]: adding candidates to table 0.639 * * [progress]: iteration 4 / 4 0.639 * * * [progress]: picking best candidate 0.648 * * * * [pick]: Picked # 0.649 * * * [progress]: localizing error 0.659 * * * [progress]: generating rewritten candidates 0.659 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.660 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 1) 0.661 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 1) 0.662 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.703 * * * [progress]: generating series expansions 0.703 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.703 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 0.703 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.703 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.703 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.704 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.707 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 0.707 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.707 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.708 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.708 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.711 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 0.711 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.711 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.712 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.712 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.715 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 1) 0.715 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 0.715 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.715 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.715 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.715 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.719 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 0.719 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.719 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.719 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.719 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.722 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 0.722 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.722 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.723 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.723 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.726 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 1) 0.726 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 0.726 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.726 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.726 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.726 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.730 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 0.730 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.730 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.730 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.730 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.733 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 0.733 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.733 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.734 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.734 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.737 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.738 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 0.738 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.738 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.738 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 0.738 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.738 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.739 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 0.739 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.739 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.740 * * * [progress]: simplifying candidates 0.741 * [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)))) (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 (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))))) (log1p (* (* (sqrt (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))))) (+ (+ 1/2 1/2) 1) (+ (+ 1/2 (/ 1 2)) 1) (+ (+ (/ 1/2 2) (/ 1/2 2)) 1/2) (+ (+ (/ 1/2 2) (/ 1/2 2)) (/ 1 2)) (+ (+ (/ 1/2 2) (/ (/ 1 2) 2)) 1/2) (+ (+ (/ 1/2 2) (/ (/ 1 2) 2)) (/ 1 2)) (+ (+ (/ 1 2) 1/2) 1) (+ (+ (/ 1 2) (/ 1 2)) 1) (+ (+ (/ (/ 1 2) 2) (/ 1/2 2)) 1/2) (+ (+ (/ (/ 1 2) 2) (/ 1/2 2)) (/ 1 2)) (+ (+ (/ (/ 1 2) 2) (/ (/ 1 2) 2)) 1/2) (+ (+ (/ (/ 1 2) 2) (/ (/ 1 2) 2)) (/ 1 2)) (+ (* 2 1/2) 1) (+ (* 2 (/ 1/2 2)) 1/2) (+ (* 2 (/ 1/2 2)) (/ 1 2)) (+ (* 2 (/ 1 2)) 1) (+ (* 2 (/ (/ 1 2) 2)) 1/2) (+ (* 2 (/ (/ 1 2) 2)) (/ 1 2)) (* (* (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))) (* (* (sqrt (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)))) (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 (atan2 1.0 (fma N (+ N 1.0) 1)))) (+ (+ 1/2 1/2) 1) (+ (+ 1/2 (/ 1 2)) 1) (+ (+ (/ 1 2) 1/2) 1) (+ (+ (/ 1 2) (/ 1 2)) 1) (+ (* 2 1/2) 1) (+ (* 2 (/ 1 2)) 1) (+ (+ (log (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (log (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))))) (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (+ (log (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))))) (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (log (* (* (sqrt (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))))) (exp (* (* (sqrt (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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)))) (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (* (* (sqrt (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 (* (* (sqrt (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 (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)))) (sqrt (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 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (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 (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 (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) (* (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 (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)) 0.753 * * [simplify]: iteration 0 : 197 enodes (cost 608 ) 0.756 * * [simplify]: iteration 1 : 590 enodes (cost 481 ) 0.776 * * [simplify]: iteration 2 : 3838 enodes (cost 465 ) 0.930 * * [simplify]: iteration 3 : 5001 enodes (cost 465 ) 0.933 * [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 (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 (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))))) (log1p (* (* (sqrt (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))))) 2 2 1 1 1 1 2 2 1 1 1 1 2 1 1 2 1 1 (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 4) (atan2 1.0 (fma N (+ N 1.0) 1)) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 4) (atan2 1.0 (fma N (+ N 1.0) 1)) 2 2 2 2 2 2 (* 2 (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* 2 (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (* 2 (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (pow (exp 1) (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) (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) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 4) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (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))) (* (* (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))))) (* (fabs (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) (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 (sqrt (sqrt (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))) (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)) 0.933 * * * [progress]: adding candidates to table 1.114 * [progress]: [Phase 3 of 3] Extracting. 1.114 * * [regime]: Finding splitpoints for: (# # # # # #) 1.115 * * * [regime-changes]: Trying 2 branch expressions: ((- (atan (+ N 1.0)) (atan N)) N) 1.115 * * * * [regimes]: Trying to branch on (- (atan (+ N 1.0)) (atan N)) from (# # # # # #) 1.140 * * * * [regimes]: Trying to branch on N from (# # # # # #) 1.166 * * * [regime]: Found split indices: #