8.127 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.017 * * * [progress]: [2/2] Setting up program. 0.019 * [progress]: [Phase 2 of 3] Improving. 0.019 * [simplify]: Simplifying using # : (/ a (- (acos a))) 0.022 * * [simplify]: iteration 0 : 4 enodes (cost 3 ) 0.022 * [simplify]: Simplified to: (/ a (- (acos a))) 0.022 * * [progress]: iteration 1 / 4 0.022 * * * [progress]: picking best candidate 0.024 * * * * [pick]: Picked # 0.024 * * * [progress]: localizing error 0.029 * * * [progress]: generating rewritten candidates 0.029 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.036 * * * [progress]: generating series expansions 0.036 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.036 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.036 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.036 * [taylor]: Taking taylor expansion of -1 in a 0.036 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.036 * [taylor]: Taking taylor expansion of a in a 0.036 * [taylor]: Taking taylor expansion of (acos a) in a 0.036 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.036 * [taylor]: Taking taylor expansion of -1 in a 0.036 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.036 * [taylor]: Taking taylor expansion of a in a 0.036 * [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 0.046 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.046 * [taylor]: Taking taylor expansion of -1 in a 0.046 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.046 * [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 0.063 * * * [progress]: simplifying candidates 0.064 * [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))) 0.070 * * [simplify]: iteration 0 : 166 enodes (cost 384 ) 0.075 * * [simplify]: iteration 1 : 493 enodes (cost 372 ) 0.085 * * [simplify]: iteration 2 : 1439 enodes (cost 367 ) 0.111 * * [simplify]: iteration 3 : 3705 enodes (cost 366 ) 0.172 * * [simplify]: iteration 4 : 5002 enodes (cost 366 ) 0.174 * [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))) 0.175 * * * [progress]: adding candidates to table 0.254 * * [progress]: iteration 2 / 4 0.254 * * * [progress]: picking best candidate 0.268 * * * * [pick]: Picked # 0.268 * * * [progress]: localizing error 0.274 * * * [progress]: generating rewritten candidates 0.274 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.287 * * * * [progress]: [ 2 / 2 ] rewriting at (2 2) 0.304 * * * [progress]: generating series expansions 0.304 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.304 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.305 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.305 * [taylor]: Taking taylor expansion of -1 in a 0.305 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.305 * [taylor]: Taking taylor expansion of a in a 0.305 * [taylor]: Taking taylor expansion of (acos a) in a 0.305 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.305 * [taylor]: Taking taylor expansion of -1 in a 0.305 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.305 * [taylor]: Taking taylor expansion of a in a 0.305 * [taylor]: Taking taylor expansion of (acos a) in a 0.318 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.318 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.318 * [taylor]: Taking taylor expansion of -1 in a 0.318 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.318 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.318 * [taylor]: Taking taylor expansion of a in a 0.319 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.319 * [taylor]: Taking taylor expansion of -1 in a 0.319 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.319 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.319 * [taylor]: Taking taylor expansion of a in a 0.326 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 0.326 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.326 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.326 * [taylor]: Taking taylor expansion of a in a 0.326 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.326 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.326 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.326 * [taylor]: Taking taylor expansion of a in a 0.326 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.337 * * * * [progress]: [ 2 / 2 ] generating series at (2 2) 0.337 * [approximate]: Taking taylor expansion of (* -1 (/ (acos a) a)) in (a) around 0 0.337 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.337 * [taylor]: Taking taylor expansion of -1 in a 0.337 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.337 * [taylor]: Taking taylor expansion of (acos a) in a 0.337 * [taylor]: Taking taylor expansion of a in a 0.337 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.337 * [taylor]: Taking taylor expansion of -1 in a 0.337 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.337 * [taylor]: Taking taylor expansion of (acos a) in a 0.337 * [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 0.353 * [taylor]: Taking taylor expansion of -1 in a 0.353 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.353 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.353 * [taylor]: Taking taylor expansion of a in a 0.353 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 0.353 * [taylor]: Taking taylor expansion of -1 in a 0.353 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.353 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.353 * [taylor]: Taking taylor expansion of a in a 0.367 * [approximate]: Taking taylor expansion of (* a (acos (/ -1 a))) in (a) around 0 0.367 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.367 * [taylor]: Taking taylor expansion of a in a 0.367 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.367 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.367 * [taylor]: Taking taylor expansion of a in a 0.367 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.375 * * * [progress]: simplifying candidates 0.379 * [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))) 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(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)) 1) (/ (cbrt 1) (/ (- (acos a)) a)) (/ (* (cbrt 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(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) 0.467 * * * [progress]: adding candidates to table 0.670 * * [progress]: iteration 3 / 4 0.670 * * * [progress]: picking best candidate 0.692 * * * * [pick]: Picked # 0.692 * * * [progress]: localizing error 0.699 * * * [progress]: generating rewritten candidates 0.699 * * * * [progress]: [ 1 / 2 ] rewriting at (2 2) 0.710 * * * * [progress]: [ 2 / 2 ] rewriting at (2) 0.740 * * * [progress]: generating series expansions 0.740 * * * * [progress]: [ 1 / 2 ] generating series at (2 2) 0.741 * [approximate]: Taking taylor expansion of (* -1 (/ (acos a) a)) in (a) around 0 0.741 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.741 * [taylor]: Taking taylor expansion of -1 in a 0.741 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.741 * [taylor]: Taking taylor expansion of (acos a) in a 0.741 * [taylor]: Taking taylor expansion of a in a 0.741 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.741 * [taylor]: Taking taylor expansion of -1 in a 0.741 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.741 * [taylor]: Taking taylor expansion of (acos a) in a 0.741 * [taylor]: Taking taylor expansion of a in a 0.757 * [approximate]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.757 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 0.757 * [taylor]: Taking taylor expansion of -1 in a 0.757 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.757 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.757 * [taylor]: Taking taylor expansion of a in a 0.757 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 0.757 * [taylor]: Taking taylor expansion of -1 in a 0.757 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.757 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.757 * [taylor]: Taking taylor expansion of a in a 0.776 * [approximate]: Taking taylor expansion of (* a (acos (/ -1 a))) in (a) around 0 0.776 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.776 * [taylor]: Taking taylor expansion of a in a 0.776 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.776 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.776 * [taylor]: Taking taylor expansion of a in a 0.776 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.785 * * * * [progress]: [ 2 / 2 ] generating series at (2) 0.785 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.786 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.786 * [taylor]: Taking taylor expansion of -1 in a 0.786 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.786 * [taylor]: Taking taylor expansion of a in a 0.786 * [taylor]: Taking taylor expansion of (acos a) in a 0.786 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.786 * [taylor]: Taking taylor expansion of -1 in a 0.786 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.786 * [taylor]: Taking taylor expansion of a in a 0.786 * [taylor]: Taking taylor expansion of (acos a) in a 0.794 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.794 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.794 * [taylor]: Taking taylor expansion of -1 in a 0.794 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.794 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.794 * [taylor]: Taking taylor expansion of a in a 0.795 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.795 * [taylor]: Taking taylor expansion of -1 in a 0.795 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.795 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.795 * [taylor]: Taking taylor expansion of a in a 0.801 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 0.801 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.801 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.801 * [taylor]: Taking taylor expansion of a in a 0.802 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.802 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.802 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.802 * [taylor]: Taking taylor expansion of a in a 0.802 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.813 * * * [progress]: simplifying candidates 0.816 * [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 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1 (* (- (acos a)) (/ 1 (sqrt a)))) (/ 1 (* (- (acos a)) (/ 1 1))) (/ 1 (* (- (acos a)) 1)) (/ 1 (* (- (acos a)) 1)) (/ 1 (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ 1 (sqrt (- (acos a)))) (/ 1 1) (/ 1 -1) (/ 1 (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ 1 (- (sqrt (acos a)))) (/ 1 (- 1)) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ 1 (sqrt (acos a))) (/ 1 1) (/ 1 (/ 1 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 (- (acos a))) (/ 1 (* (- (acos a)) 1)) (/ 1 (* (- (acos a)) (- 1))) (/ 1 (* (- (acos a)) 1)) (/ 1 (* (- (acos a)) (/ 1 (* (cbrt a) (cbrt a))))) (/ 1 (* (- (acos a)) (/ 1 (sqrt a)))) (/ 1 (* (- (acos a)) (/ 1 1))) (/ 1 (* (- (acos a)) (* (cbrt 1) (cbrt 1)))) (/ 1 (* (- (acos a)) (sqrt 1))) (/ 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))) 0.829 * * [simplify]: iteration 0 : 723 enodes (cost 1813 ) 0.847 * * [simplify]: iteration 1 : 3279 enodes (cost 1446 ) 0.889 * * [simplify]: iteration 2 : 5001 enodes (cost 1207 ) 0.898 * [simplify]: Simplified to: (expm1 (* (- (acos a)) (/ 1 a))) (log1p (* (- (acos a)) (/ 1 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)) (/ 1 a))) (cbrt (* (- (acos a)) (/ 1 a)))) (cbrt (* (- (acos a)) (/ 1 a))) (pow (/ (- (acos a)) a) 3) (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 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)) 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(* (- (acos a)) (/ 1 a)))) 1 (/ 1 (* (sqrt (- (acos a))) (sqrt (/ 1 a)))) (/ (sqrt a) (sqrt (- (acos a)))) (/ (sqrt a) (sqrt (- (acos a)))) (/ 1 (* (- (acos a)) (* (cbrt (/ 1 a)) (cbrt (/ 1 a))))) (/ 1 (* (- (acos a)) (sqrt (/ 1 a)))) (/ (* (cbrt a) (cbrt a)) (- (acos a))) (/ (sqrt a) (- (acos a))) (* -1 (/ 1 (acos a))) (/ (* (cbrt a) (cbrt a)) (- (acos a))) (/ (sqrt a) (- (acos a))) (* -1 (/ 1 (acos a))) (/ (* (cbrt a) (cbrt a)) (- (acos a))) (/ (sqrt a) (- (acos a))) (* -1 (/ 1 (acos a))) (* -1 (/ 1 (acos a))) (* -1 (/ 1 (acos a))) (/ 1 (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ 1 (sqrt (- (acos a)))) 1 -1 (/ 1 (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ 1 (- (sqrt (acos a)))) (/ 1 (- 1)) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ 1 (sqrt (acos a))) 1 a (/ (- (acos a)) a) (/ (- (acos a)) a) (/ (- (acos a)) a) (* -1 (/ 1 (acos a))) (* -1 (/ 1 (acos a))) (* -1 (/ 1 (acos a))) (* -1 (/ 1 (acos a))) (/ 1 (acos a)) (* -1 (/ 1 (acos a))) (/ (* (cbrt a) (cbrt a)) (- (acos a))) (/ (sqrt a) (- (acos a))) (* -1 (/ 1 (acos a))) (* -1 (/ 1 (acos a))) (* -1 (/ 1 (acos a))) (* -1 (/ 1 (acos a))) (/ (- (acos a)) a) (/ (- (acos a)) a) (/ (- (acos a)) a) (/ a (- (acos a))) (/ a (- (acos a))) (/ a (- (acos a))) 0.899 * * * [progress]: adding candidates to table 1.082 * * [progress]: iteration 4 / 4 1.082 * * * [progress]: picking best candidate 1.102 * * * * [pick]: Picked # 1.102 * * * [progress]: localizing error 1.110 * * * [progress]: generating rewritten candidates 1.110 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 1.197 * * * [progress]: generating series expansions 1.197 * * * * [progress]: [ 1 / 1 ] generating series at (2) 1.198 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 1.198 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 1.198 * [taylor]: Taking taylor expansion of -1 in a 1.198 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 1.198 * [taylor]: Taking taylor expansion of a in a 1.198 * [taylor]: Taking taylor expansion of (acos a) in a 1.199 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 1.199 * [taylor]: Taking taylor expansion of -1 in a 1.199 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 1.199 * [taylor]: Taking taylor expansion of a in a 1.199 * [taylor]: Taking taylor expansion of (acos a) in a 1.217 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 1.217 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 1.217 * [taylor]: Taking taylor expansion of -1 in a 1.217 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 1.217 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 1.217 * [taylor]: Taking taylor expansion of a in a 1.218 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 1.218 * [taylor]: Taking taylor expansion of -1 in a 1.218 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 1.218 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 1.218 * [taylor]: Taking taylor expansion of a in a 1.225 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 1.225 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 1.225 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 1.225 * [taylor]: Taking taylor expansion of a in a 1.225 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 1.225 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 1.225 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 1.225 * [taylor]: Taking taylor expansion of a in a 1.226 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 1.236 * * * [progress]: simplifying candidates 1.248 * [simplify]: Simplifying using # : (expm1 (/ (* -1 (/ 1 (acos a))) (/ (sqrt 1) a))) (log1p (/ (* -1 (/ 1 (acos a))) (/ (sqrt 1) a))) (- (+ (log -1) (- (log (acos a)))) (- (log (sqrt 1)) (log a))) (- (+ (log -1) (- (log (acos a)))) 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(sqrt a)) (/ -1 (acos a)) (* (/ -1 (acos a)) (* (cbrt a) (cbrt a))) (* (/ -1 (acos a)) (sqrt a)) (/ -1 (acos a)) (* (/ -1 (acos a)) (* (cbrt a) (cbrt a))) (* (/ -1 (acos a)) (sqrt a)) (/ -1 (acos a)) (/ -1 (acos a)) (/ -1 (acos a)) (* (/ 1 a) (acos a)) (/ (/ (sqrt 1) a) (cbrt (* -1 (/ 1 (acos a))))) (/ (/ (sqrt 1) a) (sqrt (* -1 (/ 1 (acos a))))) (/ (sqrt 1) (* (/ -1 (acos a)) a)) (/ (/ (sqrt 1) a) (* (sqrt -1) (sqrt (/ 1 (acos a))))) (/ (/ (sqrt 1) a) (* (sqrt -1) (/ 1 (sqrt (acos a))))) (/ (/ (sqrt 1) a) (* (sqrt -1) (/ 1 (sqrt (acos a))))) (/ (/ (sqrt 1) a) (cbrt (/ 1 (acos a)))) (/ (/ 1 a) (sqrt (/ 1 (acos a)))) (/ (/ (sqrt 1) a) (/ (cbrt 1) (cbrt (acos a)))) (/ (/ (sqrt 1) a) (/ (cbrt 1) (sqrt (acos a)))) (/ (/ (sqrt 1) a) (/ (cbrt 1) (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 a) (acos a)) (/ (/ (sqrt 1) a) (* (cbrt -1) (/ 1 (acos a)))) (/ (/ (sqrt 1) a) (* (sqrt -1) (/ 1 (acos a)))) (/ (sqrt 1) (* (/ -1 (acos a)) a)) (/ (/ (sqrt 1) a) -1) (/ -1 (acos a)) (/ 1 (acos a)) (/ -1 (acos a)) (* (/ -1 (acos a)) (* (cbrt a) (cbrt a))) (* (/ -1 (acos a)) (sqrt a)) (/ -1 (acos a)) (/ (/ (/ -1 (acos a)) (cbrt (sqrt 1))) (cbrt (sqrt 1))) (/ -1 (/ (fabs (cbrt 1)) (/ 1 (acos a)))) (/ -1 (acos a)) (/ -1 (acos a)) (/ -1 (acos a)) (/ -1 (acos a)) (* (/ 1 a) (acos a)) (* (/ 1 a) (acos a)) (* (/ 1 a) (acos a)) (* (/ 1 a) (acos a)) (* (/ (sqrt 1) a) (- (acos a))) (* (/ 1 a) (acos a)) (* (/ 1 a) (cbrt (acos a))) (* (/ 1 a) (sqrt (acos a))) (* (/ 1 a) (acos a)) (* (/ (sqrt 1) a) (/ (acos a) (cbrt 1))) (* (/ 1 a) (acos a)) (* (/ 1 a) (acos a)) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) 1.391 * * * [progress]: adding candidates to table 2.030 * [progress]: [Phase 3 of 3] Extracting. 2.031 * * [regime]: Finding splitpoints for: (# # # # # # # # # # # #) 2.033 * * * [regime-changes]: Trying 2 branch expressions: ((/ a (- (acos a))) a) 2.033 * * * * [regimes]: Trying to branch on (/ a (- (acos a))) from (# # # # # # # # # # # #) 2.078 * * * * [regimes]: Trying to branch on a from (# # # # # # # # # # # #) 2.120 * * * [regime]: Found split indices: #