19.228 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.027 * * * [progress]: [2/2] Setting up program. 0.030 * [progress]: [Phase 2 of 3] Improving. 0.030 * [simplify]: Simplifying using # : (- (atan (+ N 1.0)) (atan N)) 0.032 * * [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)) 0.034 * * [progress]: iteration 1 / 4 0.034 * * * [progress]: picking best candidate 0.037 * * * * [pick]: Picked # 0.037 * * * [progress]: localizing error 0.042 * * * [progress]: generating rewritten candidates 0.042 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.046 * * * [progress]: generating series expansions 0.046 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.046 * [approximate]: Approximating (- (atan (+ N 1.0)) (atan N)) in (N) around 0 0.050 * [approximate]: Approximating (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in (N) around 0 0.055 * [approximate]: Approximating (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in (N) around 0 0.059 * * * [progress]: simplifying candidates 0.059 * [simplify]: Simplifying using # : (- (+ 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)))) (neg (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)) (neg (atan N)) (- (atan (+ N 1.0)) (atan N)) (- (atan (+ N 1.0)) (atan N)) (- (atan (+ N 1.0)) (atan N)) 0.062 * * [simplify]: iteration 0 : 72 enodes (cost 123 ) 0.064 * * [simplify]: iteration 1 : 142 enodes (cost 114 ) 0.066 * * [simplify]: iteration 2 : 286 enodes (cost 112 ) 0.070 * * [simplify]: iteration 3 : 678 enodes (cost 111 ) 0.083 * * [simplify]: iteration 4 : 2444 enodes (cost 111 ) 0.131 * * [simplify]: iteration 5 : 5002 enodes (cost 111 ) 0.132 * [simplify]: Simplified to: 1.0 (+ 1 (* (+ N 1.0) N)) (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)) (+ (* (atan (+ N 1.0)) (+ (atan (+ N 1.0)) (atan N))) (* (atan N) (atan N))) (- 0 (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)) (- 0 (atan N)) (- (atan (+ N 1.0)) (atan N)) (- (atan (+ N 1.0)) (atan N)) (- (atan (+ N 1.0)) (atan N)) 0.132 * * * [progress]: adding candidates to table 0.159 * * [progress]: iteration 2 / 4 0.159 * * * [progress]: picking best candidate 0.161 * * * * [pick]: Picked # 0.161 * * * [progress]: localizing error 0.167 * * * [progress]: generating rewritten candidates 0.167 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.168 * * * [progress]: generating series expansions 0.168 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.168 * [approximate]: Approximating (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.168 * [approximate]: Approximating (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.169 * [approximate]: Approximating (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.170 * * * [progress]: simplifying candidates 0.170 * [simplify]: Simplifying using # : (log (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (exp (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (* (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.173 * * [simplify]: iteration 0 : 35 enodes (cost 65 ) 0.174 * * [simplify]: iteration 1 : 50 enodes (cost 53 ) 0.175 * * [simplify]: iteration 2 : 113 enodes (cost 53 ) 0.178 * * [simplify]: iteration 3 : 224 enodes (cost 53 ) 0.184 * * [simplify]: iteration 4 : 669 enodes (cost 53 ) 0.227 * * [simplify]: iteration 5 : 4281 enodes (cost 53 ) 0.482 * * [simplify]: iteration 6 : 5002 enodes (cost 53 ) 0.484 * [simplify]: Simplified to: (log (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (exp (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 3) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 0.484 * * * [progress]: adding candidates to table 0.496 * * [progress]: iteration 3 / 4 0.496 * * * [progress]: picking best candidate 0.505 * * * * [pick]: Picked # 0.505 * * * [progress]: localizing error 0.513 * * * [progress]: generating rewritten candidates 0.513 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.514 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 0.515 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 0.522 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 0.528 * * * [progress]: generating series expansions 0.528 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.528 * [approximate]: Approximating (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 0.533 * [approximate]: Approximating (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 0.538 * [approximate]: Approximating (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 0.543 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 0.544 * [approximate]: Approximating (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 0.548 * [approximate]: Approximating (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 0.554 * [approximate]: Approximating (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 0.559 * * * * [progress]: [ 3 / 4 ] generating series at (2) 0.559 * [approximate]: Approximating (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.560 * [approximate]: Approximating (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.561 * [approximate]: Approximating (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.561 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 0.561 * [approximate]: Approximating (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.562 * [approximate]: Approximating (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.563 * [approximate]: Approximating (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.563 * * * [progress]: simplifying candidates 0.565 * [simplify]: Simplifying using # : (log (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt 1) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (/ 1 2) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (log (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt 1) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (/ 1 2) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (+ 1/2 1/2) (+ 1/2 (/ 1 2)) (+ 1 1) (+ (/ 1 2) 1/2) (+ (/ 1 2) (/ 1 2)) (* (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (+ 1 1) (+ (log (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (log (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (log (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (exp (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (* (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (cbrt (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (cbrt (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (* (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt 1) (sqrt 1)) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* 1 1) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* 2 1/2) (* 2 1) (* 2 (/ 1 2)) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt 1)) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 1) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (log (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (exp (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (* (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.570 * * [simplify]: iteration 0 : 110 enodes (cost 649 ) 0.573 * * [simplify]: iteration 1 : 391 enodes (cost 565 ) 0.585 * * [simplify]: iteration 2 : 2248 enodes (cost 539 ) 0.668 * * [simplify]: iteration 3 : 5001 enodes (cost 520 ) 0.671 * [simplify]: Simplified to: (log (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (pow (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 3) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 1 (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 1/2 (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (log (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (pow (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 3) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 1 (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 1/2 (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 1 1 2 1 1 (pow (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 4) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (pow (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 4) 2 (log (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (log (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (exp (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 3) (pow (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 4) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 3) (pow (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 4) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (pow (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 4) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (pow (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 4) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 1 (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 1 (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 1 2 1 (pow (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 5) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (pow (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 3) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (pow (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 3) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (pow (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 4) (* (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (pow (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 3) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (pow (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 3) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (log (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (exp (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (pow (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 4) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 3) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 0.672 * * * [progress]: adding candidates to table 0.776 * * [progress]: iteration 4 / 4 0.776 * * * [progress]: picking best candidate 0.793 * * * * [pick]: Picked # 0.793 * * * [progress]: localizing error 0.806 * * * [progress]: generating rewritten candidates 0.806 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 1) 0.808 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 1) 0.809 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.810 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2) 0.817 * * * [progress]: generating series expansions 0.817 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 1) 0.818 * [approximate]: Approximating (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) in (N) around 0 0.865 * [approximate]: Approximating (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/3) in (N) around 0 0.908 * [approximate]: Approximating (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/3) in (N) around 0 0.956 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 1) 0.956 * [approximate]: Approximating (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) in (N) around 0 1.003 * [approximate]: Approximating (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/3) in (N) around 0 1.047 * [approximate]: Approximating (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/3) in (N) around 0 1.095 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 1.095 * [approximate]: Approximating (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 1.100 * [approximate]: Approximating (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 1.105 * [approximate]: Approximating (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 1.110 * * * * [progress]: [ 4 / 4 ] generating series at (2 2) 1.110 * [approximate]: Approximating (* (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/6) (fabs (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3))) in (N) around 0 1.165 * [approximate]: Approximating (* (fabs (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/3)) (pow (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1/6)) in (N) around 0 1.216 * [approximate]: Approximating (* (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/6) (fabs (pow (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1/3))) in (N) around 0 1.273 * * * [progress]: simplifying candidates 1.274 * [simplify]: Simplifying using # : (log (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt 1) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (log (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt 1) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (log (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt 1) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (/ 1 2) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (+ (log (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (log (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (log (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (exp (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (* (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (* (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (cbrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (cbrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))) (cbrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (* (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (sqrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (sqrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (cbrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt 1))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (* (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt 1)) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 1) (* (cbrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) (* (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/6) (fabs (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3))) (* (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/6) (fabs (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3))) (* (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/6) (fabs (pow (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1/3))) 1.279 * * [simplify]: iteration 0 : 137 enodes (cost 815 ) 1.281 * * [simplify]: iteration 1 : 390 enodes (cost 742 ) 1.289 * * [simplify]: iteration 2 : 1504 enodes (cost 732 ) 1.318 * * [simplify]: iteration 3 : 5002 enodes (cost 724 ) 1.322 * [simplify]: Simplified to: (log (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 1 (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (log (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 1 (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (atan2 1.0 (+ 1 (* (+ N 1.0) N))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (log (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (exp (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (pow (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 3) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 1 (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) 1/2 (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (log (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (log (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (exp (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (pow (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) 3) (* (cbrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (cbrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))) (cbrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (pow (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) 3) (sqrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (sqrt (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (cbrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (fabs (cbrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (* (cbrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (sqrt (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 1/6) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 1/6) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) (* (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 1/6) (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))) 1.322 * * * [progress]: adding candidates to table 1.487 * [progress]: [Phase 3 of 3] Extracting. 1.487 * * [regime]: Finding splitpoints for: (# # # # # # # #) 1.489 * * * [regime-changes]: Trying 1 branch expressions: (N) 1.489 * * * * [regimes]: Trying to branch on N from (# # # # # # # #) 1.539 * * * [regime]: Found split indices: #