5.022 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.041 * * * [progress]: [2/2] Setting up program. 0.043 * [progress]: [Phase 2 of 3] Improving. 0.043 * [simplify]: Simplifying using # : (- (log (+ N 1.0)) (log N)) 0.043 * [simplify]: Sending expressions to egg_math: (- (log (+ h0 h1)) (log h0)) 0.045 * * [simplify]: iteration 0 : 9 enodes (cost 4 ) 0.047 * * [simplify]: iteration 1 : 10 enodes (cost 4 ) 0.048 * * [simplify]: iteration 2 : 10 enodes (cost 4 ) 0.048 * [simplify]: Simplified to: (- (log (+ N 1.0)) (log N)) 0.048 * * [progress]: iteration 1 / 4 0.048 * * * [progress]: picking best candidate 0.049 * * * * [pick]: Picked # 0.050 * * * [progress]: localizing error 0.056 * * * [progress]: generating rewritten candidates 0.056 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.070 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 0.076 * * * [progress]: generating series expansions 0.076 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.076 * [approximate]: Taking taylor expansion of (- (log (+ N 1.0)) (log N)) in (N) around 0 0.076 * [taylor]: Taking taylor expansion of (- (log (+ N 1.0)) (log N)) in N 0.076 * [taylor]: Taking taylor expansion of (log (+ N 1.0)) in N 0.076 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.076 * [taylor]: Taking taylor expansion of N in N 0.076 * [taylor]: Taking taylor expansion of 1.0 in N 0.077 * [taylor]: Taking taylor expansion of (log N) in N 0.077 * [taylor]: Taking taylor expansion of N in N 0.077 * [taylor]: Taking taylor expansion of (- (log (+ N 1.0)) (log N)) in N 0.078 * [taylor]: Taking taylor expansion of (log (+ N 1.0)) in N 0.078 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.078 * [taylor]: Taking taylor expansion of N in N 0.078 * [taylor]: Taking taylor expansion of 1.0 in N 0.078 * [taylor]: Taking taylor expansion of (log N) in N 0.078 * [taylor]: Taking taylor expansion of N in N 0.095 * [approximate]: Taking taylor expansion of (- (log (+ (/ 1 N) 1.0)) (log (/ 1 N))) in (N) around 0 0.095 * [taylor]: Taking taylor expansion of (- (log (+ (/ 1 N) 1.0)) (log (/ 1 N))) in N 0.095 * [taylor]: Taking taylor expansion of (log (+ (/ 1 N) 1.0)) in N 0.100 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.100 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.100 * [taylor]: Taking taylor expansion of N in N 0.100 * [taylor]: Taking taylor expansion of 1.0 in N 0.101 * [taylor]: Taking taylor expansion of (log (/ 1 N)) in N 0.101 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.101 * [taylor]: Taking taylor expansion of N in N 0.101 * [taylor]: Taking taylor expansion of (- (log (+ (/ 1 N) 1.0)) (log (/ 1 N))) in N 0.101 * [taylor]: Taking taylor expansion of (log (+ (/ 1 N) 1.0)) in N 0.101 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.101 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.101 * [taylor]: Taking taylor expansion of N in N 0.101 * [taylor]: Taking taylor expansion of 1.0 in N 0.102 * [taylor]: Taking taylor expansion of (log (/ 1 N)) in N 0.102 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.102 * [taylor]: Taking taylor expansion of N in N 0.130 * [approximate]: Taking taylor expansion of (- (log (- 1.0 (/ 1 N))) (log (/ -1 N))) in (N) around 0 0.130 * [taylor]: Taking taylor expansion of (- (log (- 1.0 (/ 1 N))) (log (/ -1 N))) in N 0.130 * [taylor]: Taking taylor expansion of (log (- 1.0 (/ 1 N))) in N 0.130 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.130 * [taylor]: Taking taylor expansion of 1.0 in N 0.130 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.130 * [taylor]: Taking taylor expansion of N in N 0.131 * [taylor]: Taking taylor expansion of (log (/ -1 N)) in N 0.131 * [taylor]: Taking taylor expansion of (/ -1 N) in N 0.131 * [taylor]: Taking taylor expansion of -1 in N 0.131 * [taylor]: Taking taylor expansion of N in N 0.132 * [taylor]: Taking taylor expansion of (- (log (- 1.0 (/ 1 N))) (log (/ -1 N))) in N 0.132 * [taylor]: Taking taylor expansion of (log (- 1.0 (/ 1 N))) in N 0.132 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.132 * [taylor]: Taking taylor expansion of 1.0 in N 0.132 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.132 * [taylor]: Taking taylor expansion of N in N 0.133 * [taylor]: Taking taylor expansion of (log (/ -1 N)) in N 0.133 * [taylor]: Taking taylor expansion of (/ -1 N) in N 0.133 * [taylor]: Taking taylor expansion of -1 in N 0.133 * [taylor]: Taking taylor expansion of N in N 0.164 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 0.164 * [approximate]: Taking taylor expansion of (log (+ N 1.0)) in (N) around 0 0.164 * [taylor]: Taking taylor expansion of (log (+ N 1.0)) in N 0.164 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.164 * [taylor]: Taking taylor expansion of N in N 0.165 * [taylor]: Taking taylor expansion of 1.0 in N 0.165 * [taylor]: Taking taylor expansion of (log (+ N 1.0)) in N 0.165 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.165 * [taylor]: Taking taylor expansion of N in N 0.165 * [taylor]: Taking taylor expansion of 1.0 in N 0.176 * [approximate]: Taking taylor expansion of (log (+ (/ 1 N) 1.0)) in (N) around 0 0.176 * [taylor]: Taking taylor expansion of (log (+ (/ 1 N) 1.0)) in N 0.176 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.176 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.176 * [taylor]: Taking taylor expansion of N in N 0.176 * [taylor]: Taking taylor expansion of 1.0 in N 0.177 * [taylor]: Taking taylor expansion of (log (+ (/ 1 N) 1.0)) in N 0.177 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.177 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.182 * [taylor]: Taking taylor expansion of N in N 0.183 * [taylor]: Taking taylor expansion of 1.0 in N 0.194 * [approximate]: Taking taylor expansion of (log (- 1.0 (/ 1 N))) in (N) around 0 0.194 * [taylor]: Taking taylor expansion of (log (- 1.0 (/ 1 N))) in N 0.194 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.194 * [taylor]: Taking taylor expansion of 1.0 in N 0.194 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.194 * [taylor]: Taking taylor expansion of N in N 0.195 * [taylor]: Taking taylor expansion of (log (- 1.0 (/ 1 N))) in N 0.195 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.195 * [taylor]: Taking taylor expansion of 1.0 in N 0.195 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.195 * [taylor]: Taking taylor expansion of N in N 0.208 * * * [progress]: simplifying candidates 0.209 * [simplify]: Simplifying using # : (fma 1 (log (+ N 1.0)) (- (* (log N) 1))) (fma (- (log N)) 1 (* (log N) 1)) (fma 1 (log (+ N 1.0)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N)))))) (fma (- (cbrt (log N))) (* (cbrt (log N)) (cbrt (log N))) (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))) (fma 1 (log (+ N 1.0)) (- (* (sqrt (log N)) (sqrt (log N))))) (fma (- (sqrt (log N))) (sqrt (log N)) (* (sqrt (log N)) (sqrt (log N)))) (fma 1 (log (+ N 1.0)) (- (* (log N) 1))) (fma (- (log N)) 1 (* (log N) 1)) (fma (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (- (* (log N) 1))) (fma (- (log N)) 1 (* (log N) 1)) (fma (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N)))))) (fma (- (cbrt (log N))) (* (cbrt (log N)) (cbrt (log N))) (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))) (fma (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (- (* (sqrt (log N)) (sqrt (log N))))) (fma (- (sqrt (log N))) (sqrt (log N)) (* (sqrt (log N)) (sqrt (log N)))) (fma (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (- (* (log N) 1))) (fma (- (log N)) 1 (* (log N) 1)) (fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (- (* (log N) 1))) (fma (- (log N)) 1 (* (log N) 1)) (fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N)))))) (fma (- (cbrt (log N))) (* (cbrt (log N)) (cbrt (log N))) (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))) (fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (- (* (sqrt (log N)) (sqrt (log N))))) (fma (- (sqrt (log N))) (sqrt (log N)) (* (sqrt (log N)) (sqrt (log N)))) (fma (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (- (* (log N) 1))) (fma (- (log N)) 1 (* (log N) 1)) (fma 1 (log (+ N 1.0)) (- (* (log N) 1))) (fma (- (log N)) 1 (* (log N) 1)) (fma 1 (log (+ N 1.0)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N)))))) (fma (- (cbrt (log N))) (* (cbrt (log N)) (cbrt (log N))) (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))) (fma 1 (log (+ N 1.0)) (- (* (sqrt (log N)) (sqrt (log N))))) (fma (- (sqrt (log N))) (sqrt (log N)) (* (sqrt (log N)) (sqrt (log N)))) (fma 1 (log (+ N 1.0)) (- (* (log N) 1))) (fma (- (log N)) 1 (* (log N) 1)) (expm1 (- (log (+ N 1.0)) (log N))) (log1p (- (log (+ N 1.0)) (log N))) (- (log N)) (- (log N)) (- (log N)) (- (log N)) (/ (+ N 1.0) N) (log (- (log (+ N 1.0)) (log N))) (exp (- (log (+ N 1.0)) (log N))) (* (cbrt (- (log (+ N 1.0)) (log N))) (cbrt (- (log (+ N 1.0)) (log N)))) (cbrt (- (log (+ N 1.0)) (log N))) (* (* (- (log (+ N 1.0)) (log N)) (- (log (+ N 1.0)) (log N))) (- (log (+ N 1.0)) (log N))) (sqrt (- (log (+ N 1.0)) (log N))) (sqrt (- (log (+ N 1.0)) (log N))) (- (pow (log (+ N 1.0)) 3) (pow (log N) 3)) (+ (* (log (+ N 1.0)) (log (+ N 1.0))) (+ (* (log N) (log N)) (* (log (+ N 1.0)) (log N)))) (- (log N)) (- (* (log (+ N 1.0)) (log (+ N 1.0))) (* (log N) (log N))) (+ (log (+ N 1.0)) (log N)) (+ (sqrt (log (+ N 1.0))) (sqrt (log N))) (- (sqrt (log (+ N 1.0))) (sqrt (log N))) (- (log (+ N 1.0)) (log N)) (- (log (+ N 1.0)) (log N)) (- (log (+ N 1.0)) (log N)) (- (log (+ N 1.0)) (log N)) (- (log (+ N 1.0)) (log (* (cbrt N) (cbrt N)))) (- (log (+ N 1.0)) (log (sqrt N))) (- (log (+ N 1.0)) (log 1)) (- (log (cbrt (+ N 1.0))) (log N)) (- (log (sqrt (+ N 1.0))) (log N)) (- (log (+ N 1.0)) (log N)) (- (log (+ N 1.0)) (log N)) (+ (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (log N)) (+ (log (- N 1.0)) (log N)) (- (log N)) (expm1 (log (+ N 1.0))) (log1p (log (+ N 1.0))) (log (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))) (log (cbrt (+ N 1.0))) (log (sqrt (+ N 1.0))) (log (sqrt (+ N 1.0))) (log 1) (log (+ N 1.0)) (log 1) (log (+ N 1.0)) (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (log (- (* N N) (* 1.0 1.0))) (log (- N 1.0)) (log (+ N 1.0)) (log (log (+ N 1.0))) (exp (log (+ N 1.0))) (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (* (* (log (+ N 1.0)) (log (+ N 1.0))) (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (- (+ (* 1.0 N) (log 1.0)) (+ (* 1/2 (/ (pow N 2) (pow 1.0 2))) (log N))) (- (+ (* 0.3333333333333333 (/ 1 (pow N 3))) (* 1.0 (/ 1 N))) (* 0.5 (/ 1 (pow N 2)))) (- (+ (* 0.3333333333333333 (/ 1 (pow N 3))) (* 1.0 (/ 1 N))) (* 0.5 (/ 1 (pow N 2)))) (- (+ (* 1.0 N) (log 1.0)) (* 1/2 (/ (pow N 2) (pow 1.0 2)))) (- (* 1.0 (/ 1 N)) (+ (* 0.5 (/ 1 (pow N 2))) (log (/ 1 N)))) (- (+ (* 1.0 (/ 1 N)) (log -1)) (+ (* 0.5 (/ 1 (pow N 2))) (log (/ -1 N)))) 0.209 * [simplify]: Sending expressions to egg_math: (fma 1 (log (+ h0 h1)) (- (* (log h0) 1))) (fma (- (log h0)) 1 (* (log h0) 1)) (fma 1 (log (+ h0 h1)) (- (* (cbrt (log h0)) (* (cbrt (log h0)) (cbrt (log h0)))))) (fma (- (cbrt (log h0))) (* (cbrt (log h0)) (cbrt (log h0))) (* (cbrt (log h0)) (* (cbrt (log h0)) (cbrt (log h0))))) (fma 1 (log (+ h0 h1)) (- (* (sqrt (log h0)) (sqrt (log h0))))) (fma (- (sqrt (log h0))) (sqrt (log h0)) (* (sqrt (log h0)) (sqrt (log h0)))) (fma 1 (log (+ h0 h1)) (- (* (log h0) 1))) (fma (- (log h0)) 1 (* (log h0) 1)) (fma (* (cbrt (log (+ h0 h1))) (cbrt (log (+ h0 h1)))) (cbrt (log (+ h0 h1))) (- (* (log h0) 1))) (fma (- (log h0)) 1 (* (log h0) 1)) (fma (* (cbrt (log (+ h0 h1))) (cbrt (log (+ h0 h1)))) (cbrt (log (+ h0 h1))) (- (* (cbrt (log h0)) (* (cbrt (log h0)) (cbrt (log h0)))))) (fma (- (cbrt (log h0))) (* (cbrt (log h0)) (cbrt (log h0))) (* (cbrt (log h0)) (* (cbrt (log h0)) (cbrt (log h0))))) (fma (* (cbrt (log (+ h0 h1))) (cbrt (log (+ h0 h1)))) (cbrt (log (+ h0 h1))) (- (* (sqrt (log h0)) (sqrt (log h0))))) (fma (- (sqrt (log h0))) (sqrt (log h0)) (* (sqrt (log h0)) (sqrt (log h0)))) (fma (* (cbrt (log (+ h0 h1))) (cbrt (log (+ h0 h1)))) (cbrt (log (+ h0 h1))) (- (* (log h0) 1))) (fma (- (log h0)) 1 (* (log h0) 1)) (fma (sqrt (log (+ h0 h1))) (sqrt (log (+ h0 h1))) (- (* (log h0) 1))) (fma (- (log h0)) 1 (* (log h0) 1)) (fma (sqrt (log (+ h0 h1))) (sqrt (log (+ h0 h1))) (- (* (cbrt (log h0)) (* (cbrt (log h0)) (cbrt (log h0)))))) (fma (- (cbrt (log h0))) (* (cbrt (log h0)) (cbrt (log h0))) (* (cbrt (log h0)) (* (cbrt (log h0)) (cbrt (log h0))))) (fma (sqrt (log (+ h0 h1))) (sqrt (log (+ h0 h1))) (- (* (sqrt (log h0)) (sqrt (log h0))))) (fma (- (sqrt (log h0))) (sqrt (log h0)) (* (sqrt (log h0)) (sqrt (log h0)))) (fma (sqrt (log (+ h0 h1))) (sqrt (log (+ h0 h1))) (- (* (log h0) 1))) (fma (- (log h0)) 1 (* (log h0) 1)) (fma 1 (log (+ h0 h1)) (- (* (log h0) 1))) (fma (- (log h0)) 1 (* (log h0) 1)) (fma 1 (log (+ h0 h1)) (- (* (cbrt (log h0)) (* (cbrt (log h0)) (cbrt (log h0)))))) (fma (- (cbrt (log h0))) (* (cbrt (log h0)) (cbrt (log h0))) (* (cbrt (log h0)) (* (cbrt (log h0)) (cbrt (log h0))))) (fma 1 (log (+ h0 h1)) (- (* (sqrt (log h0)) (sqrt (log h0))))) (fma (- (sqrt (log h0))) (sqrt (log h0)) (* (sqrt (log h0)) (sqrt (log h0)))) (fma 1 (log (+ h0 h1)) (- (* (log h0) 1))) (fma (- (log h0)) 1 (* (log h0) 1)) (expm1 (- (log (+ h0 h1)) (log h0))) (log1p (- (log (+ h0 h1)) (log h0))) (- (log h0)) (- (log h0)) (- (log h0)) (- (log h0)) (/ (+ h0 h1) h0) (log (- (log (+ h0 h1)) (log h0))) (exp (- (log (+ h0 h1)) (log h0))) (* (cbrt (- (log (+ h0 h1)) (log h0))) (cbrt (- (log (+ h0 h1)) (log h0)))) (cbrt (- (log (+ h0 h1)) (log h0))) (* (* (- (log (+ h0 h1)) (log h0)) (- (log (+ h0 h1)) (log h0))) (- (log (+ h0 h1)) (log h0))) (sqrt (- (log (+ h0 h1)) (log h0))) (sqrt (- (log (+ h0 h1)) (log h0))) (- (pow (log (+ h0 h1)) 3) (pow (log h0) 3)) (+ (* (log (+ h0 h1)) (log (+ h0 h1))) (+ (* (log h0) (log h0)) (* (log (+ h0 h1)) (log h0)))) (- (log h0)) (- (* (log (+ h0 h1)) (log (+ h0 h1))) (* (log h0) (log h0))) (+ (log (+ h0 h1)) (log h0)) (+ (sqrt (log (+ h0 h1))) (sqrt (log h0))) (- (sqrt (log (+ h0 h1))) (sqrt (log h0))) (- (log (+ h0 h1)) (log h0)) (- (log (+ h0 h1)) (log h0)) (- (log (+ h0 h1)) (log h0)) (- (log (+ h0 h1)) (log h0)) (- (log (+ h0 h1)) (log (* (cbrt h0) (cbrt h0)))) (- (log (+ h0 h1)) (log (sqrt h0))) (- (log (+ h0 h1)) (log 1)) (- (log (cbrt (+ h0 h1))) (log h0)) (- (log (sqrt (+ h0 h1))) (log h0)) (- (log (+ h0 h1)) (log h0)) (- (log (+ h0 h1)) (log h0)) (+ (log (+ (* h0 h0) (- (* h1 h1) (* h0 h1)))) (log h0)) (+ (log (- h0 h1)) (log h0)) (- (log h0)) (expm1 (log (+ h0 h1))) (log1p (log (+ h0 h1))) (log (* (cbrt (+ h0 h1)) (cbrt (+ h0 h1)))) (log (cbrt (+ h0 h1))) (log (sqrt (+ h0 h1))) (log (sqrt (+ h0 h1))) (log 1) (log (+ h0 h1)) (log 1) (log (+ h0 h1)) (log (+ (pow h0 3) (pow h1 3))) (log (+ (* h0 h0) (- (* h1 h1) (* h0 h1)))) (log (- (* h0 h0) (* h1 h1))) (log (- h0 h1)) (log (+ h0 h1)) (log (log (+ h0 h1))) (exp (log (+ h0 h1))) (* (cbrt (log (+ h0 h1))) (cbrt (log (+ h0 h1)))) (cbrt (log (+ h0 h1))) (* (* (log (+ h0 h1)) (log (+ h0 h1))) (log (+ h0 h1))) (sqrt (log (+ h0 h1))) (sqrt (log (+ h0 h1))) (- (+ (* h1 h0) (log h1)) (+ (* 1/2 (/ (pow h0 2) (pow h1 2))) (log h0))) (- (+ (* h2 (/ 1 (pow h0 3))) (* h1 (/ 1 h0))) (* h3 (/ 1 (pow h0 2)))) (- (+ (* h2 (/ 1 (pow h0 3))) (* h1 (/ 1 h0))) (* h3 (/ 1 (pow h0 2)))) (- (+ (* h1 h0) (log h1)) (* 1/2 (/ (pow h0 2) (pow h1 2)))) (- (* h1 (/ 1 h0)) (+ (* h3 (/ 1 (pow h0 2))) (log (/ 1 h0)))) (- (+ (* h1 (/ 1 h0)) (log -1)) (+ (* h3 (/ 1 (pow h0 2))) (log (/ -1 h0)))) 0.214 * * [simplify]: iteration 0 : 277 enodes (cost 598 ) 0.218 * * [simplify]: iteration 1 : 837 enodes (cost 444 ) 0.235 * * [simplify]: iteration 2 : 3748 enodes (cost 347 ) 0.328 * * [simplify]: iteration 3 : 5001 enodes (cost 343 ) 0.330 * [simplify]: Simplified to: (- (log (+ N 1.0)) (log N)) 0 (- (log (+ N 1.0)) (log N)) 0 (- (log (+ N 1.0)) (log N)) 0 (- (log (+ N 1.0)) (log N)) 0 (+ (pow (cbrt (log (+ N 1.0))) 3) (log (/ 1 N))) 0 (+ (pow (cbrt (log (+ N 1.0))) 3) (log (/ 1 N))) 0 (+ (pow (cbrt (log (+ N 1.0))) 3) (log (/ 1 N))) 0 (+ (pow (cbrt (log (+ N 1.0))) 3) (log (/ 1 N))) 0 (- (log (+ N 1.0)) (log N)) 0 (- (log (+ N 1.0)) (log N)) 0 (- (log (+ N 1.0)) (log N)) 0 (- (log (+ N 1.0)) (log N)) 0 (- (log (+ N 1.0)) (log N)) 0 (- (log (+ N 1.0)) (log N)) 0 (- (log (+ N 1.0)) (log N)) 0 (- (log (+ N 1.0)) (log N)) 0 (expm1 (- (log (+ N 1.0)) (log N))) (log1p (- (log (+ N 1.0)) (log N))) (log (/ 1 N)) (log (/ 1 N)) (log (/ 1 N)) (log (/ 1 N)) (/ (+ N 1.0) N) (log (- (log (+ N 1.0)) (log N))) (/ (+ N 1.0) N) (* (cbrt (- (log (+ N 1.0)) (log N))) (cbrt (- (log (+ N 1.0)) (log N)))) (cbrt (- (log (+ N 1.0)) (log N))) (pow (- (log (+ N 1.0)) (log N)) 3) (sqrt (- (log (+ N 1.0)) (log N))) (sqrt (- (log (+ N 1.0)) (log N))) (- (pow (log (+ N 1.0)) 3) (pow (log N) 3)) (fma (log (+ N 1.0)) (+ (log (+ N 1.0)) (log N)) (* (log N) (log N))) (log (/ 1 N)) (- (* (log (+ N 1.0)) (log (+ N 1.0))) (* (log N) (log N))) (+ (log (+ N 1.0)) (log N)) (+ (sqrt (log (+ N 1.0))) (sqrt (log N))) (- (sqrt (log (+ N 1.0))) (sqrt (log N))) (- (log (+ N 1.0)) (log N)) (- (log (+ N 1.0)) (log N)) (- (log (+ N 1.0)) (log N)) (- (log (+ N 1.0)) (log N)) (- (log (+ N 1.0)) (* 2 (log (cbrt N)))) (- (log (+ N 1.0)) (log (sqrt N))) (log (+ N 1.0)) (- (log (cbrt (+ N 1.0))) (log N)) (- (log (sqrt (+ N 1.0))) (log N)) (- (log (+ N 1.0)) (log N)) (- (log (+ N 1.0)) (log N)) (+ (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (log N)) (+ (log (- N 1.0)) (log N)) (log (/ 1 N)) (expm1 (log (+ N 1.0))) (log1p (log (+ N 1.0))) (* 2 (log (cbrt (+ N 1.0)))) (log (cbrt (+ N 1.0))) (log (sqrt (+ N 1.0))) (log (sqrt (+ N 1.0))) 0 (log (+ N 1.0)) 0 (log (+ N 1.0)) (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (log (- (* N N) (* 1.0 1.0))) (log (- N 1.0)) (log (+ N 1.0)) (log (log (+ N 1.0))) (+ N 1.0) (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0))) (pow (log (+ N 1.0)) 3) (sqrt (log (+ N 1.0))) (sqrt (log (+ N 1.0))) (fma 1.0 N (- (log 1.0) (fma 1/2 (/ (pow N 2) (pow 1.0 2)) (log N)))) (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)) (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)) (fma 1.0 N (- (log 1.0) (* 1/2 (/ (pow N 2) (pow 1.0 2))))) (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (log N)) (fma 1.0 (/ 1 N) (- (log -1) (fma 0.5 (/ 1 (pow N 2)) (log (/ -1 N))))) 0.331 * * * [progress]: adding candidates to table 0.454 * * [progress]: iteration 2 / 4 0.454 * * * [progress]: picking best candidate 0.459 * * * * [pick]: Picked # 0.459 * * * [progress]: localizing error 0.463 * * * [progress]: generating rewritten candidates 0.464 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.470 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 0.492 * * * [progress]: generating series expansions 0.492 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.492 * [approximate]: Taking taylor expansion of (log (/ (+ N 1.0) N)) in (N) around 0 0.492 * [taylor]: Taking taylor expansion of (log (/ (+ N 1.0) N)) in N 0.492 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 0.492 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.492 * [taylor]: Taking taylor expansion of N in N 0.492 * [taylor]: Taking taylor expansion of 1.0 in N 0.492 * [taylor]: Taking taylor expansion of N in N 0.493 * [taylor]: Taking taylor expansion of (log (/ (+ N 1.0) N)) in N 0.494 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 0.494 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.494 * [taylor]: Taking taylor expansion of N in N 0.494 * [taylor]: Taking taylor expansion of 1.0 in N 0.494 * [taylor]: Taking taylor expansion of N in N 0.507 * [approximate]: Taking taylor expansion of (log (* N (+ (/ 1 N) 1.0))) in (N) around 0 0.507 * [taylor]: Taking taylor expansion of (log (* N (+ (/ 1 N) 1.0))) in N 0.507 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 0.507 * [taylor]: Taking taylor expansion of N in N 0.507 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.507 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.507 * [taylor]: Taking taylor expansion of N in N 0.507 * [taylor]: Taking taylor expansion of 1.0 in N 0.509 * [taylor]: Taking taylor expansion of (log (* N (+ (/ 1 N) 1.0))) in N 0.509 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 0.509 * [taylor]: Taking taylor expansion of N in N 0.509 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.509 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.509 * [taylor]: Taking taylor expansion of N in N 0.509 * [taylor]: Taking taylor expansion of 1.0 in N 0.533 * [approximate]: Taking taylor expansion of (log (* -1 (* N (- 1.0 (/ 1 N))))) in (N) around 0 0.533 * [taylor]: Taking taylor expansion of (log (* -1 (* N (- 1.0 (/ 1 N))))) in N 0.533 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 0.533 * [taylor]: Taking taylor expansion of -1 in N 0.533 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 0.534 * [taylor]: Taking taylor expansion of N in N 0.534 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.534 * [taylor]: Taking taylor expansion of 1.0 in N 0.534 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.534 * [taylor]: Taking taylor expansion of N in N 0.536 * [taylor]: Taking taylor expansion of (log (* -1 (* N (- 1.0 (/ 1 N))))) in N 0.536 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 0.537 * [taylor]: Taking taylor expansion of -1 in N 0.537 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 0.537 * [taylor]: Taking taylor expansion of N in N 0.537 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.537 * [taylor]: Taking taylor expansion of 1.0 in N 0.537 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.537 * [taylor]: Taking taylor expansion of N in N 0.572 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 0.573 * [approximate]: Taking taylor expansion of (/ (+ N 1.0) N) in (N) around 0 0.573 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 0.573 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.573 * [taylor]: Taking taylor expansion of N in N 0.573 * [taylor]: Taking taylor expansion of 1.0 in N 0.573 * [taylor]: Taking taylor expansion of N in N 0.573 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 0.573 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.573 * [taylor]: Taking taylor expansion of N in N 0.573 * [taylor]: Taking taylor expansion of 1.0 in N 0.573 * [taylor]: Taking taylor expansion of N in N 0.579 * [approximate]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in (N) around 0 0.579 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 0.579 * [taylor]: Taking taylor expansion of N in N 0.579 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.579 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.579 * [taylor]: Taking taylor expansion of N in N 0.579 * [taylor]: Taking taylor expansion of 1.0 in N 0.580 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 0.580 * [taylor]: Taking taylor expansion of N in N 0.580 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.580 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.580 * [taylor]: Taking taylor expansion of N in N 0.580 * [taylor]: Taking taylor expansion of 1.0 in N 0.593 * [approximate]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in (N) around 0 0.593 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 0.593 * [taylor]: Taking taylor expansion of -1 in N 0.593 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 0.593 * [taylor]: Taking taylor expansion of N in N 0.593 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.593 * [taylor]: Taking taylor expansion of 1.0 in N 0.593 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.593 * [taylor]: Taking taylor expansion of N in N 0.593 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 0.593 * [taylor]: Taking taylor expansion of -1 in N 0.593 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 0.593 * [taylor]: Taking taylor expansion of N in N 0.593 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.593 * [taylor]: Taking taylor expansion of 1.0 in N 0.593 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.593 * [taylor]: Taking taylor expansion of N in N 0.615 * * * [progress]: simplifying candidates 0.616 * [simplify]: Simplifying using # : (expm1 (log (/ (+ N 1.0) N))) (log1p (log (/ (+ N 1.0) N))) (log (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))) (log (cbrt (/ (+ N 1.0) N))) (log (sqrt (/ (+ N 1.0) N))) (log (sqrt (/ (+ N 1.0) N))) (log (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt N) (cbrt N)))) (log (/ (cbrt (+ N 1.0)) (cbrt N))) (log (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))) (log (/ (cbrt (+ N 1.0)) (sqrt N))) (log (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) 1)) (log (/ (cbrt (+ N 1.0)) N)) (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))) (log (/ (sqrt (+ N 1.0)) (sqrt N))) (log (/ (sqrt (+ N 1.0)) (sqrt N))) (log (/ (sqrt (+ N 1.0)) 1)) (log (/ (sqrt (+ N 1.0)) N)) (log (/ 1 (* (cbrt N) (cbrt N)))) (log (/ (+ N 1.0) (cbrt N))) (log (/ 1 (sqrt N))) (log (/ (+ N 1.0) (sqrt N))) (log (/ 1 1)) (log (/ (+ N 1.0) N)) (log (/ 1 (* (cbrt N) (cbrt N)))) (log (/ (+ N 1.0) (cbrt N))) (log (/ 1 (sqrt N))) (log (/ (+ N 1.0) (sqrt N))) (log (/ 1 1)) (log (/ (+ N 1.0) N)) (log 1) (log (/ (+ N 1.0) N)) (log (+ N 1.0)) (log (/ 1 N)) (log (+ N 1.0)) (log N) (log (/ (+ N 1.0) N)) (log (log (/ (+ N 1.0) N))) (exp (log (/ (+ N 1.0) N))) (* (cbrt (log (/ (+ N 1.0) N))) (cbrt (log (/ (+ N 1.0) N)))) (cbrt (log (/ (+ N 1.0) N))) (* (* (log (/ (+ N 1.0) N)) (log (/ (+ N 1.0) N))) (log (/ (+ N 1.0) N))) (sqrt (log (/ (+ N 1.0) N))) (sqrt (log (/ (+ N 1.0) N))) (expm1 (/ (+ N 1.0) N)) (log1p (/ (+ 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)) (- (+ N 1.0)) (- N) (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt N) (cbrt N))) (/ (cbrt (+ N 1.0)) (cbrt N)) (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N)) (/ (cbrt (+ N 1.0)) (sqrt N)) (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) 1) (/ (cbrt (+ N 1.0)) N) (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))) (/ (sqrt (+ N 1.0)) (cbrt N)) (/ (sqrt (+ N 1.0)) (sqrt N)) (/ (sqrt (+ N 1.0)) (sqrt N)) (/ (sqrt (+ N 1.0)) 1) (/ (sqrt (+ N 1.0)) N) (/ 1 (* (cbrt N) (cbrt N))) (/ (+ N 1.0) (cbrt N)) (/ 1 (sqrt N)) (/ (+ N 1.0) (sqrt N)) (/ 1 1) (/ (+ N 1.0) N) (/ 1 (* (cbrt N) (cbrt N))) (/ (+ N 1.0) (cbrt N)) (/ 1 (sqrt N)) (/ (+ N 1.0) (sqrt N)) (/ 1 1) (/ (+ N 1.0) N) (/ 1 N) (/ N (+ N 1.0)) (/ (+ N 1.0) (* (cbrt N) (cbrt N))) (/ (+ N 1.0) (sqrt N)) (/ (+ N 1.0) 1) (/ N (cbrt (+ N 1.0))) (/ N (sqrt (+ N 1.0))) (/ N (+ N 1.0)) (/ N (+ N 1.0)) (* N (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (* N (- N 1.0)) (- (+ (* 1.0 N) (log 1.0)) (+ (* 1/2 (/ (pow N 2) (pow 1.0 2))) (log N))) (- (+ (* 0.3333333333333333 (/ 1 (pow N 3))) (* 1.0 (/ 1 N))) (* 0.5 (/ 1 (pow N 2)))) (- (+ (* 0.3333333333333333 (/ 1 (pow N 3))) (* 1.0 (/ 1 N))) (* 0.5 (/ 1 (pow N 2)))) (+ (* 1.0 (/ 1 N)) 1) (+ (* 1.0 (/ 1 N)) 1) (+ (* 1.0 (/ 1 N)) 1) 0.616 * [simplify]: Sending expressions to egg_math: (expm1 (log (/ (+ h0 h1) h0))) (log1p (log (/ (+ h0 h1) h0))) (log (* (cbrt (/ (+ h0 h1) h0)) (cbrt (/ (+ h0 h1) h0)))) (log (cbrt (/ (+ h0 h1) h0))) (log (sqrt (/ (+ h0 h1) h0))) (log (sqrt (/ (+ h0 h1) h0))) (log (/ (* (cbrt (+ h0 h1)) (cbrt (+ h0 h1))) (* (cbrt h0) (cbrt h0)))) (log (/ (cbrt (+ h0 h1)) (cbrt h0))) (log (/ (* (cbrt (+ h0 h1)) (cbrt (+ h0 h1))) (sqrt h0))) (log (/ (cbrt (+ h0 h1)) (sqrt h0))) (log (/ (* (cbrt (+ h0 h1)) (cbrt (+ h0 h1))) 1)) (log (/ (cbrt (+ h0 h1)) h0)) (log (/ (sqrt (+ h0 h1)) (* (cbrt h0) (cbrt h0)))) (log (/ (sqrt (+ h0 h1)) (cbrt h0))) (log (/ (sqrt (+ h0 h1)) (sqrt h0))) (log (/ (sqrt (+ h0 h1)) (sqrt h0))) (log (/ (sqrt (+ h0 h1)) 1)) (log (/ (sqrt (+ h0 h1)) h0)) (log (/ 1 (* (cbrt h0) (cbrt h0)))) (log (/ (+ h0 h1) (cbrt h0))) (log (/ 1 (sqrt h0))) (log (/ (+ h0 h1) (sqrt h0))) (log (/ 1 1)) (log (/ (+ h0 h1) h0)) (log (/ 1 (* (cbrt h0) (cbrt h0)))) (log (/ (+ h0 h1) (cbrt h0))) (log (/ 1 (sqrt h0))) (log (/ (+ h0 h1) (sqrt h0))) (log (/ 1 1)) (log (/ (+ h0 h1) h0)) (log 1) (log (/ (+ h0 h1) h0)) (log (+ h0 h1)) (log (/ 1 h0)) (log (+ h0 h1)) (log h0) (log (/ (+ h0 h1) h0)) (log (log (/ (+ h0 h1) h0))) (exp (log (/ (+ h0 h1) h0))) (* (cbrt (log (/ (+ h0 h1) h0))) (cbrt (log (/ (+ h0 h1) h0)))) (cbrt (log (/ (+ h0 h1) h0))) (* (* (log (/ (+ h0 h1) h0)) (log (/ (+ h0 h1) h0))) (log (/ (+ h0 h1) h0))) (sqrt (log (/ (+ h0 h1) h0))) (sqrt (log (/ (+ h0 h1) h0))) (expm1 (/ (+ h0 h1) h0)) (log1p (/ (+ 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)) (- (+ h0 h1)) (- h0) (/ (* (cbrt (+ h0 h1)) (cbrt (+ h0 h1))) (* (cbrt h0) (cbrt h0))) (/ (cbrt (+ h0 h1)) (cbrt h0)) (/ (* (cbrt (+ h0 h1)) (cbrt (+ h0 h1))) (sqrt h0)) (/ (cbrt (+ h0 h1)) (sqrt h0)) (/ (* (cbrt (+ h0 h1)) (cbrt (+ h0 h1))) 1) (/ (cbrt (+ h0 h1)) h0) (/ (sqrt (+ h0 h1)) (* (cbrt h0) (cbrt h0))) (/ (sqrt (+ h0 h1)) (cbrt h0)) (/ (sqrt (+ h0 h1)) (sqrt h0)) (/ (sqrt (+ h0 h1)) (sqrt h0)) (/ (sqrt (+ h0 h1)) 1) (/ (sqrt (+ h0 h1)) h0) (/ 1 (* (cbrt h0) (cbrt h0))) (/ (+ h0 h1) (cbrt h0)) (/ 1 (sqrt h0)) (/ (+ h0 h1) (sqrt h0)) (/ 1 1) (/ (+ h0 h1) h0) (/ 1 (* (cbrt h0) (cbrt h0))) (/ (+ h0 h1) (cbrt h0)) (/ 1 (sqrt h0)) (/ (+ h0 h1) (sqrt h0)) (/ 1 1) (/ (+ h0 h1) h0) (/ 1 h0) (/ h0 (+ h0 h1)) (/ (+ h0 h1) (* (cbrt h0) (cbrt h0))) (/ (+ h0 h1) (sqrt h0)) (/ (+ h0 h1) 1) (/ h0 (cbrt (+ h0 h1))) (/ h0 (sqrt (+ h0 h1))) (/ h0 (+ h0 h1)) (/ h0 (+ h0 h1)) (* h0 (+ (* h0 h0) (- (* h1 h1) (* h0 h1)))) (* h0 (- h0 h1)) (- (+ (* h1 h0) (log h1)) (+ (* 1/2 (/ (pow h0 2) (pow h1 2))) (log h0))) (- (+ (* h2 (/ 1 (pow h0 3))) (* h1 (/ 1 h0))) (* h3 (/ 1 (pow h0 2)))) (- (+ (* h2 (/ 1 (pow h0 3))) (* h1 (/ 1 h0))) (* h3 (/ 1 (pow h0 2)))) (+ (* h1 (/ 1 h0)) 1) (+ (* h1 (/ 1 h0)) 1) (+ (* h1 (/ 1 h0)) 1) 0.620 * * [simplify]: iteration 0 : 243 enodes (cost 383 ) 0.624 * * [simplify]: iteration 1 : 808 enodes (cost 358 ) 0.638 * * [simplify]: iteration 2 : 3663 enodes (cost 347 ) 0.715 * * [simplify]: iteration 3 : 5001 enodes (cost 344 ) 0.717 * [simplify]: Simplified to: (expm1 (log (/ (+ N 1.0) N))) (log1p (log (/ (+ N 1.0) N))) (* 2 (log (cbrt (/ (+ N 1.0) N)))) (log (cbrt (/ (+ N 1.0) N))) (log (sqrt (/ (+ N 1.0) N))) (log (sqrt (/ (+ N 1.0) N))) (* 2 (log (/ (cbrt (+ N 1.0)) (cbrt N)))) (log (/ (cbrt (+ N 1.0)) (cbrt N))) (fma 2 (log (cbrt (+ N 1.0))) (log (/ 1 (sqrt N)))) (log (/ (cbrt (+ N 1.0)) (sqrt N))) (* 2 (log (cbrt (+ N 1.0)))) (log (/ (cbrt (+ N 1.0)) N)) (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))) (log (/ (sqrt (+ N 1.0)) (sqrt N))) (log (/ (sqrt (+ N 1.0)) (sqrt N))) (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)) (log (/ 1 (* (cbrt N) (cbrt N)))) (log (/ (+ N 1.0) (cbrt N))) (log (/ 1 (sqrt N))) (log (/ (+ N 1.0) (sqrt N))) 0 (log (/ (+ N 1.0) N)) (log (/ 1 (* (cbrt N) (cbrt N)))) (log (/ (+ N 1.0) (cbrt N))) (log (/ 1 (sqrt N))) (log (/ (+ N 1.0) (sqrt N))) 0 (log (/ (+ N 1.0) N)) 0 (log (/ (+ N 1.0) N)) (log (+ N 1.0)) (log (/ 1 N)) (log (+ N 1.0)) (log N) (log (/ (+ N 1.0) N)) (log (log (/ (+ N 1.0) N))) (/ (+ N 1.0) N) (* (cbrt (log (/ (+ N 1.0) N))) (cbrt (log (/ (+ N 1.0) N)))) (cbrt (log (/ (+ N 1.0) N))) (pow (log (/ (+ N 1.0) N)) 3) (sqrt (log (/ (+ N 1.0) N))) (sqrt (log (/ (+ N 1.0) N))) (expm1 (/ (+ N 1.0) N)) (log1p (/ (+ N 1.0) N)) (log (/ (+ N 1.0) N)) (log (/ (+ N 1.0) N)) (exp (/ (+ N 1.0) N)) (pow (/ (+ N 1.0) N) 3) (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N))) (cbrt (/ (+ N 1.0) N)) (pow (/ (+ N 1.0) N) 3) (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N)) (- (+ N 1.0)) (- N) (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt N) (cbrt N))) (/ (cbrt (+ N 1.0)) (cbrt N)) (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N)) (/ (cbrt (+ N 1.0)) (sqrt N)) (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (/ (cbrt (+ N 1.0)) N) (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))) (/ (sqrt (+ N 1.0)) (cbrt N)) (/ (sqrt (+ N 1.0)) (sqrt N)) (/ (sqrt (+ N 1.0)) (sqrt N)) (sqrt (+ N 1.0)) (/ (sqrt (+ N 1.0)) N) (/ 1 (* (cbrt N) (cbrt N))) (/ (+ N 1.0) (cbrt N)) (/ 1 (sqrt N)) (/ (+ N 1.0) (sqrt N)) 1 (/ (+ N 1.0) N) (/ 1 (* (cbrt N) (cbrt N))) (/ (+ N 1.0) (cbrt N)) (/ 1 (sqrt N)) (/ (+ N 1.0) (sqrt N)) 1 (/ (+ N 1.0) N) (/ 1 N) (/ N (+ N 1.0)) (/ (+ N 1.0) (* (cbrt N) (cbrt N))) (/ (+ N 1.0) (sqrt N)) (+ N 1.0) (/ N (cbrt (+ N 1.0))) (/ N (sqrt (+ N 1.0))) (/ N (+ N 1.0)) (/ N (+ N 1.0)) (fma N (* 1.0 (- 1.0 N)) (pow N 3)) (* N (- N 1.0)) (fma 1.0 N (- (log 1.0) (fma 1/2 (/ (pow N 2) (pow 1.0 2)) (log N)))) (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3))) (fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3))) (fma 1.0 (/ 1 N) 1) (fma 1.0 (/ 1 N) 1) (fma 1.0 (/ 1 N) 1) 0.717 * * * [progress]: adding candidates to table 0.834 * * [progress]: iteration 3 / 4 0.834 * * * [progress]: picking best candidate 0.838 * * * * [pick]: Picked # 0.839 * * * [progress]: localizing error 0.845 * * * [progress]: generating rewritten candidates 0.845 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.852 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 0.859 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 0.869 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 0.883 * * * [progress]: generating series expansions 0.883 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.883 * [approximate]: Taking taylor expansion of (log (sqrt (/ (+ N 1.0) N))) in (N) around 0 0.883 * [taylor]: Taking taylor expansion of (log (sqrt (/ (+ N 1.0) N))) in N 0.884 * [taylor]: Taking taylor expansion of (sqrt (/ (+ N 1.0) N)) in N 0.884 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 0.884 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.884 * [taylor]: Taking taylor expansion of N in N 0.884 * [taylor]: Taking taylor expansion of 1.0 in N 0.884 * [taylor]: Taking taylor expansion of N in N 0.886 * [taylor]: Taking taylor expansion of (log (sqrt (/ (+ N 1.0) N))) in N 0.886 * [taylor]: Taking taylor expansion of (sqrt (/ (+ N 1.0) N)) in N 0.886 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 0.886 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 0.886 * [taylor]: Taking taylor expansion of N in N 0.886 * [taylor]: Taking taylor expansion of 1.0 in N 0.886 * [taylor]: Taking taylor expansion of N in N 0.908 * [approximate]: Taking taylor expansion of (log (sqrt (* N (+ (/ 1 N) 1.0)))) in (N) around 0 0.908 * [taylor]: Taking taylor expansion of (log (sqrt (* N (+ (/ 1 N) 1.0)))) in N 0.908 * [taylor]: Taking taylor expansion of (sqrt (* N (+ (/ 1 N) 1.0))) in N 0.908 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 0.908 * [taylor]: Taking taylor expansion of N in N 0.908 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.908 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.908 * [taylor]: Taking taylor expansion of N in N 0.909 * [taylor]: Taking taylor expansion of 1.0 in N 0.913 * [taylor]: Taking taylor expansion of (log (sqrt (* N (+ (/ 1 N) 1.0)))) in N 0.913 * [taylor]: Taking taylor expansion of (sqrt (* N (+ (/ 1 N) 1.0))) in N 0.913 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 0.913 * [taylor]: Taking taylor expansion of N in N 0.913 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 0.913 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.913 * [taylor]: Taking taylor expansion of N in N 0.913 * [taylor]: Taking taylor expansion of 1.0 in N 0.948 * [approximate]: Taking taylor expansion of (log (sqrt (* -1 (* N (- 1.0 (/ 1 N)))))) in (N) around 0 0.948 * [taylor]: Taking taylor expansion of (log (sqrt (* -1 (* N (- 1.0 (/ 1 N)))))) in N 0.948 * [taylor]: Taking taylor expansion of (sqrt (* -1 (* N (- 1.0 (/ 1 N))))) in N 0.948 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 0.948 * [taylor]: Taking taylor expansion of -1 in N 0.948 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 0.949 * [taylor]: Taking taylor expansion of N in N 0.949 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.949 * [taylor]: Taking taylor expansion of 1.0 in N 0.949 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.949 * [taylor]: Taking taylor expansion of N in N 0.956 * [taylor]: Taking taylor expansion of (log (sqrt (* -1 (* N (- 1.0 (/ 1 N)))))) in N 0.956 * [taylor]: Taking taylor expansion of (sqrt (* -1 (* N (- 1.0 (/ 1 N))))) in N 0.956 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 0.956 * [taylor]: Taking taylor expansion of -1 in N 0.956 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 0.956 * [taylor]: Taking taylor expansion of N in N 0.956 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 0.956 * [taylor]: Taking taylor expansion of 1.0 in N 0.956 * [taylor]: Taking taylor expansion of (/ 1 N) in N 0.956 * [taylor]: Taking taylor expansion of N in N 1.002 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 1.002 * [approximate]: Taking taylor expansion of (log (sqrt (/ (+ N 1.0) N))) in (N) around 0 1.002 * [taylor]: Taking taylor expansion of (log (sqrt (/ (+ N 1.0) N))) in N 1.002 * [taylor]: Taking taylor expansion of (sqrt (/ (+ N 1.0) N)) in N 1.002 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 1.002 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 1.002 * [taylor]: Taking taylor expansion of N in N 1.002 * [taylor]: Taking taylor expansion of 1.0 in N 1.002 * [taylor]: Taking taylor expansion of N in N 1.004 * [taylor]: Taking taylor expansion of (log (sqrt (/ (+ N 1.0) N))) in N 1.004 * [taylor]: Taking taylor expansion of (sqrt (/ (+ N 1.0) N)) in N 1.004 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 1.004 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 1.004 * [taylor]: Taking taylor expansion of N in N 1.004 * [taylor]: Taking taylor expansion of 1.0 in N 1.004 * [taylor]: Taking taylor expansion of N in N 1.022 * [approximate]: Taking taylor expansion of (log (sqrt (* N (+ (/ 1 N) 1.0)))) in (N) around 0 1.022 * [taylor]: Taking taylor expansion of (log (sqrt (* N (+ (/ 1 N) 1.0)))) in N 1.022 * [taylor]: Taking taylor expansion of (sqrt (* N (+ (/ 1 N) 1.0))) in N 1.022 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 1.022 * [taylor]: Taking taylor expansion of N in N 1.022 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 1.022 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.022 * [taylor]: Taking taylor expansion of N in N 1.022 * [taylor]: Taking taylor expansion of 1.0 in N 1.027 * [taylor]: Taking taylor expansion of (log (sqrt (* N (+ (/ 1 N) 1.0)))) in N 1.027 * [taylor]: Taking taylor expansion of (sqrt (* N (+ (/ 1 N) 1.0))) in N 1.027 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 1.027 * [taylor]: Taking taylor expansion of N in N 1.027 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 1.027 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.027 * [taylor]: Taking taylor expansion of N in N 1.027 * [taylor]: Taking taylor expansion of 1.0 in N 1.069 * [approximate]: Taking taylor expansion of (log (sqrt (* -1 (* N (- 1.0 (/ 1 N)))))) in (N) around 0 1.069 * [taylor]: Taking taylor expansion of (log (sqrt (* -1 (* N (- 1.0 (/ 1 N)))))) in N 1.069 * [taylor]: Taking taylor expansion of (sqrt (* -1 (* N (- 1.0 (/ 1 N))))) in N 1.069 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 1.069 * [taylor]: Taking taylor expansion of -1 in N 1.069 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 1.069 * [taylor]: Taking taylor expansion of N in N 1.069 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 1.069 * [taylor]: Taking taylor expansion of 1.0 in N 1.069 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.069 * [taylor]: Taking taylor expansion of N in N 1.076 * [taylor]: Taking taylor expansion of (log (sqrt (* -1 (* N (- 1.0 (/ 1 N)))))) in N 1.076 * [taylor]: Taking taylor expansion of (sqrt (* -1 (* N (- 1.0 (/ 1 N))))) in N 1.076 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 1.076 * [taylor]: Taking taylor expansion of -1 in N 1.076 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 1.076 * [taylor]: Taking taylor expansion of N in N 1.076 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 1.076 * [taylor]: Taking taylor expansion of 1.0 in N 1.076 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.076 * [taylor]: Taking taylor expansion of N in N 1.115 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 1.115 * [approximate]: Taking taylor expansion of (sqrt (/ (+ N 1.0) N)) in (N) around 0 1.115 * [taylor]: Taking taylor expansion of (sqrt (/ (+ N 1.0) N)) in N 1.115 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 1.115 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 1.115 * [taylor]: Taking taylor expansion of N in N 1.115 * [taylor]: Taking taylor expansion of 1.0 in N 1.115 * [taylor]: Taking taylor expansion of N in N 1.117 * [taylor]: Taking taylor expansion of (sqrt (/ (+ N 1.0) N)) in N 1.117 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 1.117 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 1.117 * [taylor]: Taking taylor expansion of N in N 1.117 * [taylor]: Taking taylor expansion of 1.0 in N 1.117 * [taylor]: Taking taylor expansion of N in N 1.124 * [approximate]: Taking taylor expansion of (sqrt (* N (+ (/ 1 N) 1.0))) in (N) around 0 1.124 * [taylor]: Taking taylor expansion of (sqrt (* N (+ (/ 1 N) 1.0))) in N 1.124 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 1.124 * [taylor]: Taking taylor expansion of N in N 1.124 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 1.124 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.124 * [taylor]: Taking taylor expansion of N in N 1.124 * [taylor]: Taking taylor expansion of 1.0 in N 1.128 * [taylor]: Taking taylor expansion of (sqrt (* N (+ (/ 1 N) 1.0))) in N 1.128 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 1.128 * [taylor]: Taking taylor expansion of N in N 1.128 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 1.128 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.128 * [taylor]: Taking taylor expansion of N in N 1.129 * [taylor]: Taking taylor expansion of 1.0 in N 1.136 * [approximate]: Taking taylor expansion of (sqrt (* -1 (* N (- 1.0 (/ 1 N))))) in (N) around 0 1.136 * [taylor]: Taking taylor expansion of (sqrt (* -1 (* N (- 1.0 (/ 1 N))))) in N 1.136 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 1.136 * [taylor]: Taking taylor expansion of -1 in N 1.137 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 1.137 * [taylor]: Taking taylor expansion of N in N 1.137 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 1.137 * [taylor]: Taking taylor expansion of 1.0 in N 1.137 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.137 * [taylor]: Taking taylor expansion of N in N 1.149 * [taylor]: Taking taylor expansion of (sqrt (* -1 (* N (- 1.0 (/ 1 N))))) in N 1.149 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 1.149 * [taylor]: Taking taylor expansion of -1 in N 1.149 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 1.149 * [taylor]: Taking taylor expansion of N in N 1.149 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 1.149 * [taylor]: Taking taylor expansion of 1.0 in N 1.149 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.149 * [taylor]: Taking taylor expansion of N in N 1.160 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 1.160 * [approximate]: Taking taylor expansion of (sqrt (/ (+ N 1.0) N)) in (N) around 0 1.160 * [taylor]: Taking taylor expansion of (sqrt (/ (+ N 1.0) N)) in N 1.161 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 1.161 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 1.161 * [taylor]: Taking taylor expansion of N in N 1.161 * [taylor]: Taking taylor expansion of 1.0 in N 1.161 * [taylor]: Taking taylor expansion of N in N 1.162 * [taylor]: Taking taylor expansion of (sqrt (/ (+ N 1.0) N)) in N 1.162 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 1.162 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 1.162 * [taylor]: Taking taylor expansion of N in N 1.162 * [taylor]: Taking taylor expansion of 1.0 in N 1.162 * [taylor]: Taking taylor expansion of N in N 1.169 * [approximate]: Taking taylor expansion of (sqrt (* N (+ (/ 1 N) 1.0))) in (N) around 0 1.169 * [taylor]: Taking taylor expansion of (sqrt (* N (+ (/ 1 N) 1.0))) in N 1.169 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 1.169 * [taylor]: Taking taylor expansion of N in N 1.169 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 1.169 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.169 * [taylor]: Taking taylor expansion of N in N 1.169 * [taylor]: Taking taylor expansion of 1.0 in N 1.173 * [taylor]: Taking taylor expansion of (sqrt (* N (+ (/ 1 N) 1.0))) in N 1.173 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 1.173 * [taylor]: Taking taylor expansion of N in N 1.173 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 1.173 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.173 * [taylor]: Taking taylor expansion of N in N 1.174 * [taylor]: Taking taylor expansion of 1.0 in N 1.181 * [approximate]: Taking taylor expansion of (sqrt (* -1 (* N (- 1.0 (/ 1 N))))) in (N) around 0 1.181 * [taylor]: Taking taylor expansion of (sqrt (* -1 (* N (- 1.0 (/ 1 N))))) in N 1.181 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 1.181 * [taylor]: Taking taylor expansion of -1 in N 1.181 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 1.181 * [taylor]: Taking taylor expansion of N in N 1.181 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 1.181 * [taylor]: Taking taylor expansion of 1.0 in N 1.181 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.181 * [taylor]: Taking taylor expansion of N in N 1.188 * [taylor]: Taking taylor expansion of (sqrt (* -1 (* N (- 1.0 (/ 1 N))))) in N 1.188 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 1.188 * [taylor]: Taking taylor expansion of -1 in N 1.188 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 1.188 * [taylor]: Taking taylor expansion of N in N 1.188 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 1.188 * [taylor]: Taking taylor expansion of 1.0 in N 1.188 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.188 * [taylor]: Taking taylor expansion of N in N 1.199 * * * [progress]: simplifying candidates 1.201 * [simplify]: Simplifying using # : (expm1 (log (sqrt (/ (+ N 1.0) N)))) (log1p (log (sqrt (/ (+ N 1.0) N)))) (log (* (cbrt (sqrt (/ (+ N 1.0) N))) (cbrt (sqrt (/ (+ N 1.0) N))))) (log (cbrt (sqrt (/ (+ N 1.0) N)))) (log (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N))))) (log (sqrt (cbrt (/ (+ N 1.0) N)))) (log (sqrt (sqrt (/ (+ N 1.0) N)))) (log (sqrt (sqrt (/ (+ N 1.0) N)))) (log (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt N) (cbrt N))))) (log (sqrt (/ (cbrt (+ N 1.0)) (cbrt N)))) (log (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N)))) (log (sqrt (/ (cbrt (+ N 1.0)) (sqrt N)))) (log (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) 1))) (log (sqrt (/ (cbrt (+ N 1.0)) N))) (log (sqrt (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))))) (log (sqrt (/ (sqrt (+ N 1.0)) (cbrt N)))) (log (sqrt (/ (sqrt (+ N 1.0)) (sqrt N)))) (log (sqrt (/ (sqrt (+ N 1.0)) (sqrt N)))) (log (sqrt (/ (sqrt (+ N 1.0)) 1))) (log (sqrt (/ (sqrt (+ N 1.0)) N))) (log (sqrt (/ 1 (* (cbrt N) (cbrt N))))) (log (sqrt (/ (+ N 1.0) (cbrt N)))) (log (sqrt (/ 1 (sqrt N)))) (log (sqrt (/ (+ N 1.0) (sqrt N)))) (log (sqrt (/ 1 1))) (log (sqrt (/ (+ N 1.0) N))) (log (sqrt (/ 1 (* (cbrt N) (cbrt N))))) (log (sqrt (/ (+ N 1.0) (cbrt N)))) (log (sqrt (/ 1 (sqrt N)))) (log (sqrt (/ (+ N 1.0) (sqrt N)))) (log (sqrt (/ 1 1))) (log (sqrt (/ (+ N 1.0) N))) (log (sqrt 1)) (log (sqrt (/ (+ N 1.0) N))) (log (sqrt (+ N 1.0))) (log (sqrt (/ 1 N))) (log (sqrt (sqrt (/ (+ N 1.0) N)))) (log (sqrt (sqrt (/ (+ N 1.0) N)))) (log 1) (log (sqrt (/ (+ N 1.0) N))) (log (sqrt (+ N 1.0))) (log (sqrt N)) (log (/ (+ N 1.0) N)) (log (sqrt (/ (+ N 1.0) N))) (log (/ (+ N 1.0) N)) (log (log (sqrt (/ (+ N 1.0) N)))) (exp (log (sqrt (/ (+ N 1.0) N)))) (* (cbrt (log (sqrt (/ (+ N 1.0) N)))) (cbrt (log (sqrt (/ (+ N 1.0) N))))) (cbrt (log (sqrt (/ (+ N 1.0) N)))) (* (* (log (sqrt (/ (+ N 1.0) N))) (log (sqrt (/ (+ N 1.0) N)))) (log (sqrt (/ (+ N 1.0) N)))) (sqrt (log (sqrt (/ (+ N 1.0) N)))) (sqrt (log (sqrt (/ (+ N 1.0) N)))) (expm1 (log (sqrt (/ (+ N 1.0) N)))) (log1p (log (sqrt (/ (+ N 1.0) N)))) (log (* (cbrt (sqrt (/ (+ N 1.0) N))) (cbrt (sqrt (/ (+ N 1.0) N))))) (log (cbrt (sqrt (/ (+ N 1.0) N)))) (log (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N))))) (log (sqrt (cbrt (/ (+ N 1.0) N)))) (log (sqrt (sqrt (/ (+ N 1.0) N)))) (log (sqrt (sqrt (/ (+ N 1.0) N)))) (log (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt N) (cbrt N))))) (log (sqrt (/ (cbrt (+ N 1.0)) (cbrt N)))) (log (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N)))) (log (sqrt (/ (cbrt (+ N 1.0)) (sqrt N)))) (log (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) 1))) (log (sqrt (/ (cbrt (+ N 1.0)) N))) (log (sqrt (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))))) (log (sqrt (/ (sqrt (+ N 1.0)) (cbrt N)))) (log (sqrt (/ (sqrt (+ N 1.0)) (sqrt N)))) (log (sqrt (/ (sqrt (+ N 1.0)) (sqrt N)))) (log (sqrt (/ (sqrt (+ N 1.0)) 1))) (log (sqrt (/ (sqrt (+ N 1.0)) N))) (log (sqrt (/ 1 (* (cbrt N) (cbrt N))))) (log (sqrt (/ (+ N 1.0) (cbrt N)))) (log (sqrt (/ 1 (sqrt N)))) (log (sqrt (/ (+ N 1.0) (sqrt N)))) (log (sqrt (/ 1 1))) (log (sqrt (/ (+ N 1.0) N))) (log (sqrt (/ 1 (* (cbrt N) (cbrt N))))) (log (sqrt (/ (+ N 1.0) (cbrt N)))) (log (sqrt (/ 1 (sqrt N)))) (log (sqrt (/ (+ N 1.0) (sqrt N)))) (log (sqrt (/ 1 1))) (log (sqrt (/ (+ N 1.0) N))) (log (sqrt 1)) (log (sqrt (/ (+ N 1.0) N))) (log (sqrt (+ N 1.0))) (log (sqrt (/ 1 N))) (log (sqrt (sqrt (/ (+ N 1.0) N)))) (log (sqrt (sqrt (/ (+ N 1.0) N)))) (log 1) (log (sqrt (/ (+ N 1.0) N))) (log (sqrt (+ N 1.0))) (log (sqrt N)) (log (/ (+ N 1.0) N)) (log (sqrt (/ (+ N 1.0) N))) (log (/ (+ N 1.0) N)) (log (log (sqrt (/ (+ N 1.0) N)))) (exp (log (sqrt (/ (+ N 1.0) N)))) (* (cbrt (log (sqrt (/ (+ N 1.0) N)))) (cbrt (log (sqrt (/ (+ N 1.0) N))))) (cbrt (log (sqrt (/ (+ N 1.0) N)))) (* (* (log (sqrt (/ (+ N 1.0) N))) (log (sqrt (/ (+ N 1.0) N)))) (log (sqrt (/ (+ N 1.0) N)))) (sqrt (log (sqrt (/ (+ N 1.0) N)))) (sqrt (log (sqrt (/ (+ N 1.0) N)))) (expm1 (sqrt (/ (+ N 1.0) N))) (log1p (sqrt (/ (+ N 1.0) N))) (log (sqrt (/ (+ N 1.0) N))) (exp (sqrt (/ (+ N 1.0) N))) (* (cbrt (sqrt (/ (+ N 1.0) N))) (cbrt (sqrt (/ (+ N 1.0) N)))) (cbrt (sqrt (/ (+ N 1.0) N))) (* (* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N))) (sqrt (/ (+ N 1.0) N))) (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))) (sqrt (cbrt (/ (+ N 1.0) N))) (sqrt (sqrt (/ (+ N 1.0) N))) (sqrt (sqrt (/ (+ N 1.0) N))) (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt N) (cbrt N)))) (sqrt (/ (cbrt (+ N 1.0)) (cbrt N))) (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))) (sqrt (/ (cbrt (+ N 1.0)) (sqrt N))) (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) 1)) (sqrt (/ (cbrt (+ N 1.0)) N)) (sqrt (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (sqrt (/ (sqrt (+ N 1.0)) (cbrt N))) (sqrt (/ (sqrt (+ N 1.0)) (sqrt N))) (sqrt (/ (sqrt (+ N 1.0)) (sqrt N))) (sqrt (/ (sqrt (+ N 1.0)) 1)) (sqrt (/ (sqrt (+ N 1.0)) N)) (sqrt (/ 1 (* (cbrt N) (cbrt N)))) (sqrt (/ (+ N 1.0) (cbrt N))) (sqrt (/ 1 (sqrt N))) (sqrt (/ (+ N 1.0) (sqrt N))) (sqrt (/ 1 1)) (sqrt (/ (+ N 1.0) N)) (sqrt (/ 1 (* (cbrt N) (cbrt N)))) (sqrt (/ (+ N 1.0) (cbrt N))) (sqrt (/ 1 (sqrt N))) (sqrt (/ (+ N 1.0) (sqrt N))) (sqrt (/ 1 1)) (sqrt (/ (+ N 1.0) N)) (sqrt 1) (sqrt (/ (+ N 1.0) N)) (sqrt (+ N 1.0)) (sqrt (/ 1 N)) (sqrt (+ N 1.0)) (sqrt N) (/ 1 2) (sqrt (sqrt (/ (+ N 1.0) N))) (sqrt (sqrt (/ (+ N 1.0) N))) (expm1 (sqrt (/ (+ N 1.0) N))) (log1p (sqrt (/ (+ N 1.0) N))) (log (sqrt (/ (+ N 1.0) N))) (exp (sqrt (/ (+ N 1.0) N))) (* (cbrt (sqrt (/ (+ N 1.0) N))) (cbrt (sqrt (/ (+ N 1.0) N)))) (cbrt (sqrt (/ (+ N 1.0) N))) (* (* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N))) (sqrt (/ (+ N 1.0) N))) (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))) (sqrt (cbrt (/ (+ N 1.0) N))) (sqrt (sqrt (/ (+ N 1.0) N))) (sqrt (sqrt (/ (+ N 1.0) N))) (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt N) (cbrt N)))) (sqrt (/ (cbrt (+ N 1.0)) (cbrt N))) (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))) (sqrt (/ (cbrt (+ N 1.0)) (sqrt N))) (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) 1)) (sqrt (/ (cbrt (+ N 1.0)) N)) (sqrt (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (sqrt (/ (sqrt (+ N 1.0)) (cbrt N))) (sqrt (/ (sqrt (+ N 1.0)) (sqrt N))) (sqrt (/ (sqrt (+ N 1.0)) (sqrt N))) (sqrt (/ (sqrt (+ N 1.0)) 1)) (sqrt (/ (sqrt (+ N 1.0)) N)) (sqrt (/ 1 (* (cbrt N) (cbrt N)))) (sqrt (/ (+ N 1.0) (cbrt N))) (sqrt (/ 1 (sqrt N))) (sqrt (/ (+ N 1.0) (sqrt N))) (sqrt (/ 1 1)) (sqrt (/ (+ N 1.0) N)) (sqrt (/ 1 (* (cbrt N) (cbrt N)))) (sqrt (/ (+ N 1.0) (cbrt N))) (sqrt (/ 1 (sqrt N))) (sqrt (/ (+ N 1.0) (sqrt N))) (sqrt (/ 1 1)) (sqrt (/ (+ N 1.0) N)) (sqrt 1) (sqrt (/ (+ N 1.0) N)) (sqrt (+ N 1.0)) (sqrt (/ 1 N)) (sqrt (+ N 1.0)) (sqrt N) (/ 1 2) (sqrt (sqrt (/ (+ N 1.0) N))) (sqrt (sqrt (/ (+ N 1.0) N))) (- (log +nan.0) (+ (* +nan.0 (pow N 2)) (- (* +nan.0 N)))) (- (+ (* 0.16666666666666666 (/ 1 (pow N 3))) (* 0.5 (/ 1 N))) (* 0.25 (/ 1 (pow N 2)))) (- (+ (* 0.16666666666666666 (/ 1 (pow N 3))) (* 0.5 (/ 1 N))) (* 0.25 (/ 1 (pow N 2)))) (- (log +nan.0) (+ (* +nan.0 (pow N 2)) (- (* +nan.0 N)))) (- (+ (* 0.16666666666666666 (/ 1 (pow N 3))) (* 0.5 (/ 1 N))) (* 0.25 (/ 1 (pow N 2)))) (- (+ (* 0.16666666666666666 (/ 1 (pow N 3))) (* 0.5 (/ 1 N))) (* 0.25 (/ 1 (pow N 2)))) (- (+ (* +nan.0 (pow N 2)) (- (+ (* +nan.0 N) (- +nan.0))))) (- (+ (* 0.5 (/ 1 N)) 1) (* 0.125 (/ 1 (pow N 2)))) (- (+ (* 0.5 (/ 1 N)) 1) (* 0.125 (/ 1 (pow N 2)))) (- (+ (* +nan.0 (pow N 2)) (- (+ (* +nan.0 N) (- +nan.0))))) (- (+ (* 0.5 (/ 1 N)) 1) (* 0.125 (/ 1 (pow N 2)))) (- (+ (* 0.5 (/ 1 N)) 1) (* 0.125 (/ 1 (pow N 2)))) 1.202 * [simplify]: Sending expressions to egg_math: (expm1 (log (sqrt (/ (+ h0 h1) h0)))) (log1p (log (sqrt (/ (+ h0 h1) h0)))) (log (* (cbrt (sqrt (/ (+ h0 h1) h0))) (cbrt (sqrt (/ (+ h0 h1) h0))))) (log (cbrt (sqrt (/ (+ h0 h1) h0)))) (log (sqrt (* (cbrt (/ (+ h0 h1) h0)) (cbrt (/ (+ h0 h1) h0))))) (log (sqrt (cbrt (/ (+ h0 h1) h0)))) (log (sqrt (sqrt (/ (+ h0 h1) h0)))) (log (sqrt (sqrt (/ (+ h0 h1) h0)))) (log (sqrt (/ (* (cbrt (+ h0 h1)) (cbrt (+ h0 h1))) (* (cbrt h0) (cbrt h0))))) (log (sqrt (/ (cbrt (+ h0 h1)) (cbrt h0)))) (log (sqrt (/ (* (cbrt (+ h0 h1)) (cbrt (+ h0 h1))) (sqrt h0)))) (log (sqrt (/ (cbrt (+ h0 h1)) (sqrt h0)))) (log (sqrt (/ (* (cbrt (+ h0 h1)) (cbrt (+ h0 h1))) 1))) (log (sqrt (/ 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[simplify]: iteration 0 : 205 enodes (cost 1000 ) 1.210 * * [simplify]: iteration 1 : 482 enodes (cost 936 ) 1.219 * * [simplify]: iteration 2 : 1903 enodes (cost 904 ) 1.259 * * [simplify]: iteration 3 : 5001 enodes (cost 886 ) 1.264 * [simplify]: Simplified to: (expm1 (log (sqrt (/ (+ N 1.0) N)))) (log1p (log (sqrt (/ (+ N 1.0) N)))) (* 2 (log (cbrt (sqrt (/ (+ N 1.0) N))))) (log (cbrt (sqrt (/ (+ N 1.0) N)))) (log (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N))))) (log (sqrt (cbrt (/ (+ N 1.0) N)))) (log (sqrt (sqrt (/ (+ N 1.0) N)))) (log (sqrt (sqrt (/ (+ N 1.0) N)))) (log (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt N) (cbrt N))))) (log (sqrt (/ (cbrt (+ N 1.0)) (cbrt N)))) (log (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N)))) (log (sqrt (/ (cbrt (+ N 1.0)) (sqrt N)))) (log (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) 1))) (log (sqrt (/ (cbrt (+ N 1.0)) N))) (log (sqrt (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))))) (log (sqrt (/ (sqrt (+ N 1.0)) (cbrt 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1.0)) (sqrt (/ 1 N)) (sqrt (+ N 1.0)) (sqrt N) 1/2 (sqrt (sqrt (/ (+ N 1.0) N))) (sqrt (sqrt (/ (+ N 1.0) N))) (expm1 (sqrt (/ (+ N 1.0) N))) (log1p (sqrt (/ (+ N 1.0) N))) (log (sqrt (/ (+ N 1.0) N))) (exp (sqrt (/ (+ N 1.0) N))) (* (cbrt (sqrt (/ (+ N 1.0) N))) (cbrt (sqrt (/ (+ N 1.0) N)))) (cbrt (sqrt (/ (+ N 1.0) N))) (pow (sqrt (/ (+ N 1.0) N)) 3) (fabs (cbrt (/ (+ N 1.0) N))) (sqrt (cbrt (/ (+ N 1.0) N))) (sqrt (sqrt (/ (+ N 1.0) N))) (sqrt (sqrt (/ (+ N 1.0) N))) (fabs (/ (cbrt (+ N 1.0)) (cbrt N))) (sqrt (/ (cbrt (+ N 1.0)) (cbrt N))) (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))) (sqrt (/ (cbrt (+ N 1.0)) (sqrt N))) (fabs (cbrt (+ N 1.0))) (sqrt (/ (cbrt (+ N 1.0)) N)) (sqrt (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (sqrt (/ (sqrt (+ N 1.0)) (cbrt N))) (sqrt (/ (sqrt (+ N 1.0)) (sqrt N))) (sqrt (/ (sqrt (+ N 1.0)) (sqrt N))) (sqrt (/ (sqrt (+ N 1.0)) 1)) (sqrt (/ (sqrt (+ N 1.0)) N)) (fabs (/ 1 (cbrt N))) (sqrt (/ (+ N 1.0) (cbrt N))) (sqrt (/ 1 (sqrt N))) (sqrt (/ (+ N 1.0) (sqrt N))) 1 (sqrt (/ (+ N 1.0) N)) (fabs (/ 1 (cbrt N))) (sqrt (/ (+ N 1.0) (cbrt N))) (sqrt (/ 1 (sqrt N))) (sqrt (/ (+ N 1.0) (sqrt N))) 1 (sqrt (/ (+ N 1.0) N)) 1 (sqrt (/ (+ N 1.0) N)) (sqrt (+ N 1.0)) (sqrt (/ 1 N)) (sqrt (+ N 1.0)) (sqrt N) 1/2 (sqrt (sqrt (/ (+ N 1.0) N))) (sqrt (sqrt (/ (+ N 1.0) N))) (fma (- +nan.0) (- (pow N 2) N) (log +nan.0)) (fma (/ 1 N) (- 0.5 (/ 0.25 N)) (/ 0.16666666666666666 (pow N 3))) (fma (/ 1 N) (- 0.5 (/ 0.25 N)) (/ 0.16666666666666666 (pow N 3))) (fma (- +nan.0) (- (pow N 2) N) (log +nan.0)) (fma (/ 1 N) (- 0.5 (/ 0.25 N)) (/ 0.16666666666666666 (pow N 3))) (fma (/ 1 N) (- 0.5 (/ 0.25 N)) (/ 0.16666666666666666 (pow N 3))) (fma (- (pow N 2)) +nan.0 (fma +nan.0 N (- +nan.0))) (fma (/ 1 N) (- 0.5 (/ 0.125 N)) 1) (fma (/ 1 N) (- 0.5 (/ 0.125 N)) 1) (fma (- (pow N 2)) +nan.0 (fma +nan.0 N (- +nan.0))) (fma (/ 1 N) (- 0.5 (/ 0.125 N)) 1) (fma (/ 1 N) (- 0.5 (/ 0.125 N)) 1) 1.264 * * * [progress]: adding candidates to table 1.584 * * [progress]: iteration 4 / 4 1.584 * * * [progress]: picking best candidate 1.588 * * * * [pick]: Picked # 1.588 * * * [progress]: localizing error 1.599 * * * [progress]: generating rewritten candidates 1.599 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1) 1.606 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2) 1.612 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 1.625 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2 1) 1.647 * * * [progress]: generating series expansions 1.647 * * * * [progress]: [ 1 / 4 ] generating series at (2 1) 1.647 * [approximate]: Taking taylor expansion of (log (sqrt (/ (+ N 1.0) N))) in (N) around 0 1.647 * [taylor]: Taking taylor expansion of (log (sqrt (/ (+ N 1.0) N))) in N 1.647 * [taylor]: Taking taylor expansion of (sqrt (/ (+ N 1.0) N)) in N 1.648 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 1.648 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 1.648 * [taylor]: Taking taylor expansion of N in N 1.648 * [taylor]: Taking taylor expansion of 1.0 in N 1.648 * [taylor]: Taking taylor expansion of N in N 1.650 * [taylor]: Taking taylor expansion of (log (sqrt (/ (+ N 1.0) N))) in N 1.650 * [taylor]: Taking taylor expansion of (sqrt (/ (+ N 1.0) N)) in N 1.650 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 1.650 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 1.650 * [taylor]: Taking taylor expansion of N in N 1.650 * [taylor]: Taking taylor expansion of 1.0 in N 1.650 * [taylor]: Taking taylor expansion of N in N 1.668 * [approximate]: Taking taylor expansion of (log (sqrt (* N (+ (/ 1 N) 1.0)))) in (N) around 0 1.669 * [taylor]: Taking taylor expansion of (log (sqrt (* N (+ (/ 1 N) 1.0)))) in N 1.669 * [taylor]: Taking taylor expansion of (sqrt (* N (+ (/ 1 N) 1.0))) in N 1.669 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 1.669 * [taylor]: Taking taylor expansion of N in N 1.669 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 1.669 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.669 * [taylor]: Taking taylor expansion of N in N 1.669 * [taylor]: Taking taylor expansion of 1.0 in N 1.673 * [taylor]: Taking taylor expansion of (log (sqrt (* N (+ (/ 1 N) 1.0)))) in N 1.673 * [taylor]: Taking taylor expansion of (sqrt (* N (+ (/ 1 N) 1.0))) in N 1.674 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 1.674 * [taylor]: Taking taylor expansion of N in N 1.674 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 1.674 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.674 * [taylor]: Taking taylor expansion of N in N 1.674 * [taylor]: Taking taylor expansion of 1.0 in N 1.714 * [approximate]: Taking taylor expansion of (log (sqrt (* -1 (* N (- 1.0 (/ 1 N)))))) in (N) around 0 1.715 * [taylor]: Taking taylor expansion of (log (sqrt (* -1 (* N (- 1.0 (/ 1 N)))))) in N 1.715 * [taylor]: Taking taylor expansion of (sqrt (* -1 (* N (- 1.0 (/ 1 N))))) in N 1.715 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 1.715 * [taylor]: Taking taylor expansion of -1 in N 1.715 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 1.715 * [taylor]: Taking taylor expansion of N in N 1.715 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 1.715 * [taylor]: Taking taylor expansion of 1.0 in N 1.715 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.715 * [taylor]: Taking taylor expansion of N in N 1.722 * [taylor]: Taking taylor expansion of (log (sqrt (* -1 (* N (- 1.0 (/ 1 N)))))) in N 1.722 * [taylor]: Taking taylor expansion of (sqrt (* -1 (* N (- 1.0 (/ 1 N))))) in N 1.722 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 1.722 * [taylor]: Taking taylor expansion of -1 in N 1.722 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 1.722 * [taylor]: Taking taylor expansion of N in N 1.722 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 1.722 * [taylor]: Taking taylor expansion of 1.0 in N 1.722 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.722 * [taylor]: Taking taylor expansion of N in N 1.761 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2) 1.761 * [approximate]: Taking taylor expansion of (log (/ (+ N 1.0) N)) in (N) around 0 1.761 * [taylor]: Taking taylor expansion of (log (/ (+ N 1.0) N)) in N 1.761 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 1.762 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 1.762 * [taylor]: Taking taylor expansion of N in N 1.762 * [taylor]: Taking taylor expansion of 1.0 in N 1.762 * [taylor]: Taking taylor expansion of N in N 1.762 * [taylor]: Taking taylor expansion of (log (/ (+ N 1.0) N)) in N 1.762 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 1.763 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 1.763 * [taylor]: Taking taylor expansion of N in N 1.763 * [taylor]: Taking taylor expansion of 1.0 in N 1.763 * [taylor]: Taking taylor expansion of N in N 1.781 * [approximate]: Taking taylor expansion of (log (* N (+ (/ 1 N) 1.0))) in (N) around 0 1.781 * [taylor]: Taking taylor expansion of (log (* N (+ (/ 1 N) 1.0))) in N 1.781 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 1.781 * [taylor]: Taking taylor expansion of N in N 1.781 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 1.781 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.781 * [taylor]: Taking taylor expansion of N in N 1.782 * [taylor]: Taking taylor expansion of 1.0 in N 1.783 * [taylor]: Taking taylor expansion of (log (* N (+ (/ 1 N) 1.0))) in N 1.783 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 1.783 * [taylor]: Taking taylor expansion of N in N 1.783 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 1.783 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.783 * [taylor]: Taking taylor expansion of N in N 1.784 * [taylor]: Taking taylor expansion of 1.0 in N 1.809 * [approximate]: Taking taylor expansion of (log (* -1 (* N (- 1.0 (/ 1 N))))) in (N) around 0 1.809 * [taylor]: Taking taylor expansion of (log (* -1 (* N (- 1.0 (/ 1 N))))) in N 1.809 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 1.809 * [taylor]: Taking taylor expansion of -1 in N 1.809 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 1.809 * [taylor]: Taking taylor expansion of N in N 1.809 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 1.809 * [taylor]: Taking taylor expansion of 1.0 in N 1.809 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.809 * [taylor]: Taking taylor expansion of N in N 1.812 * [taylor]: Taking taylor expansion of (log (* -1 (* N (- 1.0 (/ 1 N))))) in N 1.812 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 1.812 * [taylor]: Taking taylor expansion of -1 in N 1.812 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 1.812 * [taylor]: Taking taylor expansion of N in N 1.812 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 1.812 * [taylor]: Taking taylor expansion of 1.0 in N 1.812 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.812 * [taylor]: Taking taylor expansion of N in N 1.843 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 1.843 * [approximate]: Taking taylor expansion of (sqrt (/ (+ N 1.0) N)) in (N) around 0 1.843 * [taylor]: Taking taylor expansion of (sqrt (/ (+ N 1.0) N)) in N 1.843 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 1.843 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 1.843 * [taylor]: Taking taylor expansion of N in N 1.843 * [taylor]: Taking taylor expansion of 1.0 in N 1.843 * [taylor]: Taking taylor expansion of N in N 1.845 * [taylor]: Taking taylor expansion of (sqrt (/ (+ N 1.0) N)) in N 1.845 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 1.845 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 1.845 * [taylor]: Taking taylor expansion of N in N 1.845 * [taylor]: Taking taylor expansion of 1.0 in N 1.845 * [taylor]: Taking taylor expansion of N in N 1.852 * [approximate]: Taking taylor expansion of (sqrt (* N (+ (/ 1 N) 1.0))) in (N) around 0 1.852 * [taylor]: Taking taylor expansion of (sqrt (* N (+ (/ 1 N) 1.0))) in N 1.852 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 1.852 * [taylor]: Taking taylor expansion of N in N 1.852 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 1.852 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.852 * [taylor]: Taking taylor expansion of N in N 1.858 * [taylor]: Taking taylor expansion of 1.0 in N 1.863 * [taylor]: Taking taylor expansion of (sqrt (* N (+ (/ 1 N) 1.0))) in N 1.863 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 1.863 * [taylor]: Taking taylor expansion of N in N 1.863 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 1.863 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.863 * [taylor]: Taking taylor expansion of N in N 1.863 * [taylor]: Taking taylor expansion of 1.0 in N 1.871 * [approximate]: Taking taylor expansion of (sqrt (* -1 (* N (- 1.0 (/ 1 N))))) in (N) around 0 1.871 * [taylor]: Taking taylor expansion of (sqrt (* -1 (* N (- 1.0 (/ 1 N))))) in N 1.871 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 1.871 * [taylor]: Taking taylor expansion of -1 in N 1.871 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 1.871 * [taylor]: Taking taylor expansion of N in N 1.871 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 1.871 * [taylor]: Taking taylor expansion of 1.0 in N 1.871 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.871 * [taylor]: Taking taylor expansion of N in N 1.878 * [taylor]: Taking taylor expansion of (sqrt (* -1 (* N (- 1.0 (/ 1 N))))) in N 1.878 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 1.878 * [taylor]: Taking taylor expansion of -1 in N 1.878 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 1.878 * [taylor]: Taking taylor expansion of N in N 1.878 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 1.878 * [taylor]: Taking taylor expansion of 1.0 in N 1.878 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.878 * [taylor]: Taking taylor expansion of N in N 1.889 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2 1) 1.889 * [approximate]: Taking taylor expansion of (/ (+ N 1.0) N) in (N) around 0 1.889 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 1.889 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 1.889 * [taylor]: Taking taylor expansion of N in N 1.889 * [taylor]: Taking taylor expansion of 1.0 in N 1.889 * [taylor]: Taking taylor expansion of N in N 1.890 * [taylor]: Taking taylor expansion of (/ (+ N 1.0) N) in N 1.890 * [taylor]: Taking taylor expansion of (+ N 1.0) in N 1.890 * [taylor]: Taking taylor expansion of N in N 1.890 * [taylor]: Taking taylor expansion of 1.0 in N 1.890 * [taylor]: Taking taylor expansion of N in N 1.896 * [approximate]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in (N) around 0 1.896 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 1.896 * [taylor]: Taking taylor expansion of N in N 1.896 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 1.896 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.896 * [taylor]: Taking taylor expansion of N in N 1.896 * [taylor]: Taking taylor expansion of 1.0 in N 1.896 * [taylor]: Taking taylor expansion of (* N (+ (/ 1 N) 1.0)) in N 1.896 * [taylor]: Taking taylor expansion of N in N 1.896 * [taylor]: Taking taylor expansion of (+ (/ 1 N) 1.0) in N 1.896 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.896 * [taylor]: Taking taylor expansion of N in N 1.896 * [taylor]: Taking taylor expansion of 1.0 in N 1.909 * [approximate]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in (N) around 0 1.909 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 1.909 * [taylor]: Taking taylor expansion of -1 in N 1.909 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 1.909 * [taylor]: Taking taylor expansion of N in N 1.909 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 1.909 * [taylor]: Taking taylor expansion of 1.0 in N 1.909 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.909 * [taylor]: Taking taylor expansion of N in N 1.909 * [taylor]: Taking taylor expansion of (* -1 (* N (- 1.0 (/ 1 N)))) in N 1.909 * [taylor]: Taking taylor expansion of -1 in N 1.909 * [taylor]: Taking taylor expansion of (* N (- 1.0 (/ 1 N))) in N 1.909 * [taylor]: Taking taylor expansion of N in N 1.909 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 N)) in N 1.909 * [taylor]: Taking taylor expansion of 1.0 in N 1.909 * [taylor]: Taking taylor expansion of (/ 1 N) in N 1.909 * [taylor]: Taking taylor expansion of N in N 1.931 * * * [progress]: simplifying candidates 1.933 * [simplify]: Simplifying using # : (expm1 (log (sqrt (/ (+ N 1.0) N)))) (log1p (log (sqrt (/ (+ N 1.0) N)))) (log (* (cbrt (sqrt (/ (+ N 1.0) N))) (cbrt (sqrt (/ (+ N 1.0) N))))) (log (cbrt (sqrt (/ (+ N 1.0) N)))) (log (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N))))) (log (sqrt (cbrt (/ (+ N 1.0) N)))) (log (sqrt (sqrt (/ (+ N 1.0) N)))) (log (sqrt (sqrt (/ (+ N 1.0) N)))) (log (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt N) (cbrt N))))) (log (sqrt (/ (cbrt (+ N 1.0)) (cbrt N)))) (log (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N)))) (log (sqrt (/ (cbrt (+ N 1.0)) (sqrt N)))) (log (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) 1))) (log (sqrt (/ (cbrt (+ N 1.0)) N))) (log (sqrt (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))))) (log (sqrt (/ (sqrt (+ N 1.0)) (cbrt N)))) (log (sqrt (/ (sqrt (+ N 1.0)) (sqrt N)))) (log (sqrt (/ (sqrt (+ N 1.0)) (sqrt N)))) (log (sqrt (/ (sqrt (+ N 1.0)) 1))) (log (sqrt (/ (sqrt (+ N 1.0)) N))) (log (sqrt (/ 1 (* (cbrt N) (cbrt N))))) (log (sqrt (/ (+ N 1.0) (cbrt N)))) (log (sqrt (/ 1 (sqrt N)))) (log (sqrt (/ (+ N 1.0) (sqrt N)))) (log (sqrt (/ 1 1))) (log (sqrt (/ (+ N 1.0) N))) (log (sqrt (/ 1 (* (cbrt N) (cbrt N))))) (log (sqrt (/ (+ N 1.0) (cbrt N)))) (log (sqrt (/ 1 (sqrt N)))) (log (sqrt (/ (+ N 1.0) (sqrt N)))) (log (sqrt (/ 1 1))) (log (sqrt (/ (+ N 1.0) N))) (log (sqrt 1)) (log (sqrt (/ (+ N 1.0) N))) (log (sqrt (+ N 1.0))) (log (sqrt (/ 1 N))) (log (sqrt (sqrt (/ (+ N 1.0) N)))) (log (sqrt (sqrt (/ (+ N 1.0) N)))) (log 1) (log (sqrt (/ (+ N 1.0) N))) (log (sqrt (+ N 1.0))) (log (sqrt N)) (log (/ (+ N 1.0) N)) (log (sqrt (/ (+ N 1.0) N))) (log (/ (+ N 1.0) N)) (log (log (sqrt (/ (+ N 1.0) N)))) (exp (log (sqrt (/ (+ N 1.0) N)))) (* (cbrt (log (sqrt (/ (+ N 1.0) N)))) (cbrt (log (sqrt (/ (+ N 1.0) N))))) (cbrt (log (sqrt (/ (+ N 1.0) N)))) (* (* (log (sqrt (/ (+ N 1.0) N))) (log (sqrt (/ (+ N 1.0) N)))) (log (sqrt (/ (+ N 1.0) N)))) (sqrt (log (sqrt (/ (+ N 1.0) N)))) (sqrt (log (sqrt (/ (+ N 1.0) N)))) (expm1 (log (/ (+ N 1.0) N))) (log1p (log (/ (+ N 1.0) N))) (log (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))) (log (cbrt (/ (+ N 1.0) N))) (log (sqrt (/ (+ N 1.0) N))) (log (sqrt (/ (+ N 1.0) N))) (log (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt N) (cbrt N)))) (log (/ (cbrt (+ N 1.0)) (cbrt N))) (log (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))) (log (/ (cbrt (+ N 1.0)) (sqrt N))) (log (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) 1)) (log (/ (cbrt (+ N 1.0)) N)) (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))) (log (/ (sqrt (+ N 1.0)) (sqrt N))) (log (/ (sqrt (+ N 1.0)) (sqrt N))) (log (/ (sqrt (+ N 1.0)) 1)) (log (/ (sqrt (+ N 1.0)) N)) (log (/ 1 (* (cbrt N) (cbrt N)))) (log (/ (+ N 1.0) (cbrt N))) (log (/ 1 (sqrt N))) (log (/ (+ N 1.0) (sqrt N))) (log (/ 1 1)) (log (/ (+ N 1.0) N)) (log (/ 1 (* (cbrt N) (cbrt N)))) (log (/ (+ N 1.0) (cbrt N))) (log (/ 1 (sqrt N))) (log (/ (+ N 1.0) (sqrt N))) (log (/ 1 1)) (log (/ (+ N 1.0) N)) (log 1) (log (/ (+ N 1.0) N)) (log (+ N 1.0)) (log (/ 1 N)) (log (+ N 1.0)) (log N) (log (/ (+ N 1.0) N)) (log (log (/ (+ N 1.0) N))) (exp (log (/ (+ N 1.0) N))) (* (cbrt (log (/ (+ N 1.0) N))) (cbrt (log (/ (+ N 1.0) N)))) (cbrt (log (/ (+ N 1.0) N))) (* (* (log (/ (+ N 1.0) N)) (log (/ (+ N 1.0) N))) (log (/ (+ N 1.0) N))) (sqrt (log (/ (+ N 1.0) N))) (sqrt (log (/ (+ N 1.0) N))) (expm1 (sqrt (/ (+ N 1.0) N))) (log1p (sqrt (/ (+ N 1.0) N))) (log (sqrt (/ (+ N 1.0) N))) (exp (sqrt (/ (+ N 1.0) N))) (* (cbrt (sqrt (/ (+ N 1.0) N))) (cbrt (sqrt (/ (+ N 1.0) N)))) (cbrt (sqrt (/ (+ N 1.0) N))) (* (* (sqrt (/ (+ N 1.0) N)) (sqrt (/ (+ N 1.0) N))) (sqrt (/ (+ N 1.0) N))) (sqrt (* (cbrt (/ (+ N 1.0) N)) (cbrt (/ (+ N 1.0) N)))) (sqrt (cbrt (/ (+ N 1.0) N))) (sqrt (sqrt (/ (+ N 1.0) N))) (sqrt (sqrt (/ (+ N 1.0) N))) (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt N) (cbrt N)))) (sqrt (/ (cbrt (+ N 1.0)) (cbrt N))) (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))) (sqrt (/ (cbrt (+ N 1.0)) (sqrt N))) (sqrt (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) 1)) (sqrt (/ (cbrt (+ N 1.0)) N)) (sqrt (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (sqrt (/ (sqrt (+ N 1.0)) (cbrt N))) (sqrt (/ (sqrt (+ N 1.0)) (sqrt N))) (sqrt (/ (sqrt (+ N 1.0)) (sqrt N))) (sqrt (/ (sqrt (+ N 1.0)) 1)) (sqrt (/ (sqrt (+ N 1.0)) N)) (sqrt (/ 1 (* (cbrt N) (cbrt N)))) (sqrt (/ (+ N 1.0) (cbrt N))) (sqrt (/ 1 (sqrt N))) (sqrt (/ (+ N 1.0) (sqrt N))) (sqrt (/ 1 1)) (sqrt (/ (+ N 1.0) N)) (sqrt (/ 1 (* (cbrt N) (cbrt N)))) (sqrt (/ (+ N 1.0) (cbrt N))) (sqrt (/ 1 (sqrt N))) (sqrt (/ (+ N 1.0) (sqrt N))) (sqrt (/ 1 1)) (sqrt (/ (+ N 1.0) N)) (sqrt 1) (sqrt (/ (+ N 1.0) N)) (sqrt (+ N 1.0)) (sqrt (/ 1 N)) (sqrt (+ N 1.0)) (sqrt N) (/ 1 2) (sqrt (sqrt (/ (+ N 1.0) N))) (sqrt (sqrt (/ (+ N 1.0) N))) (expm1 (/ (+ N 1.0) N)) (log1p (/ (+ 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)) (- (+ N 1.0)) (- N) (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt N) (cbrt N))) (/ (cbrt (+ N 1.0)) (cbrt N)) (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N)) (/ (cbrt (+ N 1.0)) (sqrt N)) (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) 1) (/ (cbrt (+ N 1.0)) N) (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))) (/ (sqrt (+ N 1.0)) (cbrt N)) (/ (sqrt (+ N 1.0)) (sqrt N)) (/ (sqrt (+ N 1.0)) (sqrt N)) (/ (sqrt (+ N 1.0)) 1) (/ (sqrt (+ N 1.0)) N) (/ 1 (* (cbrt N) (cbrt N))) (/ (+ N 1.0) (cbrt N)) (/ 1 (sqrt N)) (/ (+ N 1.0) (sqrt N)) (/ 1 1) (/ (+ N 1.0) N) (/ 1 (* (cbrt N) (cbrt N))) (/ (+ N 1.0) (cbrt N)) (/ 1 (sqrt N)) (/ (+ N 1.0) (sqrt N)) (/ 1 1) (/ (+ N 1.0) N) (/ 1 N) (/ N (+ N 1.0)) (/ (+ N 1.0) (* (cbrt N) (cbrt N))) (/ (+ N 1.0) (sqrt N)) (/ (+ N 1.0) 1) (/ N (cbrt (+ N 1.0))) (/ N (sqrt (+ N 1.0))) (/ N (+ N 1.0)) (/ N (+ N 1.0)) (* N (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))) (* N (- N 1.0)) (- (log +nan.0) (+ (* +nan.0 (pow N 2)) (- (* +nan.0 N)))) (- (+ (* 0.16666666666666666 (/ 1 (pow N 3))) (* 0.5 (/ 1 N))) (* 0.25 (/ 1 (pow N 2)))) (- (+ (* 0.16666666666666666 (/ 1 (pow N 3))) (* 0.5 (/ 1 N))) (* 0.25 (/ 1 (pow N 2)))) (- (+ (* 1.0 N) (log 1.0)) (+ (* 1/2 (/ (pow N 2) (pow 1.0 2))) (log N))) (- (+ (* 0.3333333333333333 (/ 1 (pow N 3))) (* 1.0 (/ 1 N))) (* 0.5 (/ 1 (pow N 2)))) (- (+ (* 0.3333333333333333 (/ 1 (pow N 3))) (* 1.0 (/ 1 N))) (* 0.5 (/ 1 (pow N 2)))) (- (+ (* +nan.0 (pow N 2)) (- (+ (* +nan.0 N) (- +nan.0))))) (- (+ (* 0.5 (/ 1 N)) 1) (* 0.125 (/ 1 (pow N 2)))) (- (+ (* 0.5 (/ 1 N)) 1) (* 0.125 (/ 1 (pow N 2)))) (+ (* 1.0 (/ 1 N)) 1) (+ (* 1.0 (/ 1 N)) 1) (+ (* 1.0 (/ 1 N)) 1) 1.940 * [simplify]: Sending expressions to egg_math: (expm1 (log (sqrt (/ (+ h0 h1) h0)))) (log1p (log (sqrt (/ (+ h0 h1) h0)))) (log (* (cbrt (sqrt (/ (+ h0 h1) h0))) (cbrt (sqrt (/ (+ h0 h1) h0))))) (log (cbrt (sqrt (/ (+ h0 h1) h0)))) (log (sqrt (* (cbrt (/ (+ h0 h1) h0)) (cbrt (/ (+ h0 h1) h0))))) (log (sqrt (cbrt (/ (+ h0 h1) h0)))) (log 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(log (sqrt (/ 1 1))) (log (sqrt (/ (+ h0 h1) h0))) (log (sqrt 1)) (log (sqrt (/ (+ h0 h1) h0))) (log (sqrt (+ h0 h1))) (log (sqrt (/ 1 h0))) (log (sqrt (sqrt (/ (+ h0 h1) h0)))) (log (sqrt (sqrt (/ (+ h0 h1) h0)))) (log 1) (log (sqrt (/ (+ h0 h1) h0))) (log (sqrt (+ h0 h1))) (log (sqrt h0)) (log (/ (+ h0 h1) h0)) (log (sqrt (/ (+ h0 h1) h0))) (log (/ (+ h0 h1) h0)) (log (log (sqrt (/ (+ h0 h1) h0)))) (exp (log (sqrt (/ (+ h0 h1) h0)))) (* (cbrt (log (sqrt (/ (+ h0 h1) h0)))) (cbrt (log (sqrt (/ (+ h0 h1) h0))))) (cbrt (log (sqrt (/ (+ h0 h1) h0)))) (* (* (log (sqrt (/ (+ h0 h1) h0))) (log (sqrt (/ (+ h0 h1) h0)))) (log (sqrt (/ (+ h0 h1) h0)))) (sqrt (log (sqrt (/ (+ h0 h1) h0)))) (sqrt (log (sqrt (/ (+ h0 h1) h0)))) (expm1 (log (/ (+ h0 h1) h0))) (log1p (log (/ (+ h0 h1) h0))) (log (* (cbrt (/ (+ h0 h1) h0)) (cbrt (/ (+ h0 h1) h0)))) (log (cbrt (/ (+ h0 h1) h0))) (log (sqrt (/ (+ h0 h1) h0))) (log (sqrt (/ (+ h0 h1) h0))) (log (/ (* (cbrt (+ h0 h1)) (cbrt (+ h0 h1))) (* (cbrt h0) 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(/ (* (cbrt (+ h0 h1)) (cbrt (+ h0 h1))) (* (cbrt h0) (cbrt h0))) (/ (cbrt (+ h0 h1)) (cbrt h0)) (/ (* (cbrt (+ h0 h1)) (cbrt (+ h0 h1))) (sqrt h0)) (/ (cbrt (+ h0 h1)) (sqrt h0)) (/ (* (cbrt (+ h0 h1)) (cbrt (+ h0 h1))) 1) (/ (cbrt (+ h0 h1)) h0) (/ (sqrt (+ h0 h1)) (* (cbrt h0) (cbrt h0))) (/ (sqrt (+ h0 h1)) (cbrt h0)) (/ (sqrt (+ h0 h1)) (sqrt h0)) (/ (sqrt (+ h0 h1)) (sqrt h0)) (/ (sqrt (+ h0 h1)) 1) (/ (sqrt (+ h0 h1)) h0) (/ 1 (* (cbrt h0) (cbrt h0))) (/ (+ h0 h1) (cbrt h0)) (/ 1 (sqrt h0)) (/ (+ h0 h1) (sqrt h0)) (/ 1 1) (/ (+ h0 h1) h0) (/ 1 (* (cbrt h0) (cbrt h0))) (/ (+ h0 h1) (cbrt h0)) (/ 1 (sqrt h0)) (/ (+ h0 h1) (sqrt h0)) (/ 1 1) (/ (+ h0 h1) h0) (/ 1 h0) (/ h0 (+ h0 h1)) (/ (+ h0 h1) (* (cbrt h0) (cbrt h0))) (/ (+ h0 h1) (sqrt h0)) (/ (+ h0 h1) 1) (/ h0 (cbrt (+ h0 h1))) (/ h0 (sqrt (+ h0 h1))) (/ h0 (+ h0 h1)) (/ h0 (+ h0 h1)) (* h0 (+ (* h0 h0) (- (* h1 h1) (* h0 h1)))) (* h0 (- h0 h1)) (- (log h2) (+ (* h2 (pow h0 2)) (- (* h2 h0)))) (- (+ (* h3 (/ 1 (pow h0 3))) (* h4 (/ 1 h0))) (* h5 (/ 1 (pow h0 2)))) (- (+ (* h3 (/ 1 (pow h0 3))) (* h4 (/ 1 h0))) (* h5 (/ 1 (pow h0 2)))) (- (+ (* h1 h0) (log h1)) (+ (* 1/2 (/ (pow h0 2) (pow h1 2))) (log h0))) (- (+ (* h6 (/ 1 (pow h0 3))) (* h1 (/ 1 h0))) (* h4 (/ 1 (pow h0 2)))) (- (+ (* h6 (/ 1 (pow h0 3))) (* h1 (/ 1 h0))) (* h4 (/ 1 (pow h0 2)))) (- (+ (* h2 (pow h0 2)) (- (+ (* h2 h0) (- h2))))) (- (+ (* h4 (/ 1 h0)) 1) (* h7 (/ 1 (pow h0 2)))) (- (+ (* h4 (/ 1 h0)) 1) (* h7 (/ 1 (pow h0 2)))) (+ (* h1 (/ 1 h0)) 1) (+ (* h1 (/ 1 h0)) 1) (+ (* h1 (/ 1 h0)) 1) 1.945 * * [simplify]: iteration 0 : 377 enodes (cost 883 ) 1.951 * * [simplify]: iteration 1 : 1125 enodes (cost 826 ) 1.970 * * [simplify]: iteration 2 : 4899 enodes (cost 799 ) 2.072 * * [simplify]: iteration 3 : 5001 enodes (cost 798 ) 2.076 * [simplify]: Simplified to: (expm1 (log (sqrt (/ (+ N 1.0) N)))) (log1p (log (sqrt (/ (+ N 1.0) N)))) (* 2 (log (cbrt (sqrt (/ (+ N 1.0) N))))) (log (cbrt (sqrt (/ (+ N 1.0) N)))) (log (sqrt (* (cbrt (/ (+ N 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(+ N 1.0) N) (/ 1 N) (/ N (+ N 1.0)) (/ (+ N 1.0) (* (cbrt N) (cbrt N))) (/ (+ N 1.0) (sqrt N)) (+ N 1.0) (/ N (cbrt (+ N 1.0))) (/ N (sqrt (+ N 1.0))) (/ N (+ N 1.0)) (/ N (+ N 1.0)) (fma N (* 1.0 (- 1.0 N)) (pow N 3)) (* N (- N 1.0)) (+ (- (log +nan.0) (* +nan.0 (pow N 2))) (* +nan.0 N)) (+ (* (/ 1 (pow N 2)) (- (/ 0.16666666666666666 N) 0.25)) (/ 0.5 N)) (+ (* (/ 1 (pow N 2)) (- (/ 0.16666666666666666 N) 0.25)) (/ 0.5 N)) (fma 1.0 N (- (log 1.0) (fma 1/2 (/ (pow N 2) (pow 1.0 2)) (log N)))) (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)) (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)) (fma (- (pow N 2)) +nan.0 (fma +nan.0 N (- +nan.0))) (- 1 (- (/ (/ 0.125 N) N) (/ 0.5 N))) (- 1 (- (/ (/ 0.125 N) N) (/ 0.5 N))) (fma 1.0 (/ 1 N) 1) (fma 1.0 (/ 1 N) 1) (fma 1.0 (/ 1 N) 1) 2.077 * * * [progress]: adding candidates to table 2.404 * [progress]: [Phase 3 of 3] Extracting. 2.405 * * [regime]: Finding splitpoints for: (# # #) 2.405 * * * [regime-changes]: Trying 1 branch expressions: (N) 2.405 * * * * [regimes]: Trying to branch on N from (# # #) 2.427 * * * [regime]: Found split indices: #