7.067 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.032 * * * [progress]: [2/2] Setting up program. 0.034 * [progress]: [Phase 2 of 3] Improving. 0.034 * [simplify]: Simplifying using # : (- (atan (+ N 1.0)) (atan N)) 0.037 * * [simplify]: iteration 0 : 9 enodes (cost 4 ) 0.038 * * [simplify]: iteration 1 : 10 enodes (cost 4 ) 0.039 * * [simplify]: iteration 2 : 10 enodes (cost 4 ) 0.039 * [simplify]: Simplified to: (- (atan (+ N 1.0)) (atan N)) 0.040 * * [progress]: iteration 1 / 4 0.040 * * * [progress]: picking best candidate 0.041 * * * * [pick]: Picked # 0.041 * * * [progress]: localizing error 0.048 * * * [progress]: generating rewritten candidates 0.048 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.052 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 0.054 * * * [progress]: generating series expansions 0.054 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.054 * [approximate]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in (N) around 0 0.054 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.054 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.054 * [taylor]: Taking taylor expansion of (atan N) in N 0.054 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.054 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.054 * [taylor]: Taking taylor expansion of (atan N) in N 0.058 * [approximate]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in (N) around 0 0.058 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.058 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.058 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.058 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.058 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.058 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.061 * [approximate]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in (N) around 0 0.061 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.061 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.061 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.061 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.061 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.061 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.064 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 0.064 * [approximate]: Taking taylor expansion of (atan (+ N 1.0)) in (N) around 0 0.064 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.064 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.065 * [approximate]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in (N) around 0 0.065 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.065 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.065 * [approximate]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in (N) around 0 0.065 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.065 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.065 * * * [progress]: simplifying candidates 0.066 * [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)) 0.070 * * [simplify]: iteration 0 : 129 enodes (cost 365 ) 0.073 * * [simplify]: iteration 1 : 345 enodes (cost 264 ) 0.081 * * [simplify]: iteration 2 : 1480 enodes (cost 254 ) 0.115 * * [simplify]: iteration 3 : 5001 enodes (cost 198 ) 0.117 * [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)) 0.117 * * * [progress]: adding candidates to table 0.176 * * [progress]: iteration 2 / 4 0.176 * * * [progress]: picking best candidate 0.180 * * * * [pick]: Picked # 0.180 * * * [progress]: localizing error 0.185 * * * [progress]: generating rewritten candidates 0.186 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.186 * * * [progress]: generating series expansions 0.186 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.187 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 0.187 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.187 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.187 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 0.187 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.187 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.188 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 0.188 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.188 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.188 * * * [progress]: simplifying candidates 0.188 * [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)) 0.191 * * [simplify]: iteration 0 : 21 enodes (cost 57 ) 0.193 * * [simplify]: iteration 1 : 32 enodes (cost 50 ) 0.194 * * [simplify]: iteration 2 : 55 enodes (cost 50 ) 0.196 * * [simplify]: iteration 3 : 70 enodes (cost 50 ) 0.197 * * [simplify]: iteration 4 : 89 enodes (cost 50 ) 0.199 * * [simplify]: iteration 5 : 143 enodes (cost 50 ) 0.205 * * [simplify]: iteration 6 : 567 enodes (cost 50 ) 0.221 * * [simplify]: iteration 7 : 1779 enodes (cost 50 ) 0.288 * * [simplify]: iteration 8 : 5001 enodes (cost 50 ) 0.289 * [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)) 0.289 * * * [progress]: adding candidates to table 0.310 * * [progress]: iteration 3 / 4 0.311 * * * [progress]: picking best candidate 0.316 * * * * [pick]: Picked # 0.316 * * * [progress]: localizing error 0.324 * * * [progress]: generating rewritten candidates 0.324 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.326 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 0.327 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 0.328 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 0.329 * * * [progress]: generating series expansions 0.329 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.330 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 0.330 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.330 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.330 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.330 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.334 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 0.334 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.334 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.334 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.334 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.338 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 0.338 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.338 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.338 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.338 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.342 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 0.342 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 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 0.342 * [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 0.346 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.346 * [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 0.350 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.350 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.353 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 0.353 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 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 (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.353 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 0.354 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.354 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.354 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 0.354 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.354 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.354 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 0.355 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 0.355 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.355 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.355 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 0.355 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.355 * [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 (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 0.356 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.356 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.356 * * * [progress]: simplifying candidates 0.357 * [simplify]: Simplifying using # : (expm1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt 1) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (/ 1 2) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (expm1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt 1) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (/ 1 2) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (expm1 (atan2 1.0 (fma N (+ N 1.0) 1))) (log1p (atan2 1.0 (fma N (+ N 1.0) 1))) (log (atan2 1.0 (fma N (+ N 1.0) 1))) (exp (atan2 1.0 (fma N (+ N 1.0) 1))) (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (* (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1))) (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (expm1 (atan2 1.0 (fma N (+ N 1.0) 1))) (log1p (atan2 1.0 (fma N (+ N 1.0) 1))) (log (atan2 1.0 (fma N (+ N 1.0) 1))) (exp (atan2 1.0 (fma N (+ N 1.0) 1))) (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (* (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1))) (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) 0.360 * * [simplify]: iteration 0 : 37 enodes (cost 296 ) 0.362 * * [simplify]: iteration 1 : 62 enodes (cost 276 ) 0.364 * * [simplify]: iteration 2 : 100 enodes (cost 276 ) 0.366 * * [simplify]: iteration 3 : 148 enodes (cost 276 ) 0.369 * * [simplify]: iteration 4 : 341 enodes (cost 276 ) 0.376 * * [simplify]: iteration 5 : 975 enodes (cost 276 ) 0.405 * * [simplify]: iteration 6 : 3911 enodes (cost 274 ) 0.532 * * [simplify]: iteration 7 : 5001 enodes (cost 274 ) 0.534 * [simplify]: Simplified to: (expm1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 3) (fabs (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2) 1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2 (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2) (expm1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 3) (fabs (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2) 1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2 (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2) (expm1 (atan2 1.0 (fma N (+ N 1.0) 1))) (log1p (atan2 1.0 (fma N (+ N 1.0) 1))) (log (atan2 1.0 (fma N (+ N 1.0) 1))) (exp (atan2 1.0 (fma N (+ N 1.0) 1))) (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (expm1 (atan2 1.0 (fma N (+ N 1.0) 1))) (log1p (atan2 1.0 (fma N (+ N 1.0) 1))) (log (atan2 1.0 (fma N (+ N 1.0) 1))) (exp (atan2 1.0 (fma N (+ N 1.0) 1))) (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) 0.534 * * * [progress]: adding candidates to table 0.637 * * [progress]: iteration 4 / 4 0.637 * * * [progress]: picking best candidate 0.646 * * * * [pick]: Picked # 0.646 * * * [progress]: localizing error 0.659 * * * [progress]: generating rewritten candidates 0.659 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 1) 0.660 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 1) 0.661 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.662 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2 1 1) 0.664 * * * [progress]: generating series expansions 0.664 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 1) 0.664 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) in (N) around 0 0.664 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) in N 0.664 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma N (+ N 1.0) 1))))) in N 0.664 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma N (+ N 1.0) 1)))) in N 0.664 * [taylor]: Taking taylor expansion of 1/3 in N 0.664 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.664 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.664 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) in N 0.664 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma N (+ N 1.0) 1))))) in N 0.664 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma N (+ N 1.0) 1)))) in N 0.664 * [taylor]: Taking taylor expansion of 1/3 in N 0.665 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.665 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.698 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/3) in (N) around 0 0.698 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/3) in N 0.698 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))))) in N 0.698 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)))) in N 0.698 * [taylor]: Taking taylor expansion of 1/3 in N 0.698 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.698 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.702 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/3) in N 0.702 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))))) in N 0.702 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)))) in N 0.702 * [taylor]: Taking taylor expansion of 1/3 in N 0.702 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.702 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.737 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/3) in (N) around 0 0.737 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/3) in N 0.737 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))))) in N 0.737 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)))) in N 0.737 * [taylor]: Taking taylor expansion of 1/3 in N 0.737 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.737 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.738 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/3) in N 0.738 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))))) in N 0.738 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)))) in N 0.738 * [taylor]: Taking taylor expansion of 1/3 in N 0.738 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.738 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.772 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 1) 0.772 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) in (N) around 0 0.772 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) in N 0.772 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma N (+ N 1.0) 1))))) in N 0.772 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma N (+ N 1.0) 1)))) in N 0.772 * [taylor]: Taking taylor expansion of 1/3 in N 0.772 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.772 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.773 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) in N 0.773 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma N (+ N 1.0) 1))))) in N 0.773 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma N (+ N 1.0) 1)))) in N 0.773 * [taylor]: Taking taylor expansion of 1/3 in N 0.773 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.773 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.808 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/3) in (N) around 0 0.808 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/3) in N 0.808 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))))) in N 0.808 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)))) in N 0.808 * [taylor]: Taking taylor expansion of 1/3 in N 0.808 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.808 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.808 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) 1/3) in N 0.808 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))))) in N 0.808 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)))) in N 0.808 * [taylor]: Taking taylor expansion of 1/3 in N 0.808 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.808 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.842 * [approximate]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/3) in (N) around 0 0.842 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/3) in N 0.842 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))))) in N 0.842 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)))) in N 0.842 * [taylor]: Taking taylor expansion of 1/3 in N 0.842 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.842 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.843 * [taylor]: Taking taylor expansion of (pow (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) 1/3) in N 0.843 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))))) in N 0.843 * [taylor]: Taking taylor expansion of (* 1/3 (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)))) in N 0.843 * [taylor]: Taking taylor expansion of 1/3 in N 0.843 * [taylor]: Taking taylor expansion of (log (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.843 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.881 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 0.881 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in (N) around 0 0.881 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.881 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.881 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) in N 0.881 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.884 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in (N) around 0 0.884 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.884 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.885 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1))) in N 0.885 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.888 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in (N) around 0 0.888 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.888 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.888 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1))) in N 0.888 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.892 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2 1 1) 0.892 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in (N) around 0 0.892 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.892 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma N (+ N 1.0) 1)) in N 0.892 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in (N) around 0 0.892 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.892 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ 1 N) (+ (/ 1 N) 1.0) 1)) in N 0.893 * [approximate]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in (N) around 0 0.893 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.893 * [taylor]: Taking taylor expansion of (atan2 1.0 (fma (/ -1 N) (- 1.0 (/ 1 N)) 1)) in N 0.893 * * * [progress]: simplifying candidates 0.894 * [simplify]: Simplifying using # : (expm1 (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt 1) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (expm1 (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt 1) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (expm1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt 1) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (/ 1 2) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (expm1 (atan2 1.0 (fma N (+ N 1.0) 1))) (log1p (atan2 1.0 (fma N (+ N 1.0) 1))) (log (atan2 1.0 (fma N (+ N 1.0) 1))) (exp (atan2 1.0 (fma N (+ N 1.0) 1))) (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (* (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1))) (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) 0.898 * * [simplify]: iteration 0 : 52 enodes (cost 352 ) 0.900 * * [simplify]: iteration 1 : 109 enodes (cost 319 ) 0.902 * * [simplify]: iteration 2 : 235 enodes (cost 315 ) 0.907 * * [simplify]: iteration 3 : 808 enodes (cost 315 ) 0.945 * * [simplify]: iteration 4 : 5002 enodes (cost 315 ) 0.947 * [simplify]: Simplified to: (expm1 (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt 1) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (* (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (atan2 1.0 (fma N (+ N 1.0) 1)) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (expm1 (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (* (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))) (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt 1) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (* (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (atan2 1.0 (fma N (+ N 1.0) 1)) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (expm1 (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log1p (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (log (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (exp (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (* (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (cbrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (pow (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 3) (fabs (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3)) (sqrt (cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt 1) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) 1/2 (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (expm1 (atan2 1.0 (fma N (+ N 1.0) 1))) (log1p (atan2 1.0 (fma N (+ N 1.0) 1))) (log (atan2 1.0 (fma N (+ N 1.0) 1))) (exp (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 2/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 3) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (pow (atan2 1.0 (fma N (+ N 1.0) 1)) 1/3) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) (atan2 1.0 (fma N (+ N 1.0) 1)) 0.948 * * * [progress]: adding candidates to table 1.099 * [progress]: [Phase 3 of 3] Extracting. 1.099 * * [regime]: Finding splitpoints for: (# # # # # # # #) 1.100 * * * [regime-changes]: Trying 1 branch expressions: (N) 1.100 * * * * [regimes]: Trying to branch on N from (# # # # # # # #) 1.129 * * * [regime]: Found split indices: #