9.947 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.027 * * * [progress]: [2/2] Setting up program. 0.029 * [progress]: [Phase 2 of 3] Improving. 0.030 * [simplify]: Simplifying using # : (/ a (- (acos a))) 0.032 * * [simplify]: iteration 0 : 4 enodes (cost 3 ) 0.033 * [simplify]: Simplified to: (/ a (- (acos a))) 0.033 * * [progress]: iteration 1 / 4 0.033 * * * [progress]: picking best candidate 0.035 * * * * [pick]: Picked # 0.035 * * * [progress]: localizing error 0.039 * * * [progress]: generating rewritten candidates 0.039 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.045 * * * [progress]: generating series expansions 0.045 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.045 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.045 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.045 * [taylor]: Taking taylor expansion of -1 in a 0.045 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.045 * [taylor]: Taking taylor expansion of a in a 0.045 * [taylor]: Taking taylor expansion of (acos a) in a 0.046 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.046 * [taylor]: Taking taylor expansion of -1 in a 0.046 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.046 * [taylor]: Taking taylor expansion of a in a 0.046 * [taylor]: Taking taylor expansion of (acos a) in a 0.053 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.053 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.053 * [taylor]: Taking taylor expansion of -1 in a 0.053 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.054 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.054 * [taylor]: Taking taylor expansion of a in a 0.054 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.054 * [taylor]: Taking taylor expansion of -1 in a 0.054 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.054 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.054 * [taylor]: Taking taylor expansion of a in a 0.060 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 0.060 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.060 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.060 * [taylor]: Taking taylor expansion of a in a 0.060 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.061 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.061 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.061 * [taylor]: Taking taylor expansion of a in a 0.061 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.070 * * * [progress]: simplifying candidates 0.071 * [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))) 0.076 * * [simplify]: iteration 0 : 166 enodes (cost 384 ) 0.080 * * [simplify]: iteration 1 : 493 enodes (cost 372 ) 0.089 * * [simplify]: iteration 2 : 1442 enodes (cost 367 ) 0.111 * * [simplify]: iteration 3 : 3704 enodes (cost 366 ) 0.168 * * [simplify]: iteration 4 : 5002 enodes (cost 366 ) 0.170 * [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)))) (* -1 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)) -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)) (/ (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) -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) (/ (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 (/ 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 (* -1 (/ a (acos a))) (/ -1 (acos a)) (/ (- (acos a)) a) (/ a (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ a (sqrt (- (acos a)))) a (* -1 a) (/ a (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ a (- (sqrt (acos a)))) (* -1 a) (/ a (* (cbrt (acos a)) (cbrt (acos a)))) (/ a (sqrt (acos a))) a (/ (- (acos a)) (cbrt a)) (/ (- (acos a)) (sqrt a)) (/ (- (acos a)) a) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) 0.171 * * * [progress]: adding candidates to table 0.284 * * [progress]: iteration 2 / 4 0.284 * * * [progress]: picking best candidate 0.302 * * * * [pick]: Picked # 0.302 * * * [progress]: localizing error 0.307 * * * [progress]: generating rewritten candidates 0.308 * * * * [progress]: [ 1 / 2 ] rewriting at (2 2) 0.312 * * * * [progress]: [ 2 / 2 ] rewriting at (2) 0.339 * * * [progress]: generating series expansions 0.339 * * * * [progress]: [ 1 / 2 ] generating series at (2 2) 0.339 * [approximate]: Taking taylor expansion of (* -1 (/ (acos a) a)) in (a) around 0 0.339 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.339 * [taylor]: Taking taylor expansion of -1 in a 0.339 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.339 * [taylor]: Taking taylor expansion of (acos a) in a 0.339 * [taylor]: Taking taylor expansion of a in a 0.339 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.339 * [taylor]: Taking taylor expansion of -1 in a 0.339 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.339 * [taylor]: Taking taylor expansion of (acos a) in a 0.339 * [taylor]: Taking taylor expansion of a in a 0.353 * [approximate]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.353 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 0.354 * [taylor]: Taking taylor expansion of -1 in a 0.354 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.354 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.354 * [taylor]: Taking taylor expansion of a in a 0.354 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 0.354 * [taylor]: Taking taylor expansion of -1 in a 0.354 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.354 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.354 * [taylor]: Taking taylor expansion of a in a 0.366 * [approximate]: Taking taylor expansion of (* a (acos (/ -1 a))) in (a) around 0 0.366 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.366 * [taylor]: Taking taylor expansion of a in a 0.366 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.366 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.366 * [taylor]: Taking taylor expansion of a in a 0.366 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.373 * * * * [progress]: [ 2 / 2 ] generating series at (2) 0.374 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.374 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.374 * [taylor]: Taking taylor expansion of -1 in a 0.374 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.374 * [taylor]: Taking taylor expansion of a in a 0.374 * [taylor]: Taking taylor expansion of (acos a) in a 0.374 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.374 * [taylor]: Taking taylor expansion of -1 in a 0.374 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.374 * [taylor]: Taking taylor expansion of a in a 0.374 * [taylor]: Taking taylor expansion of (acos a) in a 0.381 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.381 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.381 * [taylor]: Taking taylor expansion of -1 in a 0.381 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.381 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.381 * [taylor]: Taking taylor expansion of a in a 0.382 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.382 * [taylor]: Taking taylor expansion of -1 in a 0.382 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.382 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.382 * [taylor]: Taking taylor expansion of a in a 0.388 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 0.388 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.388 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.388 * [taylor]: Taking taylor expansion of a in a 0.388 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.389 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.389 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.389 * [taylor]: Taking taylor expansion of a in a 0.389 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.398 * * * [progress]: simplifying candidates 0.402 * [simplify]: Simplifying using # : (expm1 (/ (- (acos a)) a)) (log1p (/ (- (acos a)) a)) (- (log (- (acos a))) (log a)) (log (/ (- (acos a)) a)) (exp (/ (- (acos a)) a)) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)) (* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a))) (cbrt (/ (- (acos a)) a)) (* (* (/ (- (acos a)) a) (/ (- (acos a)) a)) (/ (- (acos a)) a)) (sqrt (/ (- (acos a)) a)) (sqrt (/ (- (acos a)) a)) (- (- (acos a))) (- a) (/ 0 a) (/ (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)))) 1) (/ (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))) 1) (/ (sqrt (- (acos a))) a) (/ 1 (* (cbrt a) (cbrt a))) (/ (- (acos a)) (cbrt a)) (/ 1 (sqrt a)) (/ (- (acos a)) (sqrt a)) (/ 1 1) (/ (- (acos a)) a) (/ -1 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(* (* (/ (- (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) 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1 (- (sqrt (acos a)))) (/ a (sqrt (acos a))) (* -1 (* (cbrt a) (cbrt a))) (/ 1 (/ (acos a) (cbrt a))) (* -1 (sqrt a)) (/ (sqrt a) (acos a)) -1 (/ a (acos a)) (/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (* 1 (cbrt a)) (- (cbrt (acos a)))) (/ (sqrt a) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (sqrt a) (- (cbrt (acos a)))) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ a (- (cbrt (acos a)))) (/ (* (cbrt a) (cbrt a)) (sqrt (acos a))) (/ (* 1 (cbrt a)) (- (sqrt (acos a)))) (/ (sqrt a) (sqrt (acos a))) (/ (sqrt a) (- (sqrt (acos a)))) (/ 1 (sqrt (acos a))) (/ a (- (sqrt (acos a)))) (* (cbrt a) (cbrt a)) (* -1 (/ (cbrt a) (acos a))) (sqrt a) (/ (sqrt a) (- (acos a))) 1 (/ a (- (acos a))) 1 (/ a (- (acos a))) (/ 1 (- (acos a))) a (/ a (- (acos a))) (/ (- (acos a)) a) (/ (/ 1 (cbrt (/ (- (acos a)) a))) (cbrt (/ (- (acos a)) a))) (/ 1 (sqrt (/ (- (acos a)) a))) (/ (* (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 (* (cbrt a) (cbrt a))) (* -1 (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)))) (* -1 (* (cbrt a) (cbrt a))) (* -1 (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))) (/ (- (acos a)) a) (/ (- (acos a)) a) (/ (- (acos a)) a) (/ a (- (acos a))) (/ a (- (acos a))) (/ a (- (acos a))) 0.477 * * * [progress]: adding candidates to table 0.765 * * [progress]: iteration 3 / 4 0.765 * * * [progress]: picking best candidate 0.783 * * * * [pick]: Picked # 0.783 * * * [progress]: localizing error 0.791 * * * [progress]: generating rewritten candidates 0.791 * * * * [progress]: [ 1 / 2 ] rewriting at (2 2) 0.795 * * * * [progress]: [ 2 / 2 ] rewriting at (2) 0.817 * * * [progress]: generating series expansions 0.818 * * * * [progress]: [ 1 / 2 ] generating series at (2 2) 0.818 * [approximate]: Taking taylor expansion of (* -1 (/ (acos a) a)) in (a) around 0 0.818 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.818 * [taylor]: Taking taylor expansion of -1 in a 0.818 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.818 * [taylor]: Taking taylor expansion of (acos a) in a 0.818 * [taylor]: Taking taylor expansion of a in a 0.818 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.818 * [taylor]: Taking taylor expansion of -1 in a 0.818 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.818 * [taylor]: Taking taylor expansion of (acos a) in a 0.818 * [taylor]: Taking taylor expansion of a in a 0.833 * [approximate]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.833 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 0.833 * [taylor]: Taking taylor expansion of -1 in a 0.833 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.833 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.833 * [taylor]: Taking taylor expansion of a in a 0.833 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 0.833 * [taylor]: Taking taylor expansion of -1 in a 0.833 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.833 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.833 * [taylor]: Taking taylor expansion of a in a 0.845 * [approximate]: Taking taylor expansion of (* a (acos (/ -1 a))) in (a) around 0 0.845 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.845 * [taylor]: Taking taylor expansion of a in a 0.845 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.845 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.845 * [taylor]: Taking taylor expansion of a in a 0.845 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.853 * * * * [progress]: [ 2 / 2 ] generating series at (2) 0.853 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.853 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.853 * [taylor]: Taking taylor expansion of -1 in a 0.854 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.854 * [taylor]: Taking taylor expansion of a in a 0.854 * [taylor]: Taking taylor expansion of (acos a) in a 0.854 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.854 * [taylor]: Taking taylor expansion of -1 in a 0.854 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.854 * [taylor]: Taking taylor expansion of a in a 0.854 * [taylor]: Taking taylor expansion of (acos a) in a 0.861 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.861 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.861 * [taylor]: Taking taylor expansion of -1 in a 0.861 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.861 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.862 * [taylor]: Taking taylor expansion of a in a 0.862 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.862 * [taylor]: Taking taylor expansion of -1 in a 0.862 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.862 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.862 * [taylor]: Taking taylor expansion of a in a 0.868 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 0.869 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.869 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.869 * [taylor]: Taking taylor expansion of a in a 0.869 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.869 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.869 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.869 * [taylor]: Taking taylor expansion of a in a 0.869 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.879 * * * [progress]: simplifying candidates 0.881 * [simplify]: Simplifying using # : (expm1 (/ (- (acos a)) a)) (log1p (/ (- (acos a)) a)) (- (log (- (acos a))) (log a)) (log (/ (- (acos a)) a)) (exp (/ (- (acos a)) a)) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)) (* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a))) (cbrt (/ (- (acos a)) a)) (* (* (/ (- (acos a)) a) (/ (- (acos a)) a)) (/ (- (acos a)) a)) (sqrt (/ (- (acos a)) a)) (sqrt (/ (- (acos a)) a)) (- (- (acos a))) (- a) (/ 0 a) (/ (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)))) 1) (/ (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))) 1) (/ (sqrt (- (acos a))) a) (/ 1 (* (cbrt a) (cbrt a))) (/ (- (acos a)) (cbrt a)) (/ 1 (sqrt a)) (/ (- (acos a)) (sqrt a)) (/ 1 1) (/ (- (acos a)) a) (/ -1 (* (cbrt a) (cbrt a))) (/ (acos a) (cbrt a)) (/ -1 (sqrt a)) (/ (acos a) (sqrt a)) (/ -1 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)))) 1) (/ (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))) 1) (/ (sqrt (acos a)) a) (/ (- 1) (* (cbrt a) (cbrt a))) (/ (acos a) (cbrt a)) (/ (- 1) (sqrt a)) (/ (acos a) (sqrt a)) (/ (- 1) 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))) 1) (/ (- (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)) 1) (/ (- (sqrt (acos a))) a) (/ 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)) (/ (- 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(cbrt a) (cbrt a)))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (acos a)) (cbrt (acos a))) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (acos a)) (cbrt (acos a))) 1)) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (acos a)) (* (cbrt a) (cbrt a)))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (acos a)) (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (acos a)) 1)) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (* (cbrt a) (cbrt a)))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 (sqrt a))) (/ (* (cbrt 1) (cbrt 1)) (/ 1 1)) (/ (* (cbrt 1) (cbrt 1)) 1) (/ (* (cbrt 1) (cbrt 1)) (- (acos a))) (/ (/ (- (acos a)) a) (cbrt 1)) (/ (* (cbrt 1) (cbrt 1)) (- (acos a))) (* -1 (/ (acos a) a)) (* -1 (/ (acos a) a)) (* -1 (/ (acos a) a)) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) 0.889 * * [simplify]: iteration 0 : 527 enodes (cost 1309 ) 0.901 * * [simplify]: iteration 1 : 2721 enodes (cost 1241 ) 0.946 * * [simplify]: iteration 2 : 5002 enodes (cost 1025 ) 0.951 * [simplify]: Simplified to: (expm1 (/ (- (acos a)) a)) (log1p (/ (- (acos a)) a)) (log (/ (- (acos a)) a)) (log (/ (- (acos a)) a)) (exp (/ (- (acos a)) a)) (pow (* -1 (/ (acos a) a)) 3) (* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a))) (cbrt (/ (- (acos a)) a)) (pow (* -1 (/ (acos a) a)) 3) (sqrt (/ (- (acos a)) a)) (sqrt (/ (- (acos a)) a)) (acos a) (* -1 a) 0 (/ (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 (* -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 (* -1 (/ (acos a) a)) (/ 1 a) (/ -1 (/ (acos a) a)) (/ (acos a) a) (/ (- (acos a)) (* (cbrt a) (cbrt a))) (/ (- (acos a)) (sqrt a)) (- (acos a)) (/ a (cbrt (- (acos a)))) (/ a (sqrt (- (acos a)))) (/ -1 (/ (acos a) a)) (/ a (acos a)) (/ a (cbrt (acos a))) (/ a (sqrt (acos a))) (/ a (acos a)) (/ a (- (cbrt (acos a)))) (/ a (- (sqrt (acos a)))) (/ -1 (/ (acos a) a)) (expm1 (/ (* (cbrt 1) (cbrt 1)) (/ (- (acos a)) a))) (log1p (/ (* (cbrt 1) (cbrt 1)) (/ (- (acos a)) a))) (log (/ (cbrt 1) (/ (- (acos a)) a))) (log (/ (cbrt 1) (/ (- (acos a)) a))) (log (/ (cbrt 1) (/ (- (acos a)) a))) (log (/ (cbrt 1) (/ (- (acos a)) a))) (log (/ (cbrt 1) (/ (- (acos a)) a))) (exp (/ (cbrt 1) (/ (- (acos a)) a))) (pow (/ -1 (/ (acos a) a)) 3) (pow (/ -1 (/ (acos a) a)) 3) (pow (/ -1 (/ (acos a) a)) 3) (pow (/ -1 (/ (acos a) a)) 3) (* (cbrt (/ (* (cbrt 1) (cbrt 1)) (/ (- (acos a)) a))) (cbrt (/ (* (cbrt 1) (cbrt 1)) (/ (- (acos a)) a)))) (cbrt (/ (* (cbrt 1) (cbrt 1)) (/ (- (acos a)) a))) (pow (/ -1 (/ (acos a) a)) 3) (sqrt (/ (* (cbrt 1) (cbrt 1)) (/ (- (acos a)) a))) (sqrt (/ (* (cbrt 1) (cbrt 1)) (/ (- (acos a)) a))) (- 1) (/ (acos a) a) (/ 1 (* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a)))) (/ 1 (cbrt (/ (- (acos a)) a))) (/ 1 (sqrt (/ (- (acos a)) a))) (/ 1 (sqrt (/ (- (acos a)) a))) (* (/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a))))) 1) (/ 1 (/ (cbrt (- (acos a))) (cbrt a))) (* (/ (sqrt a) (* (cbrt (- (acos a))) (cbrt (- (acos a))))) 1) (/ 1 (/ (cbrt (- (acos a))) (sqrt a))) (/ 1 (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ 1 (/ (cbrt (- (acos a))) a)) (* (/ (* (cbrt a) (cbrt a)) (sqrt (- (acos a)))) 1) (/ 1 (/ (sqrt (- (acos a))) (cbrt a))) (* (/ (sqrt a) (sqrt (- (acos a)))) 1) (* (/ (sqrt a) (sqrt (- (acos a)))) 1) (/ 1 (sqrt (- (acos a)))) (/ a (sqrt (- (acos a)))) (* 1 (* (cbrt a) (cbrt a))) (/ 1 (/ (- (acos a)) (cbrt a))) (* 1 (sqrt a)) (* (/ (sqrt a) (- (acos a))) 1) 1 (/ -1 (/ (acos a) a)) (* (/ (* (cbrt 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(/ 1 (/ (- (cbrt (acos a))) a)) (* (/ (* (cbrt a) (cbrt a)) (sqrt (acos a))) 1) (/ 1 (/ (- (sqrt (acos a))) (cbrt a))) (* (/ (sqrt a) (sqrt (acos a))) 1) (* (/ (sqrt a) (- (sqrt (acos a)))) 1) (/ 1 (sqrt (acos a))) (/ a (- (sqrt (acos a)))) (* 1 (* (cbrt a) (cbrt a))) (/ 1 (/ (- (acos a)) (cbrt a))) (* 1 (sqrt a)) (* (/ (sqrt a) (- (acos a))) 1) 1 (/ -1 (/ (acos a) a)) 1 (/ -1 (/ (acos a) a)) (* -1 (/ 1 (acos a))) (* 1 a) (/ -1 (/ (acos a) a)) (* -1 (/ (acos a) a)) (/ 1 (* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a)))) (/ 1 (sqrt (/ (- (acos a)) a))) (* (/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a))))) 1) (* (/ (sqrt a) (* (cbrt (- (acos a))) (cbrt (- (acos a))))) 1) (/ 1 (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (* (/ (* (cbrt a) (cbrt a)) (sqrt (- (acos a)))) 1) (* (/ (sqrt a) (sqrt (- (acos a)))) 1) (/ 1 (sqrt (- (acos a)))) (* 1 (* (cbrt a) (cbrt a))) (* 1 (sqrt a)) 1 (* (/ (* (cbrt a) (cbrt a)) -1) 1) (* (/ (sqrt a) -1) 1) -1 (* (/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a))))) 1) (* (/ (sqrt a) (- (* (cbrt (acos a)) (cbrt (acos a))))) 1) (/ 1 (- (* (cbrt (acos a)) (cbrt (acos a))))) (* (/ (* (cbrt a) (cbrt a)) (- (sqrt (acos a)))) 1) (* (/ (sqrt a) (- (sqrt (acos a)))) 1) (/ 1 (- (sqrt (acos a)))) (* 1 (/ (* (cbrt a) (cbrt a)) (- 1))) (* 1 (/ (sqrt a) (- 1))) (/ 1 (- 1)) (* (/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a)))) 1) (* (/ (sqrt a) (* (cbrt (acos a)) (cbrt (acos a)))) 1) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (* (/ (* (cbrt a) (cbrt a)) (sqrt (acos a))) 1) (* (/ (sqrt a) (sqrt (acos a))) 1) (/ 1 (sqrt (acos a))) (* 1 (* (cbrt a) (cbrt a))) (* 1 (sqrt a)) 1 1 (* -1 (/ 1 (acos a))) (* -1 (/ (acos a) a)) (* -1 (/ 1 (acos a))) (* -1 (/ (acos a) a)) (* -1 (/ (acos a) a)) (* -1 (/ (acos a) a)) (/ -1 (/ (acos a) a)) (/ -1 (/ (acos a) a)) (/ -1 (/ (acos a) a)) 0.952 * * * [progress]: adding candidates to table 1.316 * * [progress]: iteration 4 / 4 1.317 * * * [progress]: picking best candidate 1.332 * * * * [pick]: Picked # 1.332 * * * [progress]: localizing error 1.339 * * * [progress]: generating rewritten candidates 1.339 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 1.363 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 1.418 * * * [progress]: generating series expansions 1.418 * * * * [progress]: [ 1 / 2 ] generating series at (2) 1.418 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 1.418 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 1.418 * [taylor]: Taking taylor expansion of -1 in a 1.418 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 1.418 * [taylor]: Taking taylor expansion of a in a 1.418 * [taylor]: Taking taylor expansion of (acos a) in a 1.418 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 1.418 * [taylor]: Taking taylor expansion of -1 in a 1.418 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 1.418 * [taylor]: Taking taylor expansion of a in a 1.418 * [taylor]: Taking taylor expansion of (acos a) in a 1.426 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 1.426 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 1.426 * [taylor]: Taking taylor expansion of -1 in a 1.426 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 1.426 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 1.426 * [taylor]: Taking taylor expansion of a in a 1.427 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 1.427 * [taylor]: Taking taylor expansion of -1 in a 1.427 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 1.427 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 1.427 * [taylor]: Taking taylor expansion of a in a 1.433 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 1.433 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 1.433 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 1.433 * [taylor]: Taking taylor expansion of a in a 1.433 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 1.434 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 1.434 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 1.434 * [taylor]: Taking taylor expansion of a in a 1.434 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 1.451 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 1.451 * [approximate]: Taking taylor expansion of (/ -1 (acos a)) in (a) around 0 1.451 * [taylor]: Taking taylor expansion of (/ -1 (acos a)) in a 1.451 * [taylor]: Taking taylor expansion of -1 in a 1.451 * [taylor]: Taking taylor expansion of (acos a) in a 1.451 * [taylor]: Taking taylor expansion of (/ -1 (acos a)) in a 1.451 * [taylor]: Taking taylor expansion of -1 in a 1.451 * [taylor]: Taking taylor expansion of (acos a) in a 1.452 * [approximate]: Taking taylor expansion of (/ -1 (acos (/ 1 a))) in (a) around 0 1.453 * [taylor]: Taking taylor expansion of (/ -1 (acos (/ 1 a))) in a 1.453 * [taylor]: Taking taylor expansion of -1 in a 1.453 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 1.453 * [taylor]: Taking taylor expansion of (/ -1 (acos (/ 1 a))) in a 1.453 * [taylor]: Taking taylor expansion of -1 in a 1.453 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 1.454 * [approximate]: Taking taylor expansion of (/ -1 (acos (/ -1 a))) in (a) around 0 1.455 * [taylor]: Taking taylor expansion of (/ -1 (acos (/ -1 a))) in a 1.455 * [taylor]: Taking taylor expansion of -1 in a 1.455 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 1.455 * [taylor]: Taking taylor expansion of (/ -1 (acos (/ -1 a))) in a 1.455 * [taylor]: Taking taylor expansion of -1 in a 1.455 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 1.456 * * * [progress]: simplifying candidates 1.467 * [simplify]: Simplifying using # : (expm1 (/ (/ 1 (- (acos a))) (/ 1 a))) (log1p (/ (/ 1 (- (acos 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