6.480 * [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. 0.029 * [simplify]: Simplifying using # : (- (atan (+ N 1.0)) (atan N)) 0.031 * * [simplify]: iteration 0 : 9 enodes (cost 4 ) 0.032 * * [simplify]: iteration 1 : 10 enodes (cost 4 ) 0.034 * * [simplify]: iteration 2 : 10 enodes (cost 4 ) 0.034 * [simplify]: Simplified to: (- (atan (+ N 1.0)) (atan N)) 0.034 * * [progress]: iteration 1 / 4 0.034 * * * [progress]: picking best candidate 0.035 * * * * [pick]: Picked # 0.035 * * * [progress]: localizing error 0.042 * * * [progress]: generating rewritten candidates 0.042 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.045 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 0.046 * * * [progress]: generating series expansions 0.046 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.047 * [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 0.047 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.047 * [taylor]: Taking taylor expansion of (atan N) in N 0.050 * [approximate]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in (N) around 0 0.050 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.050 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.050 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.050 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.050 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.051 * [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 0.054 * [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 0.057 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 0.057 * [approximate]: Taking taylor expansion of (atan (+ N 1.0)) in (N) around 0 0.057 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.057 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.057 * [approximate]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in (N) around 0 0.057 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.057 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.058 * [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 0.058 * * * [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)) 0.063 * * [simplify]: iteration 0 : 129 enodes (cost 365 ) 0.066 * * [simplify]: iteration 1 : 345 enodes (cost 264 ) 0.073 * * [simplify]: iteration 2 : 1480 enodes (cost 254 ) 0.105 * * [simplify]: iteration 3 : 5001 enodes (cost 198 ) 0.107 * [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)) 0.107 * * * [progress]: adding candidates to table 0.177 * * [progress]: iteration 2 / 4 0.177 * * * [progress]: picking best candidate 0.179 * * * * [pick]: Picked # 0.179 * * * [progress]: localizing error 0.188 * * * [progress]: generating rewritten candidates 0.188 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.189 * * * [progress]: generating series expansions 0.189 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.189 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 0.189 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.189 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.189 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 0.189 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.189 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.190 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 0.190 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.190 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.190 * * * [progress]: simplifying candidates 0.191 * [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)) 0.193 * * [simplify]: iteration 0 : 21 enodes (cost 57 ) 0.195 * * [simplify]: iteration 1 : 32 enodes (cost 50 ) 0.196 * * [simplify]: iteration 2 : 55 enodes (cost 50 ) 0.198 * * [simplify]: iteration 3 : 70 enodes (cost 50 ) 0.199 * * [simplify]: iteration 4 : 89 enodes (cost 50 ) 0.201 * * [simplify]: iteration 5 : 143 enodes (cost 50 ) 0.206 * * [simplify]: iteration 6 : 567 enodes (cost 50 ) 0.221 * * [simplify]: iteration 7 : 1779 enodes (cost 50 ) 0.286 * * [simplify]: iteration 8 : 5001 enodes (cost 50 ) 0.287 * [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)) 0.287 * * * [progress]: adding candidates to table 0.309 * * [progress]: iteration 3 / 4 0.309 * * * [progress]: picking best candidate 0.312 * * * * [pick]: Picked # 0.312 * * * [progress]: localizing error 0.321 * * * [progress]: generating rewritten candidates 0.321 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.322 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 0.323 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 0.330 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 0.332 * * * [progress]: generating series expansions 0.332 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.333 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 0.333 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.333 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.333 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.333 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.336 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 0.336 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.336 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.337 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.337 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.344 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 0.344 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.344 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.344 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.344 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.348 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 0.348 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 0.348 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.348 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.348 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.348 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.351 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 0.351 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.351 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.352 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.352 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.355 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 0.355 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.355 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.355 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.355 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.359 * * * * [progress]: [ 3 / 4 ] generating series at (2) 0.359 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 0.359 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.359 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.359 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 0.359 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.359 * [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 (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 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 (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.360 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 0.361 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 0.361 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.361 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.361 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 0.361 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.361 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.361 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 0.361 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.362 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.362 * * * [progress]: simplifying candidates 0.363 * [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)) 0.369 * * [simplify]: iteration 0 : 100 enodes (cost 554 ) 0.371 * * [simplify]: iteration 1 : 375 enodes (cost 496 ) 0.382 * * [simplify]: iteration 2 : 2244 enodes (cost 476 ) 0.465 * * [simplify]: iteration 3 : 5001 enodes (cost 461 ) 0.468 * [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)) 0.468 * * * [progress]: adding candidates to table 0.629 * * [progress]: iteration 4 / 4 0.629 * * * [progress]: picking best candidate 0.635 * * * * [pick]: Picked # 0.635 * * * [progress]: localizing error 0.647 * * * [progress]: generating rewritten candidates 0.647 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.648 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 1) 0.648 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 1) 0.649 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.690 * * * [progress]: generating series expansions 0.690 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.690 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 0.690 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.690 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.690 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.690 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.694 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 0.694 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.694 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.694 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.694 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.698 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 0.698 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.698 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.698 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.698 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.701 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 1) 0.701 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 0.701 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.701 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.702 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.702 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.705 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 0.705 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.705 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.705 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.705 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.709 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 0.709 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.709 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.710 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.710 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.713 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 1) 0.713 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 0.713 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.713 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.713 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.713 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.717 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 0.717 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.717 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.717 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.717 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.721 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 0.721 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.721 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.721 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.721 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.724 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.725 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 0.725 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.725 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.725 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 0.725 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.725 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.726 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 0.726 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.726 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.726 * * * [progress]: simplifying candidates 0.728 * [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)) 0.735 * * [simplify]: iteration 0 : 197 enodes (cost 608 ) 0.739 * * [simplify]: iteration 1 : 590 enodes (cost 481 ) 0.758 * * [simplify]: iteration 2 : 3838 enodes (cost 465 ) 0.910 * * [simplify]: iteration 3 : 5001 enodes (cost 465 ) 0.913 * [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)) 0.914 * * * [progress]: adding candidates to table 1.098 * [progress]: [Phase 3 of 3] Extracting. 1.098 * * [regime]: Finding splitpoints for: (# # # # # #) 1.099 * * * [regime-changes]: Trying 1 branch expressions: (N) 1.099 * * * * [regimes]: Trying to branch on N from (# # # # # #) 1.121 * * * [regime]: Found split indices: #