29.051 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.047 * * * [progress]: [2/2] Setting up program. 0.049 * [progress]: [Phase 2 of 3] Improving. 0.050 * [simplify]: Simplifying: (- (atan (+ N 1.0)) (atan N)) 0.050 * [simplify]: Sending expressions to egg_math: (- (atan (+ h0 h1)) (atan h0)) 0.051 * * [progress]: iteration 1 / 4 0.051 * * * [progress]: picking best candidate 0.053 * * * * [pick]: Picked # 0.053 * * * [progress]: localizing error 0.060 * * * [progress]: generating rewritten candidates 0.060 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.067 * * * [progress]: generating series expansions 0.067 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.067 * [backup-simplify]: Simplify (- (atan (+ N 1.0)) (atan N)) into (- (atan (+ N 1.0)) (atan N)) 0.067 * [approximate]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in (N) around 0 0.067 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.067 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.067 * [backup-simplify]: Simplify (atan (+ N 1.0)) into (atan (+ N 1.0)) 0.067 * [taylor]: Taking taylor expansion of (atan N) in N 0.067 * [backup-simplify]: Simplify (atan N) into (atan N) 0.067 * [taylor]: Taking taylor expansion of (- (atan (+ N 1.0)) (atan N)) in N 0.067 * [taylor]: Taking taylor expansion of (atan (+ N 1.0)) in N 0.068 * [backup-simplify]: Simplify (atan (+ N 1.0)) into (atan (+ N 1.0)) 0.068 * [taylor]: Taking taylor expansion of (atan N) in N 0.068 * [backup-simplify]: Simplify (atan N) into (atan N) 0.068 * [backup-simplify]: Simplify (- (atan N)) into (- (atan N)) 0.068 * [backup-simplify]: Simplify (+ (atan (+ N 1.0)) (- (atan N))) into (- (atan (+ N 1.0)) (atan N)) 0.068 * [backup-simplify]: Simplify (- (atan (+ N 1.0)) (atan N)) into (- (atan (+ N 1.0)) (atan N)) 0.069 * [backup-simplify]: Simplify (- 0) into 0 0.069 * [backup-simplify]: Simplify (+ 0 0) into 0 0.069 * [backup-simplify]: Simplify 0 into 0 0.070 * [backup-simplify]: Simplify (- 0) into 0 0.070 * [backup-simplify]: Simplify (+ 0 0) into 0 0.070 * [backup-simplify]: Simplify 0 into 0 0.070 * [backup-simplify]: Simplify (- 0) into 0 0.070 * [backup-simplify]: Simplify (+ 0 0) into 0 0.070 * [backup-simplify]: Simplify 0 into 0 0.071 * [backup-simplify]: Simplify (- 0) into 0 0.071 * [backup-simplify]: Simplify (+ 0 0) into 0 0.071 * [backup-simplify]: Simplify 0 into 0 0.071 * [backup-simplify]: Simplify (- 0) into 0 0.071 * [backup-simplify]: Simplify (+ 0 0) into 0 0.071 * [backup-simplify]: Simplify 0 into 0 0.072 * [backup-simplify]: Simplify (- 0) into 0 0.072 * [backup-simplify]: Simplify (+ 0 0) into 0 0.072 * [backup-simplify]: Simplify 0 into 0 0.072 * [backup-simplify]: Simplify (- (atan (+ N 1.0)) (atan N)) into (- (atan (+ N 1.0)) (atan N)) 0.073 * [backup-simplify]: Simplify (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) into (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) 0.073 * [approximate]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in (N) around 0 0.073 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.073 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.073 * [backup-simplify]: Simplify (atan (+ (/ 1 N) 1.0)) into (atan (+ (/ 1 N) 1.0)) 0.073 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.073 * [backup-simplify]: Simplify (atan (/ 1 N)) into (atan (/ 1 N)) 0.073 * [taylor]: Taking taylor expansion of (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) in N 0.073 * [taylor]: Taking taylor expansion of (atan (+ (/ 1 N) 1.0)) in N 0.073 * [backup-simplify]: Simplify (atan (+ (/ 1 N) 1.0)) into (atan (+ (/ 1 N) 1.0)) 0.073 * [taylor]: Taking taylor expansion of (atan (/ 1 N)) in N 0.073 * [backup-simplify]: Simplify (atan (/ 1 N)) into (atan (/ 1 N)) 0.074 * [backup-simplify]: Simplify (- (atan (/ 1 N))) into (- (atan (/ 1 N))) 0.074 * [backup-simplify]: Simplify (+ (atan (+ (/ 1 N) 1.0)) (- (atan (/ 1 N)))) into (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) 0.074 * [backup-simplify]: Simplify (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) into (- (atan (+ (/ 1 N) 1.0)) (atan (/ 1 N))) 0.074 * [backup-simplify]: Simplify (- 0) into 0 0.075 * [backup-simplify]: Simplify (+ 0 0) into 0 0.075 * [backup-simplify]: Simplify 0 into 0 0.075 * [backup-simplify]: Simplify (- 0) into 0 0.076 * [backup-simplify]: Simplify (+ 0 0) into 0 0.076 * [backup-simplify]: Simplify 0 into 0 0.076 * [backup-simplify]: Simplify (- 0) into 0 0.077 * [backup-simplify]: Simplify (+ 0 0) into 0 0.077 * [backup-simplify]: Simplify 0 into 0 0.077 * [backup-simplify]: Simplify (- 0) into 0 0.078 * [backup-simplify]: Simplify (+ 0 0) into 0 0.078 * [backup-simplify]: Simplify 0 into 0 0.078 * [backup-simplify]: Simplify (- 0) into 0 0.078 * [backup-simplify]: Simplify (+ 0 0) into 0 0.078 * [backup-simplify]: Simplify 0 into 0 0.079 * [backup-simplify]: Simplify (- 0) into 0 0.079 * [backup-simplify]: Simplify (+ 0 0) into 0 0.079 * [backup-simplify]: Simplify 0 into 0 0.080 * [backup-simplify]: Simplify (- (atan (+ (/ 1 (/ 1 N)) 1.0)) (atan (/ 1 (/ 1 N)))) into (- (atan (+ N 1.0)) (atan N)) 0.080 * [backup-simplify]: Simplify (- (atan (+ (/ 1 (- N)) 1.0)) (atan (/ 1 (- N)))) into (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) 0.080 * [approximate]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in (N) around 0 0.080 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.080 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.080 * [backup-simplify]: Simplify (atan (- 1.0 (/ 1 N))) into (atan (- 1.0 (/ 1 N))) 0.080 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.081 * [backup-simplify]: Simplify (atan (/ -1 N)) into (atan (/ -1 N)) 0.081 * [taylor]: Taking taylor expansion of (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) in N 0.081 * [taylor]: Taking taylor expansion of (atan (- 1.0 (/ 1 N))) in N 0.081 * [backup-simplify]: Simplify (atan (- 1.0 (/ 1 N))) into (atan (- 1.0 (/ 1 N))) 0.081 * [taylor]: Taking taylor expansion of (atan (/ -1 N)) in N 0.081 * [backup-simplify]: Simplify (atan (/ -1 N)) into (atan (/ -1 N)) 0.081 * [backup-simplify]: Simplify (- (atan (/ -1 N))) into (- (atan (/ -1 N))) 0.081 * [backup-simplify]: Simplify (+ (atan (- 1.0 (/ 1 N))) (- (atan (/ -1 N)))) into (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) 0.082 * [backup-simplify]: Simplify (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) into (- (atan (- 1.0 (/ 1 N))) (atan (/ -1 N))) 0.082 * [backup-simplify]: Simplify (- 0) into 0 0.083 * [backup-simplify]: Simplify (+ 0 0) into 0 0.083 * [backup-simplify]: Simplify 0 into 0 0.083 * [backup-simplify]: Simplify (- 0) into 0 0.083 * [backup-simplify]: Simplify (+ 0 0) into 0 0.083 * [backup-simplify]: Simplify 0 into 0 0.084 * [backup-simplify]: Simplify (- 0) into 0 0.084 * [backup-simplify]: Simplify (+ 0 0) into 0 0.084 * [backup-simplify]: Simplify 0 into 0 0.085 * [backup-simplify]: Simplify (- 0) into 0 0.085 * [backup-simplify]: Simplify (+ 0 0) into 0 0.085 * [backup-simplify]: Simplify 0 into 0 0.086 * [backup-simplify]: Simplify (- 0) into 0 0.086 * [backup-simplify]: Simplify (+ 0 0) into 0 0.086 * [backup-simplify]: Simplify 0 into 0 0.086 * [backup-simplify]: Simplify (- 0) into 0 0.087 * [backup-simplify]: Simplify (+ 0 0) into 0 0.087 * [backup-simplify]: Simplify 0 into 0 0.087 * [backup-simplify]: Simplify (- (atan (- 1.0 (/ 1 (/ 1 (- N))))) (atan (/ -1 (/ 1 (- N))))) into (- (atan (+ N 1.0)) (atan N)) 0.087 * * * [progress]: simplifying candidates 0.088 * [simplify]: Simplifying: (- (+ 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)) (- (atan (+ N 1.0)) (atan N)) (- (atan (+ N 1.0)) (atan N)) (- (atan (+ N 1.0)) (atan N)) 0.089 * [simplify]: Sending expressions to egg_math: (- (+ h0 h1) h0) (+ 1 (* (+ h0 h1) h0)) (/ (exp (atan (+ h0 h1))) (exp (atan h0))) (log (- (atan (+ h0 h1)) (atan h0))) (exp (- (atan (+ h0 h1)) (atan h0))) (* (cbrt (- (atan (+ h0 h1)) (atan h0))) (cbrt (- (atan (+ h0 h1)) (atan h0)))) (cbrt (- (atan (+ h0 h1)) (atan h0))) (* (* (- (atan (+ h0 h1)) (atan h0)) (- (atan (+ h0 h1)) (atan h0))) (- (atan (+ h0 h1)) (atan h0))) (sqrt (- (atan (+ h0 h1)) (atan h0))) (sqrt (- (atan (+ h0 h1)) (atan h0))) (- (pow (atan (+ h0 h1)) 3) (pow (atan h0) 3)) (+ (* (atan (+ h0 h1)) (atan (+ h0 h1))) (+ (* (atan h0) (atan h0)) (* (atan (+ h0 h1)) (atan h0)))) (- (atan h0)) (- (* (atan (+ h0 h1)) (atan (+ h0 h1))) (* (atan h0) (atan h0))) (+ (atan (+ h0 h1)) (atan h0)) (+ (sqrt (atan (+ h0 h1))) (sqrt (atan h0))) (- (sqrt (atan (+ h0 h1))) (sqrt (atan h0))) (- (atan (+ h0 h1)) (atan h0)) (- (atan h0)) (- (atan (+ h0 h1)) (atan h0)) (- (atan (+ h0 h1)) (atan h0)) (- (atan (+ h0 h1)) (atan h0)) 0.148 * * * [progress]: adding candidates to table 0.224 * * [progress]: iteration 2 / 4 0.224 * * * [progress]: picking best candidate 0.227 * * * * [pick]: Picked # 0.227 * * * [progress]: localizing error 0.242 * * * [progress]: generating rewritten candidates 0.242 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.243 * * * * [progress]: [ 2 / 2 ] rewriting at (2 2 2) 0.293 * * * [progress]: generating series expansions 0.293 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.293 * [backup-simplify]: Simplify (atan2 1.0 (+ 1 (* (+ N 1.0) N))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.293 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.293 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.294 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.294 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.294 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.294 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.294 * [backup-simplify]: Simplify 0 into 0 0.294 * [backup-simplify]: Simplify 0 into 0 0.294 * [backup-simplify]: Simplify 0 into 0 0.294 * [backup-simplify]: Simplify 0 into 0 0.295 * [backup-simplify]: Simplify 0 into 0 0.295 * [backup-simplify]: Simplify 0 into 0 0.295 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.295 * [backup-simplify]: Simplify (atan2 1.0 (+ 1 (* (+ (/ 1 N) 1.0) (/ 1 N)))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.295 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.295 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.295 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.296 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.296 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.296 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.296 * [backup-simplify]: Simplify 0 into 0 0.296 * [backup-simplify]: Simplify 0 into 0 0.296 * [backup-simplify]: Simplify 0 into 0 0.296 * [backup-simplify]: Simplify 0 into 0 0.296 * [backup-simplify]: Simplify 0 into 0 0.296 * [backup-simplify]: Simplify 0 into 0 0.297 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 (/ 1 N))) (+ (/ 1 (pow (/ 1 N) 2)) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.297 * [backup-simplify]: Simplify (atan2 1.0 (+ 1 (* (+ (/ 1 (- N)) 1.0) (/ 1 (- N))))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.297 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.297 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.298 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.298 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.298 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.298 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.298 * [backup-simplify]: Simplify 0 into 0 0.298 * [backup-simplify]: Simplify 0 into 0 0.298 * [backup-simplify]: Simplify 0 into 0 0.298 * [backup-simplify]: Simplify 0 into 0 0.298 * [backup-simplify]: Simplify 0 into 0 0.299 * [backup-simplify]: Simplify 0 into 0 0.299 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow (/ 1 (- N)) 2)) 1) (* 1.0 (/ 1 (/ 1 (- N)))))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.299 * * * * [progress]: [ 2 / 2 ] generating series at (2 2 2) 0.299 * [backup-simplify]: Simplify (* (+ N 1.0) N) into (* N (+ N 1.0)) 0.299 * [approximate]: Taking taylor expansion of (* N (+ N 1.0)) in (N) around 0 0.299 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.299 * [taylor]: Taking taylor expansion of N in N 0.299 * [backup-simplify]: Simplify 0 into 0 0.299 * [backup-simplify]: Simplify 1 into 1 0.299 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.299 * [taylor]: Taking taylor expansion of N in N 0.299 * [backup-simplify]: Simplify 0 into 0 0.299 * [backup-simplify]: Simplify 1 into 1 0.299 * [taylor]: Taking taylor expansion of 1.0 in N 0.299 * [backup-simplify]: Simplify 1.0 into 1.0 0.299 * [taylor]: Taking taylor expansion of (* N (+ N 1.0)) in N 0.299 * [taylor]: Taking taylor expansion of N in N 0.299 * [backup-simplify]: Simplify 0 into 0 0.300 * [backup-simplify]: Simplify 1 into 1 0.300 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.300 * [taylor]: Taking taylor expansion of N in N 0.300 * [backup-simplify]: Simplify 0 into 0 0.300 * [backup-simplify]: Simplify 1 into 1 0.300 * [taylor]: Taking taylor expansion of 1.0 in N 0.300 * [backup-simplify]: Simplify 1.0 into 1.0 0.300 * [backup-simplify]: Simplify (+ 0 1.0) into 1.0 0.301 * [backup-simplify]: Simplify (* 0 1.0) into 0 0.301 * [backup-simplify]: Simplify 0 into 0 0.301 * [backup-simplify]: Simplify (+ 1 0) into 1 0.303 * [backup-simplify]: Simplify (+ (* 0 1) (* 1 1.0)) into 1.0 0.303 * [backup-simplify]: Simplify 1.0 into 1.0 0.303 * [backup-simplify]: Simplify (+ 0 0) into 0 0.304 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 1) (* 0 1.0))) into 1 0.304 * [backup-simplify]: Simplify 1 into 1 0.305 * [backup-simplify]: Simplify (+ 0 0) into 0 0.306 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 1) (* 0 1.0)))) into 0 0.306 * [backup-simplify]: Simplify 0 into 0 0.307 * [backup-simplify]: Simplify (+ 0 0) into 0 0.308 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 1) (* 0 1.0))))) into 0 0.308 * [backup-simplify]: Simplify 0 into 0 0.308 * [backup-simplify]: Simplify (+ 0 0) into 0 0.310 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 1.0)))))) into 0 0.310 * [backup-simplify]: Simplify 0 into 0 0.311 * [backup-simplify]: Simplify (+ 0 0) into 0 0.313 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 1.0))))))) into 0 0.313 * [backup-simplify]: Simplify 0 into 0 0.313 * [backup-simplify]: Simplify (+ 0 0) into 0 0.316 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 1.0)))))))) into 0 0.316 * [backup-simplify]: Simplify 0 into 0 0.317 * [backup-simplify]: Simplify (+ 0 0) into 0 0.319 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 1.0))))))))) into 0 0.319 * [backup-simplify]: Simplify 0 into 0 0.320 * [backup-simplify]: Simplify (+ (* 1 (pow N 2)) (* 1.0 N)) into (+ (pow N 2) (* 1.0 N)) 0.320 * [backup-simplify]: Simplify (* (+ (/ 1 N) 1.0) (/ 1 N)) into (/ (+ (/ 1 N) 1.0) N) 0.320 * [approximate]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in (N) around 0 0.320 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.320 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.320 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.320 * [taylor]: Taking taylor expansion of N in N 0.320 * [backup-simplify]: Simplify 0 into 0 0.320 * [backup-simplify]: Simplify 1 into 1 0.321 * [backup-simplify]: Simplify (/ 1 1) into 1 0.321 * [taylor]: Taking taylor expansion of 1.0 in N 0.321 * [backup-simplify]: Simplify 1.0 into 1.0 0.321 * [taylor]: Taking taylor expansion of N in N 0.321 * [backup-simplify]: Simplify 0 into 0 0.321 * [backup-simplify]: Simplify 1 into 1 0.321 * [backup-simplify]: Simplify (+ 1 0) into 1 0.322 * [backup-simplify]: Simplify (/ 1 1) into 1 0.322 * [taylor]: Taking taylor expansion of (/ (+ (/ 1 N) 1.0) N) in N 0.322 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.322 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.322 * [taylor]: Taking taylor expansion of N in N 0.322 * [backup-simplify]: Simplify 0 into 0 0.322 * [backup-simplify]: Simplify 1 into 1 0.322 * [backup-simplify]: Simplify (/ 1 1) into 1 0.322 * [taylor]: Taking taylor expansion of 1.0 in N 0.322 * [backup-simplify]: Simplify 1.0 into 1.0 0.322 * [taylor]: Taking taylor expansion of N in N 0.322 * [backup-simplify]: Simplify 0 into 0 0.322 * [backup-simplify]: Simplify 1 into 1 0.323 * [backup-simplify]: Simplify (+ 1 0) into 1 0.323 * [backup-simplify]: Simplify (/ 1 1) into 1 0.323 * [backup-simplify]: Simplify 1 into 1 0.324 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.324 * [backup-simplify]: Simplify (+ 0 1.0) into 1.0 0.325 * [backup-simplify]: Simplify (- (/ 1.0 1) (+ (* 1 (/ 0 1)))) into 1.0 0.325 * [backup-simplify]: Simplify 1.0 into 1.0 0.326 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.326 * [backup-simplify]: Simplify (+ 0 0) into 0 0.327 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 1 (/ 0 1)) (* 1.0 (/ 0 1)))) into 0 0.327 * [backup-simplify]: Simplify 0 into 0 0.327 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.328 * [backup-simplify]: Simplify (+ 0 0) into 0 0.328 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 1 (/ 0 1)) (* 1.0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.328 * [backup-simplify]: Simplify 0 into 0 0.329 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.329 * [backup-simplify]: Simplify (+ 0 0) into 0 0.330 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 1 (/ 0 1)) (* 1.0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.330 * [backup-simplify]: Simplify 0 into 0 0.330 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.330 * [backup-simplify]: Simplify (+ 0 0) into 0 0.331 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 1 (/ 0 1)) (* 1.0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.331 * [backup-simplify]: Simplify 0 into 0 0.332 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.332 * [backup-simplify]: Simplify (+ 0 0) into 0 0.333 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 1 (/ 0 1)) (* 1.0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.333 * [backup-simplify]: Simplify 0 into 0 0.333 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.333 * [backup-simplify]: Simplify (+ 0 0) into 0 0.334 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 1 (/ 0 1)) (* 1.0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.334 * [backup-simplify]: Simplify 0 into 0 0.334 * [backup-simplify]: Simplify (+ (* 1.0 (/ 1 (/ 1 N))) (* 1 (pow (/ 1 (/ 1 N)) 2))) into (+ (pow N 2) (* 1.0 N)) 0.335 * [backup-simplify]: Simplify (* (+ (/ 1 (- N)) 1.0) (/ 1 (- N))) into (* -1 (/ (- 1.0 (/ 1 N)) N)) 0.335 * [approximate]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in (N) around 0 0.335 * [taylor]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in N 0.335 * [taylor]: Taking taylor expansion of -1 in N 0.335 * [backup-simplify]: Simplify -1 into -1 0.335 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.335 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.335 * [taylor]: Taking taylor expansion of 1.0 in N 0.335 * [backup-simplify]: Simplify 1.0 into 1.0 0.335 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.335 * [taylor]: Taking taylor expansion of N in N 0.335 * [backup-simplify]: Simplify 0 into 0 0.335 * [backup-simplify]: Simplify 1 into 1 0.335 * [backup-simplify]: Simplify (/ 1 1) into 1 0.335 * [taylor]: Taking taylor expansion of N in N 0.335 * [backup-simplify]: Simplify 0 into 0 0.335 * [backup-simplify]: Simplify 1 into 1 0.335 * [backup-simplify]: Simplify (- 1) into -1 0.336 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.336 * [backup-simplify]: Simplify (/ -1 1) into -1 0.336 * [taylor]: Taking taylor expansion of (* -1 (/ (- 1.0 (/ 1 N)) N)) in N 0.336 * [taylor]: Taking taylor expansion of -1 in N 0.336 * [backup-simplify]: Simplify -1 into -1 0.336 * [taylor]: Taking taylor expansion of (/ (- 1.0 (/ 1 N)) N) in N 0.336 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.336 * [taylor]: Taking taylor expansion of 1.0 in N 0.336 * [backup-simplify]: Simplify 1.0 into 1.0 0.336 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.336 * [taylor]: Taking taylor expansion of N in N 0.336 * [backup-simplify]: Simplify 0 into 0 0.336 * [backup-simplify]: Simplify 1 into 1 0.336 * [backup-simplify]: Simplify (/ 1 1) into 1 0.336 * [taylor]: Taking taylor expansion of N in N 0.336 * [backup-simplify]: Simplify 0 into 0 0.336 * [backup-simplify]: Simplify 1 into 1 0.337 * [backup-simplify]: Simplify (- 1) into -1 0.337 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.337 * [backup-simplify]: Simplify (/ -1 1) into -1 0.337 * [backup-simplify]: Simplify (* -1 -1) into 1 0.337 * [backup-simplify]: Simplify 1 into 1 0.338 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.338 * [backup-simplify]: Simplify (- 0) into 0 0.338 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.340 * [backup-simplify]: Simplify (- (/ 1.0 1) (+ (* -1 (/ 0 1)))) into 1.0 0.341 * [backup-simplify]: Simplify (+ (* -1 1.0) (* 0 -1)) into (- 1.0) 0.341 * [backup-simplify]: Simplify (- 1.0) into (- 1.0) 0.342 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.342 * [backup-simplify]: Simplify (- 0) into 0 0.342 * [backup-simplify]: Simplify (+ 0 0) into 0 0.343 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 1.0 (/ 0 1)))) into 0 0.344 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 1.0) (* 0 -1))) into 0 0.344 * [backup-simplify]: Simplify 0 into 0 0.344 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.344 * [backup-simplify]: Simplify (- 0) into 0 0.345 * [backup-simplify]: Simplify (+ 0 0) into 0 0.345 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 1.0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.346 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 1.0) (* 0 -1)))) into 0 0.346 * [backup-simplify]: Simplify 0 into 0 0.347 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.347 * [backup-simplify]: Simplify (- 0) into 0 0.347 * [backup-simplify]: Simplify (+ 0 0) into 0 0.348 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 1.0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.349 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1.0) (* 0 -1))))) into 0 0.349 * [backup-simplify]: Simplify 0 into 0 0.349 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.349 * [backup-simplify]: Simplify (- 0) into 0 0.350 * [backup-simplify]: Simplify (+ 0 0) into 0 0.350 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 1.0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.351 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1.0) (* 0 -1)))))) into 0 0.351 * [backup-simplify]: Simplify 0 into 0 0.352 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.352 * [backup-simplify]: Simplify (- 0) into 0 0.353 * [backup-simplify]: Simplify (+ 0 0) into 0 0.354 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 1.0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.356 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1.0) (* 0 -1))))))) into 0 0.356 * [backup-simplify]: Simplify 0 into 0 0.357 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.357 * [backup-simplify]: Simplify (- 0) into 0 0.358 * [backup-simplify]: Simplify (+ 0 0) into 0 0.359 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 1.0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.361 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1.0) (* 0 -1)))))))) into 0 0.361 * [backup-simplify]: Simplify 0 into 0 0.362 * [backup-simplify]: Simplify (+ (* (- 1.0) (/ 1 (/ 1 (- N)))) (* 1 (pow (/ 1 (/ 1 (- N))) 2))) into (+ (pow N 2) (* 1.0 N)) 0.362 * * * [progress]: simplifying candidates 0.363 * [simplify]: Simplifying: (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)))) (* (+ N 1.0) N) (+ (log (+ N 1.0)) (log N)) (log (* (+ N 1.0) N)) (exp (* (+ N 1.0) N)) (* (* (* (+ N 1.0) (+ N 1.0)) (+ N 1.0)) (* (* N N) N)) (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)) (* (* (* (+ N 1.0) N) (* (+ N 1.0) N)) (* (+ N 1.0) N)) (sqrt (* (+ N 1.0) N)) (sqrt (* (+ N 1.0) N)) (* (sqrt (+ N 1.0)) (sqrt N)) (* (sqrt (+ N 1.0)) (sqrt N)) (* (+ N 1.0) (* (cbrt N) (cbrt N))) (* (+ N 1.0) (sqrt N)) (* (+ N 1.0) 1) (* (cbrt (+ N 1.0)) N) (* (sqrt (+ N 1.0)) N) (* (+ N 1.0) N) (* (+ N 1.0) N) (* (+ (pow N 3) (pow 1.0 3)) N) (* (- (* N N) (* 1.0 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))) (+ (pow N 2) (* 1.0 N)) (+ (pow N 2) (* 1.0 N)) (+ (pow N 2) (* 1.0 N)) 0.363 * [simplify]: Sending expressions to egg_math: (log (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (exp (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (* (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (* (* (atan2 h1 (+ 1 (* (+ h0 h1) h0))) (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (* (+ h0 h1) h0) (+ (log (+ h0 h1)) (log h0)) (log (* (+ h0 h1) h0)) (exp (* (+ h0 h1) h0)) (* (* (* (+ h0 h1) (+ h0 h1)) (+ h0 h1)) (* (* h0 h0) h0)) (* (cbrt (* (+ h0 h1) h0)) (cbrt (* (+ h0 h1) h0))) (cbrt (* (+ h0 h1) h0)) (* (* (* (+ h0 h1) h0) (* (+ h0 h1) h0)) (* (+ h0 h1) h0)) (sqrt (* (+ h0 h1) h0)) (sqrt (* (+ h0 h1) h0)) (* (sqrt (+ h0 h1)) (sqrt h0)) (* (sqrt (+ h0 h1)) (sqrt h0)) (* (+ h0 h1) (* (cbrt h0) (cbrt h0))) (* (+ h0 h1) (sqrt h0)) (* (+ h0 h1) 1) (* (cbrt (+ h0 h1)) h0) (* (sqrt (+ h0 h1)) h0) (* (+ h0 h1) h0) (* (+ h0 h1) h0) (* (+ (pow h0 3) (pow h1 3)) h0) (* (- (* h0 h0) (* h1 h1)) h0) (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1))) (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1))) (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1))) (+ (pow h0 2) (* h1 h0)) (+ (pow h0 2) (* h1 h0)) (+ (pow h0 2) (* h1 h0)) 0.419 * * * [progress]: adding candidates to table 0.505 * * [progress]: iteration 3 / 4 0.505 * * * [progress]: picking best candidate 0.509 * * * * [pick]: Picked # 0.509 * * * [progress]: localizing error 0.532 * * * [progress]: generating rewritten candidates 0.532 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.534 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 0.537 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 0.537 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 0.539 * * * [progress]: generating series expansions 0.539 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.539 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.539 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 0.539 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.539 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.540 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.540 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.540 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.540 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.540 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.541 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.541 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.541 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.542 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.542 * [backup-simplify]: Simplify 0 into 0 0.549 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.549 * [backup-simplify]: Simplify 0 into 0 0.551 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.551 * [backup-simplify]: Simplify 0 into 0 0.552 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.552 * [backup-simplify]: Simplify 0 into 0 0.553 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.553 * [backup-simplify]: Simplify 0 into 0 0.555 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.555 * [backup-simplify]: Simplify 0 into 0 0.555 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.555 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ 1 (* (+ (/ 1 N) 1.0) (/ 1 N))))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 0.555 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 0.555 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.556 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.556 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.556 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 0.557 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.557 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.557 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.557 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.558 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 0.558 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.559 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 0.559 * [backup-simplify]: Simplify 0 into 0 0.560 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.560 * [backup-simplify]: Simplify 0 into 0 0.561 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.561 * [backup-simplify]: Simplify 0 into 0 0.562 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.563 * [backup-simplify]: Simplify 0 into 0 0.564 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.564 * [backup-simplify]: Simplify 0 into 0 0.565 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.565 * [backup-simplify]: Simplify 0 into 0 0.566 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 (/ 1 N))) (+ (/ 1 (pow (/ 1 N) 2)) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.566 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ 1 (* (+ (/ 1 (- N)) 1.0) (/ 1 (- N)))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 0.566 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 0.566 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.566 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.567 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.567 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 0.567 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.567 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.567 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.568 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.568 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 0.569 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.569 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 0.569 * [backup-simplify]: Simplify 0 into 0 0.570 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.570 * [backup-simplify]: Simplify 0 into 0 0.571 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.571 * [backup-simplify]: Simplify 0 into 0 0.573 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.573 * [backup-simplify]: Simplify 0 into 0 0.574 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.574 * [backup-simplify]: Simplify 0 into 0 0.576 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.576 * [backup-simplify]: Simplify 0 into 0 0.576 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow (/ 1 (- N)) 2)) 1) (* 1.0 (/ 1 (/ 1 (- N))))))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.576 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 0.576 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.577 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 0.577 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.577 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.577 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.577 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.578 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.578 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.578 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.578 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.578 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.578 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.579 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.579 * [backup-simplify]: Simplify 0 into 0 0.580 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.580 * [backup-simplify]: Simplify 0 into 0 0.581 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.581 * [backup-simplify]: Simplify 0 into 0 0.583 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.583 * [backup-simplify]: Simplify 0 into 0 0.584 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.584 * [backup-simplify]: Simplify 0 into 0 0.585 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.585 * [backup-simplify]: Simplify 0 into 0 0.585 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.586 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ 1 (* (+ (/ 1 N) 1.0) (/ 1 N))))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 0.586 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 0.586 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.586 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.586 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.587 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 0.587 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.587 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.587 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.587 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.588 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 0.589 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.589 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 0.589 * [backup-simplify]: Simplify 0 into 0 0.590 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.590 * [backup-simplify]: Simplify 0 into 0 0.592 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.592 * [backup-simplify]: Simplify 0 into 0 0.593 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.593 * [backup-simplify]: Simplify 0 into 0 0.594 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.594 * [backup-simplify]: Simplify 0 into 0 0.596 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.596 * [backup-simplify]: Simplify 0 into 0 0.596 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 (/ 1 N))) (+ (/ 1 (pow (/ 1 N) 2)) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.596 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ 1 (* (+ (/ 1 (- N)) 1.0) (/ 1 (- N)))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 0.597 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 0.597 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.597 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.597 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.597 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 0.598 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.598 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.598 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.598 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.598 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 0.599 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.599 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 0.599 * [backup-simplify]: Simplify 0 into 0 0.601 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.601 * [backup-simplify]: Simplify 0 into 0 0.602 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.602 * [backup-simplify]: Simplify 0 into 0 0.603 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.603 * [backup-simplify]: Simplify 0 into 0 0.604 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.604 * [backup-simplify]: Simplify 0 into 0 0.606 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.606 * [backup-simplify]: Simplify 0 into 0 0.606 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow (/ 1 (- N)) 2)) 1) (* 1.0 (/ 1 (/ 1 (- N))))))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.606 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 0.606 * [backup-simplify]: Simplify (atan2 1.0 (+ 1 (* (+ N 1.0) N))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.606 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.607 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.607 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.607 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.607 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.607 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.608 * [backup-simplify]: Simplify 0 into 0 0.608 * [backup-simplify]: Simplify 0 into 0 0.608 * [backup-simplify]: Simplify 0 into 0 0.608 * [backup-simplify]: Simplify 0 into 0 0.608 * [backup-simplify]: Simplify 0 into 0 0.608 * [backup-simplify]: Simplify 0 into 0 0.608 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.608 * [backup-simplify]: Simplify (atan2 1.0 (+ 1 (* (+ (/ 1 N) 1.0) (/ 1 N)))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.608 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.608 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.609 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.609 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.609 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.609 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.610 * [backup-simplify]: Simplify 0 into 0 0.610 * [backup-simplify]: Simplify 0 into 0 0.610 * [backup-simplify]: Simplify 0 into 0 0.610 * [backup-simplify]: Simplify 0 into 0 0.610 * [backup-simplify]: Simplify 0 into 0 0.610 * [backup-simplify]: Simplify 0 into 0 0.610 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 (/ 1 N))) (+ (/ 1 (pow (/ 1 N) 2)) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.610 * [backup-simplify]: Simplify (atan2 1.0 (+ 1 (* (+ (/ 1 (- N)) 1.0) (/ 1 (- N))))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.611 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.611 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.611 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.611 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.611 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.612 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.612 * [backup-simplify]: Simplify 0 into 0 0.612 * [backup-simplify]: Simplify 0 into 0 0.612 * [backup-simplify]: Simplify 0 into 0 0.612 * [backup-simplify]: Simplify 0 into 0 0.612 * [backup-simplify]: Simplify 0 into 0 0.612 * [backup-simplify]: Simplify 0 into 0 0.612 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow (/ 1 (- N)) 2)) 1) (* 1.0 (/ 1 (/ 1 (- N)))))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.612 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 0.613 * [backup-simplify]: Simplify (atan2 1.0 (+ 1 (* (+ N 1.0) N))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.613 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 0.613 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.613 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.613 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.613 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.614 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.614 * [backup-simplify]: Simplify 0 into 0 0.614 * [backup-simplify]: Simplify 0 into 0 0.614 * [backup-simplify]: Simplify 0 into 0 0.614 * [backup-simplify]: Simplify 0 into 0 0.614 * [backup-simplify]: Simplify 0 into 0 0.614 * [backup-simplify]: Simplify 0 into 0 0.614 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.614 * [backup-simplify]: Simplify (atan2 1.0 (+ 1 (* (+ (/ 1 N) 1.0) (/ 1 N)))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.615 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 0.615 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.615 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.615 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.615 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.616 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.616 * [backup-simplify]: Simplify 0 into 0 0.616 * [backup-simplify]: Simplify 0 into 0 0.616 * [backup-simplify]: Simplify 0 into 0 0.616 * [backup-simplify]: Simplify 0 into 0 0.616 * [backup-simplify]: Simplify 0 into 0 0.616 * [backup-simplify]: Simplify 0 into 0 0.616 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 (/ 1 N))) (+ (/ 1 (pow (/ 1 N) 2)) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.617 * [backup-simplify]: Simplify (atan2 1.0 (+ 1 (* (+ (/ 1 (- N)) 1.0) (/ 1 (- N))))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.617 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 0.617 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.617 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.617 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.618 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.618 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.618 * [backup-simplify]: Simplify 0 into 0 0.618 * [backup-simplify]: Simplify 0 into 0 0.618 * [backup-simplify]: Simplify 0 into 0 0.618 * [backup-simplify]: Simplify 0 into 0 0.618 * [backup-simplify]: Simplify 0 into 0 0.618 * [backup-simplify]: Simplify 0 into 0 0.619 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow (/ 1 (- N)) 2)) 1) (* 1.0 (/ 1 (/ 1 (- N)))))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.619 * * * [progress]: simplifying candidates 0.620 * [simplify]: Simplifying: (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))))) (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)))) (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))) 0.621 * [simplify]: Sending expressions to egg_math: (log (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (exp (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (* (cbrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (cbrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))))) (cbrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (* (* (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (* (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))))) (sqrt (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt 1) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (/ 1 2) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (log (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (exp (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (* (cbrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (cbrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))))) (cbrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (* (* (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (* (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))))) (sqrt (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt 1) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (/ 1 2) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (log (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (exp (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (* (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (* (* (atan2 h1 (+ 1 (* (+ h0 h1) h0))) (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (log (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (exp (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (* (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (* (* (atan2 h1 (+ 1 (* (+ h0 h1) h0))) (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (sqrt (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1)))) (sqrt (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1)))) (sqrt (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1)))) (sqrt (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1)))) (sqrt (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1)))) (sqrt (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1)))) (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1))) (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1))) (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1))) (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1))) (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1))) (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1))) 0.704 * * * [progress]: adding candidates to table 0.919 * * [progress]: iteration 4 / 4 0.919 * * * [progress]: picking best candidate 0.933 * * * * [pick]: Picked # 0.933 * * * [progress]: localizing error 0.964 * * * [progress]: generating rewritten candidates 0.964 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.965 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 1) 0.967 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 1) 0.968 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 0.969 * * * [progress]: generating series expansions 0.969 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.969 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.969 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 0.969 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.969 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.969 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.970 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.970 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.970 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.970 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.970 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.970 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.970 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.971 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.971 * [backup-simplify]: Simplify 0 into 0 0.971 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.972 * [backup-simplify]: Simplify 0 into 0 0.973 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.973 * [backup-simplify]: Simplify 0 into 0 0.973 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.973 * [backup-simplify]: Simplify 0 into 0 0.974 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.974 * [backup-simplify]: Simplify 0 into 0 0.975 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.975 * [backup-simplify]: Simplify 0 into 0 0.975 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.975 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ 1 (* (+ (/ 1 N) 1.0) (/ 1 N))))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 0.975 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 0.975 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.975 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.975 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.976 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 0.976 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.976 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.976 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.976 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.976 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 0.977 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.977 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 0.977 * [backup-simplify]: Simplify 0 into 0 0.978 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.978 * [backup-simplify]: Simplify 0 into 0 0.978 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.978 * [backup-simplify]: Simplify 0 into 0 0.979 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.979 * [backup-simplify]: Simplify 0 into 0 0.980 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.980 * [backup-simplify]: Simplify 0 into 0 0.981 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.981 * [backup-simplify]: Simplify 0 into 0 0.981 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 (/ 1 N))) (+ (/ 1 (pow (/ 1 N) 2)) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.981 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ 1 (* (+ (/ 1 (- N)) 1.0) (/ 1 (- N)))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 0.981 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 0.981 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.981 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.981 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.982 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 0.982 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.982 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 0.982 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 0.982 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 0.982 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 0.982 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.983 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 0.983 * [backup-simplify]: Simplify 0 into 0 0.983 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.983 * [backup-simplify]: Simplify 0 into 0 0.984 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.984 * [backup-simplify]: Simplify 0 into 0 0.986 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.986 * [backup-simplify]: Simplify 0 into 0 0.987 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.987 * [backup-simplify]: Simplify 0 into 0 0.988 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 0.988 * [backup-simplify]: Simplify 0 into 0 0.989 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow (/ 1 (- N)) 2)) 1) (* 1.0 (/ 1 (/ 1 (- N))))))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.989 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 1) 0.989 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.989 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 0.989 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.989 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.989 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.990 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.990 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.990 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 0.990 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 0.990 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 0.991 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.991 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.991 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.991 * [backup-simplify]: Simplify 0 into 0 0.992 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.993 * [backup-simplify]: Simplify 0 into 0 0.994 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.994 * [backup-simplify]: Simplify 0 into 0 0.995 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.995 * [backup-simplify]: Simplify 0 into 0 0.996 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.996 * [backup-simplify]: Simplify 0 into 0 0.997 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 0.997 * [backup-simplify]: Simplify 0 into 0 0.998 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 0.998 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ 1 (* (+ (/ 1 N) 1.0) (/ 1 N))))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 0.998 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 0.998 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.998 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 0.998 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 0.999 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 0.999 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 0.999 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 0.999 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 1.000 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1.000 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 1.001 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 1.001 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 1.001 * [backup-simplify]: Simplify 0 into 0 1.002 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 1.002 * [backup-simplify]: Simplify 0 into 0 1.003 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 1.004 * [backup-simplify]: Simplify 0 into 0 1.005 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 1.005 * [backup-simplify]: Simplify 0 into 0 1.006 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 1.007 * [backup-simplify]: Simplify 0 into 0 1.008 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 1.008 * [backup-simplify]: Simplify 0 into 0 1.008 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 (/ 1 N))) (+ (/ 1 (pow (/ 1 N) 2)) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 1.009 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ 1 (* (+ (/ 1 (- N)) 1.0) (/ 1 (- N)))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 1.009 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 1.009 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 1.009 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 1.009 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1.010 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 1.010 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 1.010 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 1.010 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 1.011 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1.011 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 1.011 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 1.012 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 1.012 * [backup-simplify]: Simplify 0 into 0 1.013 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 1.013 * [backup-simplify]: Simplify 0 into 0 1.014 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 1.014 * [backup-simplify]: Simplify 0 into 0 1.016 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 1.016 * [backup-simplify]: Simplify 0 into 0 1.017 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 1.017 * [backup-simplify]: Simplify 0 into 0 1.018 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 1.019 * [backup-simplify]: Simplify 0 into 0 1.019 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow (/ 1 (- N)) 2)) 1) (* 1.0 (/ 1 (/ 1 (- N))))))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 1.019 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 1) 1.019 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 1.019 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in (N) around 0 1.019 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 1.019 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 1.020 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1.020 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 1.020 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 1.020 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) in N 1.020 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 1.021 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1.021 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 1.021 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 1.022 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 1.022 * [backup-simplify]: Simplify 0 into 0 1.023 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 1.023 * [backup-simplify]: Simplify 0 into 0 1.024 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 1.024 * [backup-simplify]: Simplify 0 into 0 1.026 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 1.026 * [backup-simplify]: Simplify 0 into 0 1.027 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 1.027 * [backup-simplify]: Simplify 0 into 0 1.028 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))))) into 0 1.028 * [backup-simplify]: Simplify 0 into 0 1.028 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 1.029 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ 1 (* (+ (/ 1 N) 1.0) (/ 1 N))))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 1.029 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in (N) around 0 1.029 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 1.029 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 1.029 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1.029 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 1.030 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 1.030 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) in N 1.030 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 1.030 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1.030 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 1.031 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 1.031 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) into (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))) 1.031 * [backup-simplify]: Simplify 0 into 0 1.040 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 1.041 * [backup-simplify]: Simplify 0 into 0 1.042 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 1.042 * [backup-simplify]: Simplify 0 into 0 1.044 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 1.044 * [backup-simplify]: Simplify 0 into 0 1.045 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 1.045 * [backup-simplify]: Simplify 0 into 0 1.046 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1)))))) into 0 1.046 * [backup-simplify]: Simplify 0 into 0 1.047 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ (* 1.0 (/ 1 (/ 1 N))) (+ (/ 1 (pow (/ 1 N) 2)) 1)))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 1.047 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (+ 1 (* (+ (/ 1 (- N)) 1.0) (/ 1 (- N)))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 1.047 * [approximate]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in (N) around 0 1.047 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 1.047 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 1.048 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1.048 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 1.048 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 1.049 * [taylor]: Taking taylor expansion of (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) in N 1.049 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 1.049 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1.049 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 1.050 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 1.050 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) into (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))) 1.050 * [backup-simplify]: Simplify 0 into 0 1.051 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 1.051 * [backup-simplify]: Simplify 0 into 0 1.053 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 1.053 * [backup-simplify]: Simplify 0 into 0 1.054 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 1.054 * [backup-simplify]: Simplify 0 into 0 1.055 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 1.055 * [backup-simplify]: Simplify 0 into 0 1.057 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+ (* 2 (* 0 0)) (* 2 (* 0 0)))) (* 2 (sqrt (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N))))))) into 0 1.057 * [backup-simplify]: Simplify 0 into 0 1.057 * [backup-simplify]: Simplify (sqrt (atan2 1.0 (- (+ (/ 1 (pow (/ 1 (- N)) 2)) 1) (* 1.0 (/ 1 (/ 1 (- N))))))) into (sqrt (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))) 1.057 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 1.058 * [backup-simplify]: Simplify (atan2 1.0 (+ 1 (* (+ N 1.0) N))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1.058 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in (N) around 0 1.058 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 1.058 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1.058 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) in N 1.058 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1.058 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1.059 * [backup-simplify]: Simplify 0 into 0 1.059 * [backup-simplify]: Simplify 0 into 0 1.059 * [backup-simplify]: Simplify 0 into 0 1.059 * [backup-simplify]: Simplify 0 into 0 1.059 * [backup-simplify]: Simplify 0 into 0 1.059 * [backup-simplify]: Simplify 0 into 0 1.059 * [backup-simplify]: Simplify (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1.059 * [backup-simplify]: Simplify (atan2 1.0 (+ 1 (* (+ (/ 1 N) 1.0) (/ 1 N)))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1.059 * [approximate]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in (N) around 0 1.059 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 1.060 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1.060 * [taylor]: Taking taylor expansion of (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) in N 1.060 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1.060 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) into (atan2 1.0 (+ (* 1.0 (/ 1 N)) (+ (/ 1 (pow N 2)) 1))) 1.061 * [backup-simplify]: Simplify 0 into 0 1.061 * [backup-simplify]: Simplify 0 into 0 1.061 * [backup-simplify]: Simplify 0 into 0 1.061 * [backup-simplify]: Simplify 0 into 0 1.061 * [backup-simplify]: Simplify 0 into 0 1.061 * [backup-simplify]: Simplify 0 into 0 1.061 * [backup-simplify]: Simplify (atan2 1.0 (+ (* 1.0 (/ 1 (/ 1 N))) (+ (/ 1 (pow (/ 1 N) 2)) 1))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1.061 * [backup-simplify]: Simplify (atan2 1.0 (+ 1 (* (+ (/ 1 (- N)) 1.0) (/ 1 (- N))))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1.061 * [approximate]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in (N) around 0 1.061 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 1.062 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1.062 * [taylor]: Taking taylor expansion of (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) in N 1.062 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1.062 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) into (atan2 1.0 (- (+ (/ 1 (pow N 2)) 1) (* 1.0 (/ 1 N)))) 1.063 * [backup-simplify]: Simplify 0 into 0 1.063 * [backup-simplify]: Simplify 0 into 0 1.063 * [backup-simplify]: Simplify 0 into 0 1.063 * [backup-simplify]: Simplify 0 into 0 1.063 * [backup-simplify]: Simplify 0 into 0 1.063 * [backup-simplify]: Simplify 0 into 0 1.063 * [backup-simplify]: Simplify (atan2 1.0 (- (+ (/ 1 (pow (/ 1 (- N)) 2)) 1) (* 1.0 (/ 1 (/ 1 (- N)))))) into (atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1))) 1.063 * * * [progress]: simplifying candidates 1.065 * [simplify]: Simplifying: (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))))) (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 (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)))) (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))) 1.065 * [simplify]: Sending expressions to egg_math: (log (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (exp (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (* (cbrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (cbrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))))) (cbrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (* (* (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (* (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))))) (sqrt (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt 1) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (/ 1 2) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (log (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (exp (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (* (cbrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (cbrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))))) (cbrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (* (* (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (* (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))))) (sqrt (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt 1) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (/ 1 2) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (log (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (exp (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (* (cbrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (cbrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))))) (cbrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (* (* (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (* (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))))) (sqrt (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt 1) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (/ 1 2) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (sqrt (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (log (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (exp (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (* (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0))))) (cbrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (* (* (atan2 h1 (+ 1 (* (+ h0 h1) h0))) (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (sqrt (atan2 h1 (+ 1 (* (+ h0 h1) h0)))) (sqrt (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1)))) (sqrt (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1)))) (sqrt (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1)))) (sqrt (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1)))) (sqrt (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1)))) (sqrt (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1)))) (sqrt (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1)))) (sqrt (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1)))) (sqrt (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1)))) (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1))) (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1))) (atan2 h1 (+ (pow h0 2) (+ (* h1 h0) 1))) 1.169 * * * [progress]: adding candidates to table 1.455 * [progress]: [Phase 3 of 3] Extracting. 1.455 * * [regime]: Finding splitpoints for: (# # # # # # #) 1.458 * * * [regime-changes]: Trying 2 branch expressions: ((- (atan (+ N 1.0)) (atan N)) N) 1.458 * * * * [regimes]: Trying to branch on (- (atan (+ N 1.0)) (atan N)) from (# # # # # # #) 1.499 * * * * [regimes]: Trying to branch on N from (# # # # # # #) 1.523 * * * [regime]: Found split indices: #