23.678 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.016 * * * [progress]: [2/2] Setting up program. 0.018 * [progress]: [Phase 2 of 3] Improving. 0.019 * [simplify]: Simplifying using # : (/ a (- (acos a))) 0.020 * * [simplify]: iteration 0 : 4 enodes (cost 5 ) 0.020 * * [simplify]: iteration done : 4 enodes (cost 5 ) 0.020 * [simplify]: Simplified to: (/ a (- (acos a))) 0.020 * * [progress]: iteration 1 / 4 0.020 * * * [progress]: picking best candidate 0.022 * * * * [pick]: Picked # 0.022 * * * [progress]: localizing error 0.026 * * * [progress]: generating rewritten candidates 0.026 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.032 * * * [progress]: generating series expansions 0.032 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.032 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.032 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.032 * [taylor]: Taking taylor expansion of -1 in a 0.032 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.032 * [taylor]: Taking taylor expansion of a in a 0.032 * [taylor]: Taking taylor expansion of (acos a) in a 0.033 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.033 * [taylor]: Taking taylor expansion of -1 in a 0.033 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.033 * [taylor]: Taking taylor expansion of a in a 0.033 * [taylor]: Taking taylor expansion of (acos a) in a 0.045 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.045 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.045 * [taylor]: Taking taylor expansion of -1 in a 0.045 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.045 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.045 * [taylor]: Taking taylor expansion of a in a 0.045 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.045 * [taylor]: Taking taylor expansion of -1 in a 0.045 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.045 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.046 * [taylor]: Taking taylor expansion of a in a 0.052 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 0.052 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.052 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.052 * [taylor]: Taking taylor expansion of a in a 0.052 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.053 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.053 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.053 * [taylor]: Taking taylor expansion of a in a 0.053 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.062 * * * [progress]: simplifying candidates 0.063 * [simplify]: Simplifying using # : (expm1 (/ a (- (acos a)))) (log1p (/ a (- (acos a)))) (- (log a) (log (- (acos a)))) (log (/ a (- (acos a)))) (exp (/ a (- (acos a)))) (/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a)))) (* (cbrt (/ a (- (acos a)))) (cbrt (/ a (- (acos a))))) (cbrt (/ a (- (acos a)))) (* (* (/ a (- (acos a))) (/ a (- (acos a)))) (/ a (- (acos a)))) (sqrt (/ a (- (acos a)))) (sqrt (/ a (- (acos a)))) (- a) (- (- (acos a))) (/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ (cbrt a) (cbrt (- (acos a)))) (/ (* (cbrt a) (cbrt a)) (sqrt (- (acos a)))) (/ (cbrt a) (sqrt (- (acos a)))) (/ (* (cbrt a) (cbrt a)) 1) (/ (cbrt a) (- (acos a))) (/ (* (cbrt a) (cbrt a)) -1) (/ (cbrt a) (acos a)) (/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (cbrt a) (cbrt (acos a))) (/ (* (cbrt a) (cbrt a)) (- (sqrt (acos a)))) (/ (cbrt a) (sqrt (acos a))) (/ (* (cbrt a) (cbrt a)) (- 1)) (/ (cbrt a) (acos a)) (/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (cbrt a) (- (cbrt (acos a)))) (/ (* (cbrt a) (cbrt a)) (sqrt (acos a))) (/ (cbrt a) (- (sqrt (acos a)))) (/ (* (cbrt a) (cbrt a)) 1) (/ (cbrt a) (- (acos a))) (/ (sqrt a) (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ (sqrt a) (cbrt (- (acos a)))) (/ (sqrt a) (sqrt (- (acos a)))) (/ (sqrt a) (sqrt (- (acos a)))) (/ (sqrt a) 1) (/ (sqrt a) (- (acos a))) (/ (sqrt a) -1) (/ (sqrt a) (acos a)) (/ (sqrt a) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt a) (cbrt (acos a))) (/ (sqrt a) (- (sqrt (acos a)))) (/ (sqrt a) (sqrt (acos a))) (/ (sqrt a) (- 1)) (/ (sqrt a) (acos a)) (/ (sqrt a) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (sqrt a) (- (cbrt (acos a)))) (/ (sqrt a) (sqrt (acos a))) (/ (sqrt a) (- (sqrt (acos a)))) (/ (sqrt a) 1) (/ (sqrt a) (- (acos a))) (/ 1 (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ a (cbrt (- (acos a)))) (/ 1 (sqrt (- (acos a)))) (/ a (sqrt (- (acos a)))) (/ 1 1) (/ a (- (acos a))) (/ 1 -1) (/ a (acos a)) (/ 1 (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ a (cbrt (acos a))) (/ 1 (- (sqrt (acos a)))) (/ a (sqrt (acos a))) (/ 1 (- 1)) (/ a (acos a)) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ a (- (cbrt (acos a)))) (/ 1 (sqrt (acos a))) (/ a (- (sqrt (acos a)))) (/ 1 1) (/ a (- (acos a))) (/ 1 (- (acos a))) (/ (- (acos a)) a) (/ a (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ a (sqrt (- (acos a)))) (/ a 1) (/ a -1) (/ a (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ a (- (sqrt (acos a)))) (/ a (- 1)) (/ a (* (cbrt (acos a)) (cbrt (acos a)))) (/ a (sqrt (acos a))) (/ a 1) (/ (- (acos a)) (cbrt a)) (/ (- (acos a)) (sqrt a)) (/ (- (acos a)) a) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) 0.066 * * [simplify]: iteration 0 : 96 enodes (cost 613 ) 0.083 * * [simplify]: iteration 1 : 169 enodes (cost 581 ) 0.121 * * [simplify]: iteration 2 : 480 enodes (cost 561 ) 0.245 * * [simplify]: iteration 3 : 1406 enodes (cost 557 ) 0.941 * * [simplify]: iteration 4 : 3300 enodes (cost 556 ) 2.704 * * [simplify]: iteration done : 5001 enodes (cost 556 ) 2.704 * [simplify]: Simplified to: (expm1 (/ a (- (acos a)))) (log1p (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (exp (/ a (- (acos a)))) (pow (/ a (- (acos a))) 3) (* (cbrt (/ a (- (acos a)))) (cbrt (/ a (- (acos a))))) (cbrt (/ a (- (acos a)))) (pow (/ a (- (acos a))) 3) (sqrt (/ a (- (acos a)))) (sqrt (/ a (- (acos a)))) (- a) (acos a) (/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ (cbrt a) (cbrt (- (acos a)))) (/ (* (cbrt a) (cbrt a)) (sqrt (- (acos a)))) (/ (cbrt a) (sqrt (- (acos a)))) (* (cbrt a) (cbrt a)) (/ (cbrt a) (- (acos a))) (- (* (cbrt a) (cbrt a))) (/ (cbrt a) (acos a)) (/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (cbrt a) (cbrt (acos a))) (/ (* (cbrt a) (cbrt a)) (- (sqrt (acos a)))) (/ (cbrt a) (sqrt (acos a))) (- (* (cbrt a) (cbrt a))) (/ (cbrt a) (acos a)) (/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (cbrt a) (- (cbrt (acos a)))) (/ (* (cbrt a) (cbrt a)) (sqrt (acos a))) (/ (cbrt a) (- (sqrt (acos a)))) (* (cbrt a) (cbrt a)) (/ (cbrt a) (- (acos a))) (/ (sqrt a) (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ (sqrt a) (cbrt (- (acos a)))) (/ (sqrt a) (sqrt (- (acos a)))) (/ (sqrt a) (sqrt (- (acos a)))) (sqrt a) (/ (sqrt a) (- (acos a))) (- (sqrt a)) (/ (sqrt a) (acos a)) (/ (sqrt a) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt a) (cbrt (acos a))) (/ (sqrt a) (- (sqrt (acos a)))) (/ (sqrt a) (sqrt (acos a))) (- (sqrt a)) (/ (sqrt a) (acos a)) (/ (sqrt a) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (sqrt a) (- (cbrt (acos a)))) (/ (sqrt a) (sqrt (acos a))) (/ (sqrt a) (- (sqrt (acos a)))) (sqrt a) (/ (sqrt a) (- (acos a))) (/ 1 (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ a (cbrt (- (acos a)))) (/ 1 (sqrt (- (acos a)))) (/ a (sqrt (- (acos a)))) 1 (/ a (- (acos a))) -1 (/ a (acos a)) (/ 1 (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ a (cbrt (acos a))) (/ 1 (- (sqrt (acos a)))) (/ a (sqrt (acos a))) -1 (/ a (acos a)) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ a (- (cbrt (acos a)))) (/ 1 (sqrt (acos a))) (/ a (- (sqrt (acos a)))) 1 (/ a (- (acos a))) (/ -1 (acos a)) (/ (- (acos a)) a) (/ a (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ a (sqrt (- (acos a)))) a (- a) (/ a (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ a (- (sqrt (acos a)))) (- a) (/ a (* (cbrt (acos a)) (cbrt (acos a)))) (/ a (sqrt (acos a))) a (/ (- (acos a)) (cbrt a)) (/ (- (acos a)) (sqrt a)) (/ (- (acos a)) a) (/ a (- (acos a))) (/ a (- (acos a))) (/ a (- (acos a))) 2.705 * * * [progress]: adding candidates to table 2.814 * * [progress]: iteration 2 / 4 2.814 * * * [progress]: picking best candidate 2.828 * * * * [pick]: Picked # 2.828 * * * [progress]: localizing error 2.834 * * * [progress]: generating rewritten candidates 2.834 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 2.848 * * * * [progress]: [ 2 / 2 ] rewriting at (2 2) 2.863 * * * [progress]: generating series expansions 2.863 * * * * [progress]: [ 1 / 2 ] generating series at (2) 2.863 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 2.863 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 2.863 * [taylor]: Taking taylor expansion of -1 in a 2.863 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 2.863 * [taylor]: Taking taylor expansion of a in a 2.863 * [taylor]: Taking taylor expansion of (acos a) in a 2.863 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 2.864 * [taylor]: Taking taylor expansion of -1 in a 2.864 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 2.864 * [taylor]: Taking taylor expansion of a in a 2.864 * [taylor]: Taking taylor expansion of (acos a) in a 2.872 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 2.872 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 2.872 * [taylor]: Taking taylor expansion of -1 in a 2.872 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 2.872 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 2.872 * [taylor]: Taking taylor expansion of a in a 2.872 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 2.872 * [taylor]: Taking taylor expansion of -1 in a 2.872 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 2.872 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 2.872 * [taylor]: Taking taylor expansion of a in a 2.879 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 2.879 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 2.879 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 2.879 * [taylor]: Taking taylor expansion of a in a 2.879 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 2.879 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 2.879 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 2.879 * [taylor]: Taking taylor expansion of a in a 2.879 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 2.889 * * * * [progress]: [ 2 / 2 ] generating series at (2 2) 2.889 * [approximate]: Taking taylor expansion of (* -1 (/ (acos a) a)) in (a) around 0 2.889 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 2.889 * [taylor]: Taking taylor expansion of -1 in a 2.889 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 2.889 * [taylor]: Taking taylor expansion of (acos a) in a 2.889 * [taylor]: Taking taylor expansion of a in a 2.889 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 2.889 * [taylor]: Taking taylor expansion of -1 in a 2.889 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 2.889 * [taylor]: Taking taylor expansion of (acos a) in a 2.889 * [taylor]: Taking taylor expansion of a in a 2.905 * [approximate]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in (a) around 0 2.905 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 2.905 * [taylor]: Taking taylor expansion of -1 in a 2.905 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 2.905 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 2.905 * [taylor]: Taking taylor expansion of a in a 2.905 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 2.905 * [taylor]: Taking taylor expansion of -1 in a 2.905 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 2.905 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 2.905 * [taylor]: Taking taylor expansion of a in a 2.917 * [approximate]: Taking taylor expansion of (* a (acos (/ -1 a))) in (a) around 0 2.917 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 2.917 * [taylor]: Taking taylor expansion of a in a 2.917 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 2.917 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 2.917 * [taylor]: Taking taylor expansion of a in a 2.917 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 2.925 * * * [progress]: simplifying candidates 2.932 * [simplify]: Simplifying using # : (expm1 (/ 1 (/ (- (acos a)) a))) (log1p (/ 1 (/ (- (acos a)) a))) (- 1) (- (- (log (- (acos a))) (log a))) (- (log (/ (- (acos a)) a))) (- 0 (- (log (- (acos a))) (log a))) (- 0 (log (/ (- (acos a)) a))) (- (log 1) (- (log (- (acos a))) (log a))) (- (log 1) (log (/ (- (acos a)) a))) (log (/ 1 (/ (- (acos a)) a))) (exp (/ 1 (/ (- (acos a)) a))) (/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a))) (/ (* (* 1 1) 1) (* (* (/ (- (acos a)) a) (/ (- (acos a)) a)) (/ (- (acos a)) a))) (* (cbrt (/ 1 (/ (- (acos a)) a))) (cbrt (/ 1 (/ (- (acos a)) a)))) (cbrt (/ 1 (/ (- (acos a)) a))) (* (* (/ 1 (/ (- (acos a)) a)) (/ 1 (/ (- (acos a)) a))) (/ 1 (/ (- (acos a)) a))) (sqrt (/ 1 (/ (- (acos a)) a))) (sqrt (/ 1 (/ (- (acos a)) a))) (- 1) (- (/ (- (acos a)) a)) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a)))) (/ (cbrt 1) (cbrt (/ (- (acos a)) a))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (/ (- (acos a)) a))) (/ (cbrt 1) (sqrt (/ (- (acos a)) a))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- (acos a))) (cbrt (- (acos a)))) (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (cbrt (- (acos a))) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- (acos a))) (cbrt (- (acos a)))) (sqrt a))) (/ (cbrt 1) (/ (cbrt (- (acos a))) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- (acos a))) (cbrt (- (acos a)))) 1)) (/ (cbrt 1) (/ (cbrt (- (acos a))) a)) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (- (acos a))) (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (sqrt (- (acos a))) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (- (acos a))) (sqrt a))) (/ (cbrt 1) (/ (sqrt (- (acos a))) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (- (acos a))) 1)) (/ (cbrt 1) (/ (sqrt (- (acos a))) a)) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (- (acos a)) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt a))) (/ (cbrt 1) (/ (- (acos a)) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 1)) (/ (cbrt 1) (/ (- (acos a)) a)) (/ (* (cbrt 1) (cbrt 1)) (/ -1 (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (acos a) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ -1 (sqrt a))) (/ (cbrt 1) (/ (acos a) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ -1 1)) (/ (cbrt 1) (/ (acos a) a)) (/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (cbrt (acos a)) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt a))) (/ (cbrt 1) (/ (cbrt (acos a)) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) 1)) (/ (cbrt 1) (/ (cbrt (acos a)) a)) (/ (* (cbrt 1) (cbrt 1)) (/ (- (sqrt (acos a))) (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (sqrt (acos a)) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (- (sqrt (acos a))) (sqrt a))) (/ (cbrt 1) (/ (sqrt (acos a)) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (- (sqrt (acos a))) 1)) (/ (cbrt 1) (/ (sqrt (acos a)) a)) (/ (* (cbrt 1) (cbrt 1)) (/ (- 1) (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (acos a) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (- 1) (sqrt a))) (/ (cbrt 1) (/ (acos a) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (- 1) 1)) (/ (cbrt 1) (/ (acos a) a)) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (acos a)) (cbrt (acos a))) (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (- (cbrt (acos a))) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (acos a)) (cbrt (acos a))) (sqrt a))) (/ (cbrt 1) (/ (- (cbrt (acos a))) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (acos a)) (cbrt (acos a))) 1)) (/ (cbrt 1) (/ (- (cbrt (acos a))) a)) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (acos a)) (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (- (sqrt (acos a))) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (acos a)) (sqrt a))) (/ (cbrt 1) (/ (- (sqrt (acos a))) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (acos a)) 1)) (/ (cbrt 1) (/ (- (sqrt (acos a))) a)) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt a) (cbrt a)))) (/ (cbrt 1) (/ (- (acos a)) (cbrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt a))) (/ (cbrt 1) (/ (- (acos a)) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 1)) (/ (cbrt 1) 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1 (* (cbrt a) (cbrt a))) (/ (- (acos a)) (cbrt a)) (/ 1 (sqrt a)) (/ (- (acos a)) (sqrt a)) (/ 1 1) (/ (- (acos a)) a) (/ 1 a) (/ a (- (acos a))) (/ (acos a) a) (/ (- (acos a)) (* (cbrt a) (cbrt a))) (/ (- (acos a)) (sqrt a)) (/ (- (acos a)) 1) (/ a (cbrt (- (acos a)))) (/ a (sqrt (- (acos a)))) (/ a (- (acos a))) (/ a (acos a)) (/ a (cbrt (acos a))) (/ a (sqrt (acos a))) (/ a (acos a)) (/ a (- (cbrt (acos a)))) (/ a (- (sqrt (acos a)))) (/ a (- (acos a))) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) (* -1 (/ (acos a) a)) (* -1 (/ (acos a) a)) (* -1 (/ (acos a) a)) 2.942 * * [simplify]: iteration 0 : 292 enodes (cost 3194 ) 3.006 * * [simplify]: iteration 1 : 674 enodes (cost 2774 ) 3.224 * * [simplify]: iteration 2 : 2302 enodes (cost 2325 ) 4.807 * * [simplify]: iteration done : 5000 enodes (cost 2314 ) 4.808 * [simplify]: Simplified to: (expm1 (- (/ a (acos a)))) (log1p (- (/ a (acos a)))) -1 (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos 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(cbrt a)) (- (sqrt (acos a)))) (/ (sqrt a) (- (sqrt (acos a)))) (/ 1 (- (sqrt (acos a)))) (- (* (cbrt a) (cbrt a))) (- (sqrt a)) -1 (/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (sqrt a) (* (cbrt (acos a)) (cbrt (acos a)))) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ (* (cbrt a) (cbrt a)) (sqrt (acos a))) (/ (sqrt a) (sqrt (acos a))) (/ 1 (sqrt (acos a))) (* (cbrt a) (cbrt a)) (sqrt a) 1 1 (/ -1 (acos a)) (/ (- (acos a)) a) (/ (- (acos a)) a) (/ (- (acos a)) a) (/ -1 (acos a)) (expm1 (/ (- (acos a)) a)) (log1p (/ (- (acos a)) a)) (log (/ (- (acos a)) a)) (log (/ (- (acos a)) a)) (exp (/ (- (acos a)) a)) (pow (/ (- (acos a)) a) 3) (* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a))) (cbrt (/ (- (acos a)) a)) (pow (/ (- (acos a)) a) 3) (sqrt (/ (- (acos a)) a)) (sqrt (/ (- (acos a)) a)) (acos a) (- a) 0 (/ (acos a) a) (/ (* (cbrt (- (acos a))) (cbrt (- (acos a)))) (* (cbrt a) (cbrt a))) (/ (cbrt (- (acos a))) (cbrt a)) (* (/ (cbrt (- (acos a))) (sqrt a)) (cbrt (- (acos a)))) (/ (cbrt (- (acos a))) (sqrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a)))) (/ (cbrt (- (acos a))) a) (/ (sqrt (- (acos a))) (* (cbrt a) (cbrt a))) (/ (sqrt (- (acos a))) (cbrt a)) (/ (sqrt (- (acos a))) (sqrt a)) (/ (sqrt (- (acos a))) (sqrt a)) (sqrt (- (acos a))) (/ (sqrt (- (acos a))) a) (/ 1 (* (cbrt a) (cbrt a))) (/ (- (acos a)) (cbrt a)) (/ 1 (sqrt a)) (/ (acos a) (- (sqrt a))) 1 (/ (- (acos a)) a) (/ -1 (* (cbrt a) (cbrt a))) (/ (acos a) (cbrt a)) (/ -1 (sqrt a)) (/ (acos a) (sqrt a)) -1 (/ (acos a) a) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))) (/ (cbrt (acos a)) (cbrt a)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt a)) (/ (cbrt (acos a)) (sqrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))) (/ (cbrt (acos a)) a) (/ (- (sqrt (acos a))) (* (cbrt a) (cbrt a))) (/ (sqrt (acos a)) (cbrt a)) (/ (- (sqrt (acos a))) (sqrt a)) (/ (sqrt (acos a)) (sqrt a)) (- (sqrt (acos a))) (/ (sqrt (acos a)) a) (/ -1 (* (cbrt a) (cbrt a))) (/ (acos a) (cbrt a)) (/ -1 (sqrt a)) (/ (acos a) (sqrt a)) -1 (/ (acos a) a) (/ (* (cbrt (acos a)) (cbrt (acos a))) (* (cbrt a) (cbrt a))) (/ (- (cbrt (acos a))) (cbrt a)) (/ (* (cbrt (acos a)) (cbrt (acos a))) (sqrt a)) (- (/ (cbrt (acos a)) (sqrt a))) (* (cbrt (acos a)) (cbrt (acos a))) (- (/ (cbrt (acos a)) a)) (/ (sqrt (acos a)) (* (cbrt a) (cbrt a))) (- (/ (sqrt (acos a)) (cbrt a))) (/ (sqrt (acos a)) (sqrt a)) (/ (- (sqrt (acos a))) (sqrt a)) (sqrt (acos a)) (- (/ (sqrt (acos a)) a)) (/ 1 (* (cbrt a) (cbrt a))) (/ (- (acos a)) (cbrt a)) (/ 1 (sqrt a)) (/ (acos a) (- (sqrt a))) 1 (/ (- (acos a)) a) (/ 1 a) (- (/ a (acos a))) (/ (acos a) a) (/ (- (acos a)) (* (cbrt a) (cbrt a))) (/ (acos a) (- (sqrt a))) (- (acos a)) (/ a (cbrt (- (acos a)))) (/ a (sqrt (- (acos a)))) (- (/ a (acos a))) (/ a (acos a)) (/ a (cbrt (acos a))) (/ a (sqrt (acos a))) (/ a (acos a)) (/ a (- (cbrt (acos a)))) (/ a (- (sqrt (acos a)))) (- (/ a (acos a))) (- (/ a (acos a))) (- (/ a (acos a))) (- (/ a (acos a))) (/ (- (acos a)) a) (/ (- (acos a)) a) (/ (- (acos a)) a) 4.810 * * * [progress]: adding candidates to table 5.092 * * [progress]: iteration 3 / 4 5.092 * * * [progress]: picking best candidate 5.107 * * * * [pick]: Picked # 5.108 * * * [progress]: localizing error 5.114 * * * [progress]: generating rewritten candidates 5.114 * * * * [progress]: [ 1 / 2 ] rewriting at (2 2) 5.126 * * * * [progress]: [ 2 / 2 ] rewriting at (2) 5.140 * * * [progress]: generating series expansions 5.140 * * * * [progress]: [ 1 / 2 ] generating series at (2 2) 5.140 * [approximate]: Taking taylor expansion of (* -1 (/ (acos a) a)) in (a) around 0 5.140 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 5.140 * [taylor]: Taking taylor expansion of -1 in a 5.140 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 5.140 * [taylor]: Taking taylor expansion of (acos a) in a 5.140 * [taylor]: Taking taylor expansion of a in a 5.140 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 5.141 * [taylor]: Taking taylor expansion of -1 in a 5.141 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 5.141 * [taylor]: Taking taylor expansion of (acos a) in a 5.141 * [taylor]: Taking taylor expansion of a in a 5.155 * [approximate]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in (a) around 0 5.155 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 5.155 * [taylor]: Taking taylor expansion of -1 in a 5.155 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 5.155 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 5.155 * [taylor]: Taking taylor expansion of a in a 5.155 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 5.155 * [taylor]: Taking taylor expansion of -1 in a 5.155 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 5.155 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 5.155 * [taylor]: Taking taylor expansion of a in a 5.171 * [approximate]: Taking taylor expansion of (* a (acos (/ -1 a))) in (a) around 0 5.171 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 5.172 * [taylor]: Taking taylor expansion of a in a 5.172 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 5.172 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 5.172 * [taylor]: Taking taylor expansion of a in a 5.172 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 5.180 * * * * [progress]: [ 2 / 2 ] generating series at (2) 5.180 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 5.180 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 5.180 * [taylor]: Taking taylor expansion of -1 in a 5.180 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 5.180 * [taylor]: Taking taylor expansion of a in a 5.180 * [taylor]: Taking taylor expansion of (acos a) in a 5.180 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 5.180 * [taylor]: Taking taylor expansion of -1 in a 5.180 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 5.180 * [taylor]: Taking taylor expansion of a in a 5.180 * [taylor]: Taking taylor expansion of (acos a) in a 5.188 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 5.188 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 5.188 * [taylor]: Taking taylor expansion of -1 in a 5.188 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 5.188 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 5.188 * [taylor]: Taking taylor expansion of a in a 5.188 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 5.189 * [taylor]: Taking taylor expansion of -1 in a 5.189 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 5.189 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 5.189 * [taylor]: Taking taylor expansion of a in a 5.195 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 5.195 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 5.195 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 5.195 * [taylor]: Taking taylor expansion of a in a 5.195 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 5.196 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 5.196 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 5.196 * [taylor]: Taking taylor expansion of a in a 5.196 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 5.205 * * * [progress]: simplifying candidates 5.206 * [simplify]: Simplifying using # : (expm1 (* (- (acos a)) (/ 1 a))) (log1p (* (- (acos a)) (/ 1 a))) (* (- (acos a)) (/ 1 a)) (+ (log (- (acos a))) (- (log a))) (+ (log (- (acos a))) (- 0 (log a))) (+ (log (- (acos a))) (- (log 1) (log a))) (+ (log (- (acos a))) (log (/ 1 a))) (log (* (- (acos a)) (/ 1 a))) (exp (* (- (acos a)) (/ 1 a))) (* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (/ (* (* 1 1) 1) (* (* a a) a))) (* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a))) (* (cbrt (* (- (acos a)) (/ 1 a))) (cbrt (* (- (acos a)) (/ 1 a)))) (cbrt (* (- (acos a)) (/ 1 a))) (* (* (* (- (acos a)) (/ 1 a)) (* (- (acos a)) (/ 1 a))) (* (- (acos a)) (/ 1 a))) (sqrt (* (- (acos a)) (/ 1 a))) (sqrt (* (- (acos a)) (/ 1 a))) (* (sqrt (- (acos a))) (sqrt (/ 1 a))) (* (sqrt (- (acos a))) (sqrt (/ 1 a))) (* (sqrt (- (acos a))) (/ (sqrt 1) (sqrt a))) (* (sqrt (- (acos a))) (/ (sqrt 1) (sqrt a))) (* (sqrt (- (acos a))) (/ 1 (sqrt a))) (* (sqrt (- (acos a))) (/ 1 (sqrt a))) (* (acos a) (/ 1 a)) (* (- (acos a)) (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))) (* (- (acos a)) (sqrt (/ 1 a))) (* (- (acos a)) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a)))) (* (- (acos a)) (/ (* (cbrt 1) (cbrt 1)) (sqrt a))) (* (- (acos a)) (/ (* (cbrt 1) (cbrt 1)) 1)) (* (- (acos a)) (/ (sqrt 1) (* (cbrt a) (cbrt a)))) (* (- (acos a)) (/ (sqrt 1) (sqrt a))) (* (- (acos a)) (/ (sqrt 1) 1)) (* (- (acos a)) (/ 1 (* (cbrt a) (cbrt a)))) (* (- (acos a)) (/ 1 (sqrt a))) (* (- (acos a)) (/ 1 1)) (* (- (acos a)) 1) (* (- (acos a)) 1) (* (cbrt (- (acos a))) (/ 1 a)) (* (sqrt (- (acos a))) (/ 1 a)) (* (- (acos a)) (/ 1 a)) (* (acos a) (/ 1 a)) (* (cbrt (acos a)) (/ 1 a)) (* (sqrt (acos a)) (/ 1 a)) (* (acos a) (/ 1 a)) (* (- (cbrt (acos a))) (/ 1 a)) (* (- (sqrt (acos a))) (/ 1 a)) (* (- (acos a)) (/ 1 a)) (* (- (acos a)) 1) (expm1 (/ 1 (* (- (acos a)) (/ 1 a)))) (log1p (/ 1 (* (- (acos a)) (/ 1 a)))) (- 1) (- 1) (- (+ (log (- (acos a))) (- (log a)))) (- (+ (log (- (acos a))) (- 0 (log a)))) (- (+ (log (- (acos a))) (- (log 1) (log a)))) (- (+ (log (- (acos a))) (log (/ 1 a)))) (- (log (* (- (acos a)) (/ 1 a)))) (- 0 (+ (log (- (acos a))) (- (log a)))) (- 0 (+ (log (- (acos a))) (- 0 (log a)))) (- 0 (+ (log (- (acos a))) (- (log 1) (log a)))) (- 0 (+ (log (- (acos a))) (log (/ 1 a)))) (- 0 (log (* (- (acos a)) (/ 1 a)))) (- (log 1) (+ (log (- (acos a))) (- (log a)))) (- (log 1) (+ (log (- (acos a))) (- 0 (log a)))) (- (log 1) (+ (log (- (acos a))) (- (log 1) (log a)))) (- (log 1) (+ (log (- (acos a))) (log (/ 1 a)))) (- (log 1) (log (* (- (acos a)) (/ 1 a)))) (log (/ 1 (* (- (acos a)) (/ 1 a)))) (exp (/ 1 (* (- (acos a)) (/ 1 a)))) (/ (* (* 1 1) 1) (* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (/ (* (* 1 1) 1) (* (* a a) a)))) (/ (* (* 1 1) 1) (* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))) (/ (* (* 1 1) 1) (* (* (* (- (acos a)) (/ 1 a)) (* (- (acos a)) (/ 1 a))) (* (- (acos a)) (/ 1 a)))) (* (cbrt (/ 1 (* (- (acos a)) (/ 1 a)))) (cbrt (/ 1 (* (- (acos a)) (/ 1 a))))) (cbrt (/ 1 (* (- (acos a)) (/ 1 a)))) (* (* (/ 1 (* (- (acos a)) (/ 1 a))) (/ 1 (* (- (acos a)) (/ 1 a)))) (/ 1 (* (- (acos a)) (/ 1 a)))) (sqrt (/ 1 (* (- (acos a)) (/ 1 a)))) (sqrt (/ 1 (* (- (acos a)) (/ 1 a)))) (- 1) (- (* (- (acos a)) (/ 1 a))) (/ (* (cbrt 1) (cbrt 1)) (- (acos a))) (/ (cbrt 1) (/ 1 a)) (/ (sqrt 1) (- (acos a))) (/ (sqrt 1) (/ 1 a)) (/ 1 (- (acos a))) (/ 1 (/ 1 a)) (/ 1 (* (- (acos a)) (/ 1 a))) (/ (* (- (acos a)) (/ 1 a)) 1) (/ 1 (- (acos a))) (/ (* (- (acos a)) (/ 1 a)) (cbrt 1)) (/ (* (- (acos a)) (/ 1 a)) (sqrt 1)) (/ (* (- (acos a)) (/ 1 a)) 1) (/ 1 (- (acos a))) (/ 1 (* (- (acos a)) 1)) (* -1 (/ (acos a) a)) (* -1 (/ (acos a) a)) (* -1 (/ (acos a) a)) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) 5.210 * * [simplify]: iteration 0 : 129 enodes (cost 968 ) 5.238 * * [simplify]: iteration 1 : 363 enodes (cost 741 ) 5.345 * * [simplify]: iteration 2 : 1294 enodes (cost 559 ) 6.515 * * [simplify]: iteration 3 : 3276 enodes (cost 553 ) 8.921 * * [simplify]: iteration done : 5000 enodes (cost 553 ) 8.922 * [simplify]: Simplified to: (expm1 (/ (- (acos a)) a)) (log1p (/ (- (acos a)) a)) (- (/ (acos a) a)) (log (/ (- (acos a)) a)) (log (/ (- (acos a)) a)) (log (/ (- (acos a)) a)) (log (/ (- (acos a)) a)) (log (/ (- (acos a)) a)) (exp (/ (- (acos a)) a)) (pow (- (/ (acos a) a)) 3) (pow (- (/ (acos a) a)) 3) (* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a))) (cbrt (/ (- (acos a)) a)) (pow (- (/ (acos a) a)) 3) (sqrt (/ (- (acos a)) a)) (sqrt (/ (- (acos a)) a)) (* (sqrt (- (acos a))) (sqrt (/ 1 a))) (* (sqrt (- (acos a))) (sqrt (/ 1 a))) (/ (sqrt (- (acos a))) (sqrt a)) (/ (sqrt (- (acos a))) (sqrt a)) (/ (sqrt (- (acos a))) (sqrt a)) (/ (sqrt (- (acos a))) (sqrt a)) (/ (acos a) a) (* (- (acos a)) (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))) (* (- (acos a)) (sqrt (/ 1 a))) (/ (- (acos a)) (* (cbrt a) (cbrt a))) (/ (- (acos a)) (sqrt a)) (- (acos a)) (/ (- (acos a)) (* (cbrt a) (cbrt a))) (/ (- (acos a)) (sqrt a)) (- (acos a)) (/ (- (acos a)) (* (cbrt a) (cbrt a))) (/ (- (acos a)) (sqrt a)) (- (acos a)) (- (acos a)) (- (acos a)) (/ (cbrt (- (acos a))) a) (/ (sqrt (- (acos a))) a) (- (/ (acos a) a)) (/ (acos a) a) (/ (cbrt (acos a)) a) (/ (sqrt (acos a)) a) (/ (acos a) a) (/ (- (cbrt (acos a))) a) (/ (- (sqrt (acos a))) a) (- (/ (acos a) a)) (- (acos a)) (expm1 (/ a (- (acos a)))) (log1p (/ a (- (acos a)))) -1 -1 (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (exp (/ a (- (acos a)))) (pow (/ a (- (acos a))) 3) (pow (/ a (- (acos a))) 3) (pow (/ a (- (acos a))) 3) (* (cbrt (/ a (- (acos a)))) (cbrt (/ a (- (acos a))))) (cbrt (/ a (- (acos a)))) (pow (/ a (- (acos a))) 3) (sqrt (/ a (- (acos a)))) (sqrt (/ a (- (acos a)))) -1 (/ (acos a) a) (/ -1 (acos a)) a (/ -1 (acos a)) a (/ -1 (acos a)) a (- (/ a (acos a))) (- (/ (acos a) a)) (/ -1 (acos a)) (- (/ (acos a) a)) (- (/ (acos a) a)) (- (/ (acos a) a)) (/ -1 (acos a)) (/ -1 (acos a)) (- (/ (acos a) a)) (- (/ (acos a) a)) (- (/ (acos a) a)) (- (/ a (acos a))) (- (/ a (acos a))) (- (/ a (acos a))) 8.922 * * * [progress]: adding candidates to table 9.038 * * [progress]: iteration 4 / 4 9.038 * * * [progress]: picking best candidate 9.052 * * * * [pick]: Picked # 9.052 * * * [progress]: localizing error 9.063 * * * [progress]: generating rewritten candidates 9.063 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1) 9.064 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 1) 9.065 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2) 9.065 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 2) 9.067 * * * [progress]: generating series expansions 9.067 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1) 9.067 * [approximate]: Taking taylor expansion of (sqrt (acos a)) in (a) around 0 9.067 * [taylor]: Taking taylor expansion of (sqrt (acos a)) in a 9.067 * [taylor]: Taking taylor expansion of (acos a) in a 9.067 * [taylor]: Taking taylor expansion of (sqrt (acos a)) in a 9.067 * [taylor]: Taking taylor expansion of (acos a) in a 9.071 * [approximate]: Taking taylor expansion of (sqrt (acos (/ 1 a))) in (a) around 0 9.071 * [taylor]: Taking taylor expansion of (sqrt (acos (/ 1 a))) in a 9.071 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 9.071 * [taylor]: Taking taylor expansion of (sqrt (acos (/ 1 a))) in a 9.071 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 9.074 * [approximate]: Taking taylor expansion of (sqrt (acos (/ -1 a))) in (a) around 0 9.074 * [taylor]: Taking taylor expansion of (sqrt (acos (/ -1 a))) in a 9.074 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 9.074 * [taylor]: Taking taylor expansion of (sqrt (acos (/ -1 a))) in a 9.074 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 9.077 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 1) 9.078 * [approximate]: Taking taylor expansion of (sqrt (acos a)) in (a) around 0 9.078 * [taylor]: Taking taylor expansion of (sqrt (acos a)) in a 9.078 * [taylor]: Taking taylor expansion of (acos a) in a 9.078 * [taylor]: Taking taylor expansion of (sqrt (acos a)) in a 9.078 * [taylor]: Taking taylor expansion of (acos a) in a 9.081 * [approximate]: Taking taylor expansion of (sqrt (acos (/ 1 a))) in (a) around 0 9.081 * [taylor]: Taking taylor expansion of (sqrt (acos (/ 1 a))) in a 9.081 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 9.081 * [taylor]: Taking taylor expansion of (sqrt (acos (/ 1 a))) in a 9.081 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 9.084 * [approximate]: Taking taylor expansion of (sqrt (acos (/ -1 a))) in (a) around 0 9.084 * [taylor]: Taking taylor expansion of (sqrt (acos (/ -1 a))) in a 9.084 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 9.084 * [taylor]: Taking taylor expansion of (sqrt (acos (/ -1 a))) in a 9.084 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 9.087 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2) 9.087 * [approximate]: Taking taylor expansion of (pow a 1/3) in (a) around 0 9.087 * [taylor]: Taking taylor expansion of (pow a 1/3) in a 9.087 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log a))) in a 9.087 * [taylor]: Taking taylor expansion of (* 1/3 (log a)) in a 9.087 * [taylor]: Taking taylor expansion of 1/3 in a 9.087 * [taylor]: Taking taylor expansion of (log a) in a 9.087 * [taylor]: Taking taylor expansion of a in a 9.088 * [taylor]: Taking taylor expansion of (pow a 1/3) in a 9.088 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log a))) in a 9.088 * [taylor]: Taking taylor expansion of (* 1/3 (log a)) in a 9.088 * [taylor]: Taking taylor expansion of 1/3 in a 9.088 * [taylor]: Taking taylor expansion of (log a) in a 9.088 * [taylor]: Taking taylor expansion of a in a 9.142 * [approximate]: Taking taylor expansion of (pow (/ 1 a) 1/3) in (a) around 0 9.142 * [taylor]: Taking taylor expansion of (pow (/ 1 a) 1/3) in a 9.142 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 a)))) in a 9.142 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 a))) in a 9.142 * [taylor]: Taking taylor expansion of 1/3 in a 9.142 * [taylor]: Taking taylor expansion of (log (/ 1 a)) in a 9.142 * [taylor]: Taking taylor expansion of (/ 1 a) in a 9.142 * [taylor]: Taking taylor expansion of a in a 9.143 * [taylor]: Taking taylor expansion of (pow (/ 1 a) 1/3) in a 9.143 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 a)))) in a 9.143 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 a))) in a 9.143 * [taylor]: Taking taylor expansion of 1/3 in a 9.143 * [taylor]: Taking taylor expansion of (log (/ 1 a)) in a 9.143 * [taylor]: Taking taylor expansion of (/ 1 a) in a 9.143 * [taylor]: Taking taylor expansion of a in a 9.198 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 a) 1/3)) in (a) around 0 9.198 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 a) 1/3)) in a 9.198 * [taylor]: Taking taylor expansion of (cbrt -1) in a 9.198 * [taylor]: Taking taylor expansion of -1 in a 9.199 * [taylor]: Taking taylor expansion of (pow (/ 1 a) 1/3) in a 9.199 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 a)))) in a 9.199 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 a))) in a 9.199 * [taylor]: Taking taylor expansion of 1/3 in a 9.199 * [taylor]: Taking taylor expansion of (log (/ 1 a)) in a 9.199 * [taylor]: Taking taylor expansion of (/ 1 a) in a 9.199 * [taylor]: Taking taylor expansion of a in a 9.200 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 a) 1/3)) in a 9.200 * [taylor]: Taking taylor expansion of (cbrt -1) in a 9.200 * [taylor]: Taking taylor expansion of -1 in a 9.201 * [taylor]: Taking taylor expansion of (pow (/ 1 a) 1/3) in a 9.201 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 a)))) in a 9.201 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 a))) in a 9.201 * [taylor]: Taking taylor expansion of 1/3 in a 9.201 * [taylor]: Taking taylor expansion of (log (/ 1 a)) in a 9.201 * [taylor]: Taking taylor expansion of (/ 1 a) in a 9.201 * [taylor]: Taking taylor expansion of a in a 9.272 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 2) 9.272 * [approximate]: Taking taylor expansion of (pow a 1/3) in (a) around 0 9.272 * [taylor]: Taking taylor expansion of (pow a 1/3) in a 9.272 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log a))) in a 9.272 * [taylor]: Taking taylor expansion of (* 1/3 (log a)) in a 9.272 * [taylor]: Taking taylor expansion of 1/3 in a 9.272 * [taylor]: Taking taylor expansion of (log a) in a 9.272 * [taylor]: Taking taylor expansion of a in a 9.273 * [taylor]: Taking taylor expansion of (pow a 1/3) in a 9.273 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log a))) in a 9.273 * [taylor]: Taking taylor expansion of (* 1/3 (log a)) in a 9.273 * [taylor]: Taking taylor expansion of 1/3 in a 9.273 * [taylor]: Taking taylor expansion of (log a) in a 9.273 * [taylor]: Taking taylor expansion of a in a 9.324 * [approximate]: Taking taylor expansion of (pow (/ 1 a) 1/3) in (a) around 0 9.324 * [taylor]: Taking taylor expansion of (pow (/ 1 a) 1/3) in a 9.324 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 a)))) in a 9.324 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 a))) in a 9.324 * [taylor]: Taking taylor expansion of 1/3 in a 9.324 * [taylor]: Taking taylor expansion of (log (/ 1 a)) in a 9.324 * [taylor]: Taking taylor expansion of (/ 1 a) in a 9.324 * [taylor]: Taking taylor expansion of a in a 9.325 * [taylor]: Taking taylor expansion of (pow (/ 1 a) 1/3) in a 9.326 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 a)))) in a 9.326 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 a))) in a 9.326 * [taylor]: Taking taylor expansion of 1/3 in a 9.326 * [taylor]: Taking taylor expansion of (log (/ 1 a)) in a 9.326 * [taylor]: Taking taylor expansion of (/ 1 a) in a 9.326 * [taylor]: Taking taylor expansion of a in a 9.387 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 a) 1/3)) in (a) around 0 9.387 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 a) 1/3)) in a 9.387 * [taylor]: Taking taylor expansion of (cbrt -1) in a 9.387 * [taylor]: Taking taylor expansion of -1 in a 9.388 * [taylor]: Taking taylor expansion of (pow (/ 1 a) 1/3) in a 9.388 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 a)))) in a 9.388 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 a))) in a 9.388 * [taylor]: Taking taylor expansion of 1/3 in a 9.388 * [taylor]: Taking taylor expansion of (log (/ 1 a)) in a 9.388 * [taylor]: Taking taylor expansion of (/ 1 a) in a 9.388 * [taylor]: Taking taylor expansion of a in a 9.389 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 a) 1/3)) in a 9.390 * [taylor]: Taking taylor expansion of (cbrt -1) in a 9.390 * [taylor]: Taking taylor expansion of -1 in a 9.390 * [taylor]: Taking taylor expansion of (pow (/ 1 a) 1/3) in a 9.390 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 a)))) in a 9.390 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 a))) in a 9.390 * [taylor]: Taking taylor expansion of 1/3 in a 9.390 * [taylor]: Taking taylor expansion of (log (/ 1 a)) in a 9.390 * [taylor]: Taking taylor expansion of (/ 1 a) in a 9.390 * [taylor]: Taking taylor expansion of a in a 9.464 * * * [progress]: simplifying candidates 9.465 * [simplify]: Simplifying using # : (expm1 (sqrt (acos a))) (log1p (sqrt (acos a))) (log (sqrt (acos a))) (exp (sqrt (acos a))) (* (cbrt (sqrt (acos a))) (cbrt (sqrt (acos a)))) (cbrt (sqrt (acos a))) (* (* (sqrt (acos a)) (sqrt (acos a))) (sqrt (acos a))) (sqrt (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt (cbrt (acos a))) (sqrt (sqrt (acos a))) (sqrt (sqrt (acos a))) (sqrt 1) (sqrt (acos a)) (/ 1 2) (sqrt (sqrt (acos a))) (sqrt (sqrt (acos a))) (expm1 (sqrt (acos a))) (log1p (sqrt (acos a))) (log (sqrt (acos a))) (exp (sqrt (acos a))) (* (cbrt (sqrt (acos a))) (cbrt (sqrt (acos a)))) (cbrt (sqrt (acos a))) (* (* (sqrt (acos a)) (sqrt (acos a))) (sqrt (acos a))) (sqrt (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt (cbrt (acos a))) (sqrt (sqrt (acos a))) (sqrt (sqrt (acos a))) (sqrt 1) (sqrt (acos a)) (/ 1 2) (sqrt (sqrt (acos a))) (sqrt (sqrt (acos a))) (expm1 (cbrt a)) (log1p (cbrt a)) (log (cbrt a)) (exp (cbrt a)) (cbrt (* (cbrt a) (cbrt a))) (cbrt (cbrt a)) (cbrt (sqrt a)) (cbrt (sqrt a)) (cbrt 1) (cbrt a) (* (cbrt (cbrt a)) (cbrt (cbrt a))) (cbrt (cbrt a)) (* (* (cbrt a) (cbrt a)) (cbrt a)) (sqrt (cbrt a)) (sqrt (cbrt a)) (expm1 (cbrt a)) (log1p (cbrt a)) (log (cbrt a)) (exp (cbrt a)) (cbrt (* (cbrt a) (cbrt a))) (cbrt (cbrt a)) (cbrt (sqrt a)) (cbrt (sqrt a)) (cbrt 1) (cbrt a) (* (cbrt (cbrt a)) (cbrt (cbrt a))) (cbrt (cbrt a)) (* (* (cbrt a) (cbrt a)) (cbrt a)) (sqrt (cbrt a)) (sqrt (cbrt a)) (sqrt (acos a)) (sqrt (acos a)) (sqrt (acos a)) (sqrt (acos a)) (sqrt (acos a)) (sqrt (acos a)) (pow a 1/3) (pow (/ 1 a) -1/3) (* (pow (* -1 a) 1/3) (cbrt -1)) (pow a 1/3) (pow (/ 1 a) -1/3) (* (pow (* -1 a) 1/3) (cbrt -1)) 9.466 * * [simplify]: iteration 0 : 44 enodes (cost 312 ) 9.475 * * [simplify]: iteration 1 : 64 enodes (cost 280 ) 9.487 * * [simplify]: iteration 2 : 110 enodes (cost 266 ) 9.518 * * [simplify]: iteration 3 : 227 enodes (cost 260 ) 9.587 * * [simplify]: iteration 4 : 635 enodes (cost 260 ) 9.928 * * [simplify]: iteration 5 : 3278 enodes (cost 260 ) 11.631 * * [simplify]: iteration done : 5000 enodes (cost 260 ) 11.632 * [simplify]: Simplified to: (expm1 (sqrt (acos a))) (log1p (sqrt (acos a))) (log (sqrt (acos a))) (exp (sqrt (acos a))) (* (cbrt (sqrt (acos a))) (cbrt (sqrt (acos a)))) (cbrt (sqrt (acos a))) (pow (sqrt (acos a)) 3) (fabs (cbrt (acos a))) (sqrt (cbrt (acos a))) (sqrt (sqrt (acos a))) (sqrt (sqrt (acos a))) 1 (sqrt (acos a)) 1/2 (sqrt (sqrt (acos a))) (sqrt (sqrt (acos a))) (expm1 (sqrt (acos a))) (log1p (sqrt (acos a))) (log (sqrt (acos a))) (exp (sqrt (acos a))) (* (cbrt (sqrt (acos a))) (cbrt (sqrt (acos a)))) (cbrt (sqrt (acos a))) (pow (sqrt (acos a)) 3) (fabs (cbrt (acos a))) (sqrt (cbrt (acos a))) (sqrt (sqrt (acos a))) (sqrt (sqrt (acos a))) 1 (sqrt (acos a)) 1/2 (sqrt (sqrt (acos a))) (sqrt (sqrt (acos a))) (expm1 (cbrt a)) (log1p (cbrt a)) (log (cbrt a)) (exp (cbrt a)) (cbrt (pow a 2/3)) (cbrt (cbrt a)) (cbrt (sqrt a)) (cbrt (sqrt a)) 1 (cbrt a) (* (cbrt (cbrt a)) (cbrt (cbrt a))) (cbrt (cbrt a)) a (sqrt (cbrt a)) (sqrt (cbrt a)) (expm1 (cbrt a)) (log1p (cbrt a)) (log (cbrt a)) (exp (cbrt a)) (cbrt (pow a 2/3)) (cbrt (cbrt a)) (cbrt (sqrt a)) (cbrt (sqrt a)) 1 (cbrt a) (* (cbrt (cbrt a)) (cbrt (cbrt a))) (cbrt (cbrt a)) a (sqrt (cbrt a)) (sqrt (cbrt a)) (sqrt (acos a)) (sqrt (acos a)) (sqrt (acos a)) (sqrt (acos a)) (sqrt (acos a)) (sqrt (acos a)) (cbrt a) (pow (/ 1 a) -1/3) (* (cbrt (- a)) (cbrt -1)) (cbrt a) (pow (/ 1 a) -1/3) (* (cbrt (- a)) (cbrt -1)) 11.632 * * * [progress]: adding candidates to table 11.798 * [progress]: [Phase 3 of 3] Extracting. 11.798 * * [regime]: Finding splitpoints for: (# # # # # # # # # # #) 11.800 * * * [regime-changes]: Trying 2 branch expressions: ((/ a (- (acos a))) a) 11.800 * * * * [regimes]: Trying to branch on (/ a (- (acos a))) from (# # # # # # # # # # #) 11.840 * * * * [regimes]: Trying to branch on a from (# # # # # # # # # # #) 11.873 * * * [regime]: Found split indices: #