8.096 * [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))) 0.019 * [simplify]: Sending expressions to egg_math: (/ h0 (- (acos h0))) 0.021 * * [simplify]: iteration 0 : 4 enodes (cost 3 ) 0.021 * [simplify]: Simplified to: (/ a (- (acos a))) 0.021 * * [progress]: iteration 1 / 4 0.021 * * * [progress]: picking best candidate 0.023 * * * * [pick]: Picked # 0.023 * * * [progress]: localizing error 0.029 * * * [progress]: generating rewritten candidates 0.029 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.038 * * * [progress]: generating series expansions 0.038 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.039 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.039 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.039 * [taylor]: Taking taylor expansion of -1 in a 0.039 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.039 * [taylor]: Taking taylor expansion of a in a 0.039 * [taylor]: Taking taylor expansion of (acos a) in a 0.039 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.039 * [taylor]: Taking taylor expansion of -1 in a 0.039 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.039 * [taylor]: Taking taylor expansion of a in a 0.039 * [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 0.051 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 0.051 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.051 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.051 * [taylor]: Taking taylor expansion of a in a 0.051 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.051 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.051 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.051 * [taylor]: Taking taylor expansion of a in a 0.051 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.059 * * * [progress]: simplifying candidates 0.060 * [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))) 0.060 * [simplify]: Sending expressions to egg_math: (expm1 (/ h0 (- (acos h0)))) (log1p (/ h0 (- (acos h0)))) (- (log h0) (log (- (acos h0)))) (log (/ h0 (- (acos h0)))) (exp (/ h0 (- (acos h0)))) (/ (* (* h0 h0) h0) (* (* (- (acos h0)) (- (acos h0))) (- (acos h0)))) (* (cbrt (/ h0 (- (acos h0)))) (cbrt (/ h0 (- (acos h0))))) (cbrt (/ h0 (- (acos h0)))) (* (* (/ h0 (- (acos h0))) (/ h0 (- (acos h0)))) (/ h0 (- (acos h0)))) (sqrt (/ h0 (- (acos h0)))) (sqrt (/ h0 (- (acos h0)))) (- h0) (- (- (acos h0))) (/ (* (cbrt h0) (cbrt h0)) (* (cbrt (- (acos h0))) (cbrt (- (acos h0))))) (/ (cbrt h0) (cbrt (- (acos h0)))) (/ (* (cbrt h0) (cbrt h0)) (sqrt (- (acos h0)))) (/ (cbrt h0) (sqrt (- (acos h0)))) (/ (* (cbrt h0) (cbrt h0)) 1) (/ (cbrt h0) (- (acos h0))) (/ (* (cbrt h0) (cbrt h0)) -1) (/ (cbrt h0) (acos h0)) (/ (* (cbrt h0) (cbrt h0)) (- (* (cbrt (acos h0)) (cbrt (acos h0))))) (/ (cbrt h0) (cbrt (acos h0))) (/ (* (cbrt h0) (cbrt h0)) (- (sqrt (acos h0)))) (/ (cbrt h0) (sqrt (acos h0))) (/ (* (cbrt h0) (cbrt h0)) (- 1)) (/ (cbrt h0) (acos h0)) (/ (* (cbrt h0) (cbrt h0)) (* (cbrt (acos h0)) (cbrt (acos h0)))) (/ (cbrt h0) (- (cbrt (acos h0)))) (/ (* (cbrt h0) (cbrt h0)) (sqrt (acos h0))) (/ (cbrt h0) (- (sqrt (acos h0)))) (/ (* (cbrt h0) (cbrt h0)) 1) (/ (cbrt h0) (- (acos h0))) (/ (sqrt h0) (* (cbrt (- (acos h0))) (cbrt (- (acos h0))))) (/ (sqrt h0) (cbrt (- (acos h0)))) (/ (sqrt h0) (sqrt (- (acos h0)))) (/ (sqrt h0) (sqrt (- (acos h0)))) (/ (sqrt h0) 1) (/ (sqrt h0) (- (acos h0))) (/ (sqrt h0) -1) (/ (sqrt h0) (acos h0)) (/ (sqrt h0) (- (* (cbrt (acos h0)) (cbrt (acos h0))))) (/ (sqrt h0) (cbrt (acos h0))) (/ (sqrt h0) (- (sqrt (acos h0)))) (/ (sqrt h0) (sqrt (acos h0))) (/ (sqrt h0) (- 1)) (/ (sqrt h0) (acos h0)) (/ (sqrt h0) (* (cbrt (acos h0)) (cbrt (acos h0)))) (/ (sqrt h0) (- (cbrt (acos h0)))) (/ (sqrt h0) (sqrt (acos h0))) (/ (sqrt h0) (- (sqrt (acos h0)))) (/ (sqrt h0) 1) (/ (sqrt h0) (- (acos h0))) (/ 1 (* (cbrt (- (acos h0))) (cbrt (- (acos h0))))) (/ h0 (cbrt (- (acos h0)))) (/ 1 (sqrt (- (acos h0)))) (/ h0 (sqrt (- (acos h0)))) (/ 1 1) (/ h0 (- (acos h0))) (/ 1 -1) (/ h0 (acos h0)) (/ 1 (- (* (cbrt (acos h0)) (cbrt (acos h0))))) (/ h0 (cbrt (acos h0))) (/ 1 (- (sqrt (acos h0)))) (/ h0 (sqrt (acos h0))) (/ 1 (- 1)) (/ h0 (acos h0)) (/ 1 (* (cbrt (acos h0)) (cbrt (acos h0)))) (/ h0 (- (cbrt (acos h0)))) (/ 1 (sqrt (acos h0))) (/ h0 (- (sqrt (acos h0)))) (/ 1 1) (/ h0 (- (acos h0))) (/ 1 (- (acos h0))) (/ (- (acos h0)) h0) (/ h0 (* (cbrt (- (acos h0))) (cbrt (- (acos h0))))) (/ h0 (sqrt (- (acos h0)))) (/ h0 1) (/ h0 -1) (/ h0 (- (* (cbrt (acos h0)) (cbrt (acos h0))))) (/ h0 (- (sqrt (acos h0)))) (/ h0 (- 1)) (/ h0 (* (cbrt (acos h0)) (cbrt (acos h0)))) (/ h0 (sqrt (acos h0))) (/ h0 1) (/ (- (acos h0)) (cbrt h0)) (/ (- (acos h0)) (sqrt h0)) (/ (- (acos h0)) h0) (* -1 (/ h0 (acos h0))) (* -1 (/ h0 (acos h0))) (* -1 (/ h0 (acos h0))) 0.064 * * [simplify]: iteration 0 : 166 enodes (cost 384 ) 0.067 * * [simplify]: iteration 1 : 493 enodes (cost 372 ) 0.073 * * [simplify]: iteration 2 : 1442 enodes (cost 367 ) 0.093 * * [simplify]: iteration 3 : 3704 enodes (cost 366 ) 0.144 * * [simplify]: iteration 4 : 5002 enodes (cost 366 ) 0.146 * [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))) 0.146 * * * [progress]: adding candidates to table 0.238 * * [progress]: iteration 2 / 4 0.238 * * * [progress]: picking best candidate 0.252 * * * * [pick]: Picked # 0.253 * * * [progress]: localizing error 0.257 * * * [progress]: generating rewritten candidates 0.257 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.273 * * * * [progress]: [ 2 / 2 ] rewriting at (2 2) 0.293 * * * [progress]: generating series expansions 0.293 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.293 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.293 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.293 * [taylor]: Taking taylor expansion of -1 in a 0.293 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.293 * [taylor]: Taking taylor expansion of a in a 0.293 * [taylor]: Taking taylor expansion of (acos a) in a 0.293 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.293 * [taylor]: Taking taylor expansion of -1 in a 0.293 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.293 * [taylor]: Taking taylor expansion of a in a 0.293 * [taylor]: Taking taylor expansion of (acos a) in a 0.304 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.304 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.304 * [taylor]: Taking taylor expansion of -1 in a 0.304 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.304 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.304 * [taylor]: Taking taylor expansion of a in a 0.304 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.304 * [taylor]: Taking taylor expansion of -1 in a 0.304 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.304 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.304 * [taylor]: Taking taylor expansion of a in a 0.310 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 0.310 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.310 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.310 * [taylor]: Taking taylor expansion of a in a 0.310 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.310 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.310 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.310 * [taylor]: Taking taylor expansion of a in a 0.310 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.318 * * * * [progress]: [ 2 / 2 ] generating series at (2 2) 0.318 * [approximate]: Taking taylor expansion of (* -1 (/ (acos a) a)) in (a) around 0 0.318 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.318 * [taylor]: Taking taylor expansion of -1 in a 0.318 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.318 * [taylor]: Taking taylor expansion of (acos a) in a 0.318 * [taylor]: Taking taylor expansion of a in a 0.318 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.318 * [taylor]: Taking taylor expansion of -1 in a 0.318 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.318 * [taylor]: Taking taylor expansion of (acos a) in a 0.318 * [taylor]: Taking taylor expansion of a in a 0.329 * [approximate]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.329 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 0.329 * [taylor]: Taking taylor expansion of -1 in a 0.329 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.329 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.330 * [taylor]: Taking taylor expansion of a in a 0.330 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 0.330 * [taylor]: Taking taylor expansion of -1 in a 0.330 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.330 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.330 * [taylor]: Taking taylor expansion of a in a 0.339 * [approximate]: Taking taylor expansion of (* a (acos (/ -1 a))) in (a) around 0 0.340 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.340 * [taylor]: Taking taylor expansion of a in a 0.340 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.340 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.340 * [taylor]: Taking taylor expansion of a in a 0.340 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.346 * * * [progress]: simplifying candidates 0.349 * [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)))) (* 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(cbrt h0))) (/ (- (sqrt (acos h0))) (cbrt h0)) (/ (sqrt (acos h0)) (sqrt h0)) (/ (- (sqrt (acos h0))) (sqrt h0)) (/ (sqrt (acos h0)) 1) (/ (- (sqrt (acos h0))) h0) (/ 1 (* (cbrt h0) (cbrt h0))) (/ (- (acos h0)) (cbrt h0)) (/ 1 (sqrt h0)) (/ (- (acos h0)) (sqrt h0)) (/ 1 1) (/ (- (acos h0)) h0) (/ 1 h0) (/ h0 (- (acos h0))) (/ (acos h0) h0) (/ (- (acos h0)) (* (cbrt h0) (cbrt h0))) (/ (- (acos h0)) (sqrt h0)) (/ (- (acos h0)) 1) (/ h0 (cbrt (- (acos h0)))) (/ h0 (sqrt (- (acos h0)))) (/ h0 (- (acos h0))) (/ h0 (acos h0)) (/ h0 (cbrt (acos h0))) (/ h0 (sqrt (acos h0))) (/ h0 (acos h0)) (/ h0 (- (cbrt (acos h0)))) (/ h0 (- (sqrt (acos h0)))) (/ h0 (- (acos h0))) (* -1 (/ h0 (acos h0))) (* -1 (/ h0 (acos h0))) (* -1 (/ h0 (acos h0))) (* -1 (/ (acos h0) h0)) (* -1 (/ (acos h0) h0)) (* -1 (/ (acos h0) h0)) 0.358 * * [simplify]: iteration 0 : 663 enodes (cost 1934 ) 0.370 * * [simplify]: iteration 1 : 3064 enodes (cost 1717 ) 0.403 * * [simplify]: iteration 2 : 5001 enodes (cost 1525 ) 0.410 * [simplify]: Simplified to: (expm1 (/ 1 (/ (- (acos a)) a))) (log1p (/ 1 (/ (- (acos a)) a))) -1 (log (/ 1 (/ (- (acos a)) a))) (log (/ 1 (/ (- (acos a)) a))) (log (/ 1 (/ (- (acos a)) a))) (log (/ 1 (/ (- (acos a)) a))) (log (/ 1 (/ (- (acos a)) a))) (log (/ 1 (/ (- (acos a)) a))) (log (/ 1 (/ (- (acos a)) a))) (pow (exp -1) (/ a (acos a))) (* -1 (pow (/ a (acos a)) 3)) (* -1 (pow (/ a (acos a)) 3)) (* (cbrt (/ 1 (/ (- (acos a)) a))) (cbrt (/ 1 (/ (- (acos a)) a)))) (cbrt (/ 1 (/ (- (acos a)) a))) (* -1 (pow (/ a (acos a)) 3)) (sqrt (/ 1 (/ (- (acos a)) a))) (sqrt (/ 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 (cbrt a)) (cbrt (- (acos a)))) (/ (sqrt a) (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ (sqrt a) (cbrt (- (acos a)))) (/ 1 (* (cbrt (- (acos 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(/ (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))) (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))) (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 (* (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) 0.411 * * * [progress]: adding candidates to table 0.657 * * [progress]: iteration 3 / 4 0.658 * * * [progress]: picking best candidate 0.673 * * * * [pick]: Picked # 0.674 * * * [progress]: localizing error 0.680 * * * [progress]: generating rewritten candidates 0.680 * * * * [progress]: [ 1 / 2 ] rewriting at (2 2) 0.700 * * * * [progress]: [ 2 / 2 ] rewriting at (2) 0.725 * * * [progress]: generating series expansions 0.725 * * * * [progress]: [ 1 / 2 ] generating series at (2 2) 0.725 * [approximate]: Taking taylor expansion of (* -1 (/ (acos a) a)) in (a) around 0 0.726 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.726 * [taylor]: Taking taylor expansion of -1 in a 0.726 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.726 * [taylor]: Taking taylor expansion of (acos a) in a 0.726 * [taylor]: Taking taylor expansion of a in a 0.726 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.726 * [taylor]: Taking taylor expansion of -1 in a 0.726 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.726 * [taylor]: Taking taylor expansion of (acos a) in a 0.726 * [taylor]: Taking taylor expansion of a in a 0.740 * [approximate]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.740 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 0.740 * [taylor]: Taking taylor expansion of -1 in a 0.740 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.740 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.740 * [taylor]: Taking taylor expansion of a in a 0.740 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 0.740 * [taylor]: Taking taylor expansion of -1 in a 0.740 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.740 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.740 * [taylor]: Taking taylor expansion of a in a 0.751 * [approximate]: Taking taylor expansion of (* a (acos (/ -1 a))) in (a) around 0 0.751 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.751 * [taylor]: Taking taylor expansion of a in a 0.751 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.751 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.751 * [taylor]: Taking taylor expansion of a in a 0.751 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.757 * * * * [progress]: [ 2 / 2 ] generating series at (2) 0.757 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.757 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.757 * [taylor]: Taking taylor expansion of -1 in a 0.757 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.757 * [taylor]: Taking taylor expansion of a in a 0.757 * [taylor]: Taking taylor expansion of (acos a) in a 0.757 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.757 * [taylor]: Taking taylor expansion of -1 in a 0.758 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.758 * [taylor]: Taking taylor expansion of a in a 0.758 * [taylor]: Taking taylor expansion of (acos a) in a 0.764 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.764 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.764 * [taylor]: Taking taylor expansion of -1 in a 0.764 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.764 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.764 * [taylor]: Taking taylor expansion of a in a 0.764 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.764 * [taylor]: Taking taylor expansion of -1 in a 0.764 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.764 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.764 * [taylor]: Taking taylor expansion of a in a 0.770 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 0.770 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.770 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.770 * [taylor]: Taking taylor expansion of a in a 0.770 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.770 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.770 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.770 * [taylor]: Taking taylor expansion of a in a 0.770 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.778 * * * [progress]: simplifying candidates 0.780 * [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 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(- (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))) 0.780 * [simplify]: Sending expressions to egg_math: (expm1 (* (- (acos h0)) (/ 1 h0))) (log1p (* (- (acos h0)) (/ 1 h0))) (* (- (acos h0)) (/ 1 h0)) (+ (log (- (acos h0))) (- (log h0))) (+ (log (- (acos h0))) (- 0 (log h0))) (+ (log (- (acos h0))) (- (log 1) (log h0))) (+ (log (- (acos h0))) (log (/ 1 h0))) (log (* (- (acos h0)) (/ 1 h0))) (exp (* (- (acos h0)) (/ 1 h0))) (* (* (* (- (acos h0)) (- (acos h0))) (- (acos h0))) (/ (* (* 1 1) 1) (* (* h0 h0) h0))) (* (* (* (- (acos h0)) (- (acos h0))) (- (acos h0))) (* (* (/ 1 h0) (/ 1 h0)) (/ 1 h0))) (* (cbrt (* (- (acos h0)) (/ 1 h0))) (cbrt (* (- (acos h0)) (/ 1 h0)))) (cbrt (* (- (acos h0)) (/ 1 h0))) (* (* (* (- (acos h0)) (/ 1 h0)) (* (- (acos h0)) (/ 1 h0))) (* (- (acos h0)) (/ 1 h0))) (sqrt (* (- (acos h0)) (/ 1 h0))) (sqrt (* (- (acos h0)) (/ 1 h0))) (* (sqrt (- (acos h0))) (sqrt (/ 1 h0))) (* (sqrt (- (acos h0))) (sqrt (/ 1 h0))) (* (sqrt (- (acos h0))) (/ (sqrt 1) (sqrt h0))) (* (sqrt (- (acos h0))) (/ (sqrt 1) (sqrt h0))) (* (sqrt (- (acos h0))) (/ 1 (sqrt h0))) (* (sqrt (- (acos h0))) (/ 1 (sqrt h0))) (* (acos h0) (/ 1 h0)) (* (- (acos h0)) (* (cbrt (/ 1 h0)) (cbrt (/ 1 h0)))) (* (- (acos h0)) (sqrt (/ 1 h0))) (* (- (acos h0)) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt h0) (cbrt h0)))) (* (- (acos h0)) (/ (* (cbrt 1) (cbrt 1)) (sqrt h0))) (* (- (acos h0)) (/ (* (cbrt 1) (cbrt 1)) 1)) (* (- (acos h0)) (/ (sqrt 1) (* (cbrt h0) (cbrt h0)))) (* (- (acos h0)) (/ (sqrt 1) (sqrt h0))) (* (- (acos h0)) (/ (sqrt 1) 1)) (* (- (acos h0)) (/ 1 (* (cbrt h0) (cbrt h0)))) (* (- (acos h0)) (/ 1 (sqrt h0))) (* (- (acos h0)) (/ 1 1)) (* (- (acos h0)) 1) (* (- (acos h0)) 1) (* (cbrt (- (acos h0))) (/ 1 h0)) (* (sqrt (- (acos h0))) (/ 1 h0)) (* (- (acos h0)) (/ 1 h0)) (* (acos h0) (/ 1 h0)) (* (cbrt (acos h0)) (/ 1 h0)) (* (sqrt (acos h0)) (/ 1 h0)) (* (acos h0) (/ 1 h0)) (* (- (cbrt (acos h0))) (/ 1 h0)) (* (- (sqrt (acos h0))) (/ 1 h0)) (* (- (acos h0)) (/ 1 h0)) (* (- (acos h0)) 1) (expm1 (/ 1 (* (- (acos h0)) (/ 1 h0)))) (log1p (/ 1 (* (- (acos h0)) (/ 1 h0)))) (- 1) (- 1) (- (+ (log (- (acos h0))) (- (log h0)))) (- (+ (log (- (acos h0))) (- 0 (log h0)))) (- (+ (log (- (acos h0))) (- (log 1) (log h0)))) (- (+ (log (- (acos h0))) (log (/ 1 h0)))) (- (log (* (- (acos h0)) (/ 1 h0)))) (- 0 (+ (log (- (acos h0))) (- (log h0)))) (- 0 (+ (log (- (acos h0))) (- 0 (log h0)))) (- 0 (+ (log (- (acos h0))) (- (log 1) (log h0)))) (- 0 (+ (log (- (acos h0))) (log (/ 1 h0)))) (- 0 (log (* (- (acos h0)) (/ 1 h0)))) (- (log 1) (+ (log (- (acos h0))) (- (log h0)))) (- (log 1) (+ (log (- (acos h0))) (- 0 (log h0)))) (- (log 1) (+ (log (- (acos h0))) (- (log 1) (log h0)))) (- (log 1) (+ (log (- (acos h0))) (log (/ 1 h0)))) (- (log 1) (log (* (- (acos h0)) (/ 1 h0)))) (log (/ 1 (* (- (acos h0)) (/ 1 h0)))) (exp (/ 1 (* (- (acos h0)) (/ 1 h0)))) (/ (* (* 1 1) 1) (* (* (* (- (acos h0)) (- (acos h0))) (- (acos h0))) (/ (* (* 1 1) 1) (* (* h0 h0) h0)))) (/ (* (* 1 1) 1) (* (* (* (- (acos h0)) (- (acos h0))) (- (acos h0))) (* (* (/ 1 h0) (/ 1 h0)) (/ 1 h0)))) (/ (* (* 1 1) 1) (* (* (* (- (acos h0)) (/ 1 h0)) (* (- (acos h0)) (/ 1 h0))) (* (- (acos h0)) (/ 1 h0)))) (* (cbrt (/ 1 (* (- (acos h0)) (/ 1 h0)))) (cbrt (/ 1 (* (- (acos h0)) (/ 1 h0))))) (cbrt (/ 1 (* (- (acos h0)) (/ 1 h0)))) (* (* (/ 1 (* (- (acos h0)) (/ 1 h0))) (/ 1 (* (- (acos h0)) (/ 1 h0)))) (/ 1 (* (- (acos h0)) (/ 1 h0)))) (sqrt (/ 1 (* (- (acos h0)) (/ 1 h0)))) (sqrt (/ 1 (* (- (acos h0)) (/ 1 h0)))) (- 1) (- (* (- (acos h0)) (/ 1 h0))) (/ (* (cbrt 1) (cbrt 1)) (- (acos h0))) (/ (cbrt 1) (/ 1 h0)) (/ (sqrt 1) (- (acos h0))) (/ (sqrt 1) (/ 1 h0)) (/ 1 (- (acos h0))) (/ 1 (/ 1 h0)) (/ 1 (* (- (acos h0)) (/ 1 h0))) (/ (* (- (acos h0)) (/ 1 h0)) 1) (/ 1 (- (acos h0))) (/ (* (- (acos h0)) (/ 1 h0)) (cbrt 1)) (/ (* (- (acos h0)) (/ 1 h0)) (sqrt 1)) (/ (* (- (acos h0)) (/ 1 h0)) 1) (/ 1 (- (acos h0))) (/ 1 (* (- (acos h0)) 1)) (* -1 (/ (acos h0) h0)) (* -1 (/ (acos h0) h0)) (* -1 (/ (acos h0) h0)) (* -1 (/ h0 (acos h0))) (* -1 (/ h0 (acos h0))) (* -1 (/ h0 (acos h0))) 0.785 * * [simplify]: iteration 0 : 355 enodes (cost 529 ) 0.793 * * [simplify]: iteration 1 : 1644 enodes (cost 425 ) 0.816 * * [simplify]: iteration 2 : 5001 enodes (cost 401 ) 0.818 * [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))) 1) (sqrt a)) (/ (* (sqrt (- (acos a))) 1) (sqrt a)) (/ (* (sqrt (- (acos a))) 1) (sqrt a)) (/ (* (sqrt (- (acos a))) 1) (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 (/ 1 (* (- (acos a)) (/ 1 a)))) (log1p (/ 1 (* (- (acos a)) (/ 1 a)))) -1 -1 (- (log (/ (- (acos a)) a))) (- (log (/ (- (acos a)) a))) (- (log (/ (- (acos a)) a))) (- (log (/ (- (acos a)) a))) (- (log (/ (- (acos a)) a))) (- (log (/ (- (acos a)) a))) (- (log (/ (- (acos a)) a))) (- (log (/ (- (acos a)) a))) (- (log (/ (- (acos a)) a))) (- (log (/ (- (acos a)) a))) (- (log (/ (- (acos a)) a))) (- (log (/ (- (acos a)) a))) (- (log (/ (- (acos a)) a))) (- (log (/ (- (acos a)) a))) (- (log (/ (- (acos a)) a))) (- (log (/ (- (acos a)) a))) (pow (exp (/ 1 (- (acos a)))) a) (/ (pow a 3) (pow (- (acos a)) 3)) (/ (pow a 3) (pow (- (acos a)) 3)) (/ (pow a 3) (pow (- (acos a)) 3)) (* (cbrt (/ 1 (* (- (acos a)) (/ 1 a)))) (cbrt (/ 1 (* (- (acos a)) (/ 1 a))))) (cbrt (/ 1 (* (- (acos a)) (/ 1 a)))) (/ (pow a 3) (pow (- (acos a)) 3)) (sqrt (/ 1 (* (- (acos a)) (/ 1 a)))) (sqrt (/ 1 (* (- (acos a)) (/ 1 a)))) -1 (/ (acos a) a) (* -1 (/ 1 (acos a))) a (* -1 (/ 1 (acos a))) a (* -1 (/ 1 (acos a))) a (/ a (- (acos a))) (/ (- (acos a)) a) (* -1 (/ 1 (acos a))) (/ (- (acos a)) a) (/ (- (acos a)) a) (/ (- (acos a)) 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))) 0.818 * * * [progress]: adding candidates to table 0.931 * * [progress]: iteration 4 / 4 0.931 * * * [progress]: picking best candidate 0.946 * * * * [pick]: Picked # 0.946 * * * [progress]: localizing error 0.956 * * * [progress]: generating rewritten candidates 0.956 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1) 0.957 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 0.959 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2) 0.959 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 2) 0.961 * * * [progress]: generating series expansions 0.961 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1) 0.961 * [approximate]: Taking taylor expansion of (sqrt (acos a)) in (a) around 0 0.961 * [taylor]: Taking taylor expansion of (sqrt (acos a)) in a 0.961 * [taylor]: Taking taylor expansion of (acos a) in a 0.962 * [taylor]: Taking taylor expansion of (sqrt (acos a)) in a 0.962 * [taylor]: Taking taylor expansion of (acos a) in a 0.967 * [approximate]: Taking taylor expansion of (sqrt (acos (/ 1 a))) in (a) around 0 0.967 * [taylor]: Taking taylor expansion of (sqrt (acos (/ 1 a))) in a 0.967 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.967 * [taylor]: Taking taylor expansion of (sqrt (acos (/ 1 a))) in a 0.967 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.970 * [approximate]: Taking taylor expansion of (sqrt (acos (/ -1 a))) in (a) around 0 0.970 * [taylor]: Taking taylor expansion of (sqrt (acos (/ -1 a))) in a 0.970 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.970 * [taylor]: Taking taylor expansion of (sqrt (acos (/ -1 a))) in a 0.970 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.973 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 0.973 * [approximate]: Taking taylor expansion of (sqrt (acos a)) in (a) around 0 0.973 * [taylor]: Taking taylor expansion of (sqrt (acos a)) in a 0.973 * [taylor]: Taking taylor expansion of (acos a) in a 0.973 * [taylor]: Taking taylor expansion of (sqrt (acos a)) in a 0.973 * [taylor]: Taking taylor expansion of (acos a) in a 0.976 * [approximate]: Taking taylor expansion of (sqrt (acos (/ 1 a))) in (a) around 0 0.976 * [taylor]: Taking taylor expansion of (sqrt (acos (/ 1 a))) in a 0.976 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.976 * [taylor]: Taking taylor expansion of (sqrt (acos (/ 1 a))) in a 0.976 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.979 * [approximate]: Taking taylor expansion of (sqrt (acos (/ -1 a))) in (a) around 0 0.979 * [taylor]: Taking taylor expansion of (sqrt (acos (/ -1 a))) in a 0.979 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.979 * [taylor]: Taking taylor expansion of (sqrt (acos (/ -1 a))) in a 0.979 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.982 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2) 0.982 * [approximate]: Taking taylor expansion of (pow a 1/3) in (a) around 0 0.982 * [taylor]: Taking taylor expansion of (pow a 1/3) in a 0.982 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log a))) in a 0.982 * [taylor]: Taking taylor expansion of (* 1/3 (log a)) in a 0.982 * [taylor]: Taking taylor expansion of 1/3 in a 0.982 * [taylor]: Taking taylor expansion of (log a) in a 0.982 * [taylor]: Taking taylor expansion of a in a 0.982 * [taylor]: Taking taylor expansion of (pow a 1/3) in a 0.982 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log a))) in a 0.982 * [taylor]: Taking taylor expansion of (* 1/3 (log a)) in a 0.982 * [taylor]: Taking taylor expansion of 1/3 in a 0.982 * [taylor]: Taking taylor expansion of (log a) in a 0.983 * [taylor]: Taking taylor expansion of a in a 1.029 * [approximate]: Taking taylor expansion of (pow (/ 1 a) 1/3) in (a) around 0 1.029 * [taylor]: Taking taylor expansion of (pow (/ 1 a) 1/3) in a 1.029 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 a)))) in a 1.029 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 a))) in a 1.029 * [taylor]: Taking taylor expansion of 1/3 in a 1.029 * [taylor]: Taking taylor expansion of (log (/ 1 a)) in a 1.029 * [taylor]: Taking taylor expansion of (/ 1 a) in a 1.029 * [taylor]: Taking taylor expansion of a in a 1.030 * [taylor]: Taking taylor expansion of (pow (/ 1 a) 1/3) in a 1.030 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 a)))) in a 1.030 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 a))) in a 1.030 * [taylor]: Taking taylor expansion of 1/3 in a 1.030 * [taylor]: Taking taylor expansion of (log (/ 1 a)) in a 1.030 * [taylor]: Taking taylor expansion of (/ 1 a) in a 1.030 * [taylor]: Taking taylor expansion of a in a 1.082 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 a) 1/3)) in (a) around 0 1.082 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 a) 1/3)) in a 1.082 * [taylor]: Taking taylor expansion of (cbrt -1) in a 1.082 * [taylor]: Taking taylor expansion of -1 in a 1.083 * [taylor]: Taking taylor expansion of (pow (/ 1 a) 1/3) in a 1.083 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 a)))) in a 1.083 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 a))) in a 1.083 * [taylor]: Taking taylor expansion of 1/3 in a 1.083 * [taylor]: Taking taylor expansion of (log (/ 1 a)) in a 1.083 * [taylor]: Taking taylor expansion of (/ 1 a) in a 1.083 * [taylor]: Taking taylor expansion of a in a 1.084 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 a) 1/3)) in a 1.084 * [taylor]: Taking taylor expansion of (cbrt -1) in a 1.084 * [taylor]: Taking taylor expansion of -1 in a 1.084 * [taylor]: Taking taylor expansion of (pow (/ 1 a) 1/3) in a 1.084 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 a)))) in a 1.084 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 a))) in a 1.084 * [taylor]: Taking taylor expansion of 1/3 in a 1.084 * [taylor]: Taking taylor expansion of (log (/ 1 a)) in a 1.084 * [taylor]: Taking taylor expansion of (/ 1 a) in a 1.084 * [taylor]: Taking taylor expansion of a in a 1.148 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 2) 1.148 * [approximate]: Taking taylor expansion of (pow a 1/3) in (a) around 0 1.148 * [taylor]: Taking taylor expansion of (pow a 1/3) in a 1.148 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log a))) in a 1.148 * [taylor]: Taking taylor expansion of (* 1/3 (log a)) in a 1.148 * [taylor]: Taking taylor expansion of 1/3 in a 1.148 * [taylor]: Taking taylor expansion of (log a) in a 1.149 * [taylor]: Taking taylor expansion of a in a 1.149 * [taylor]: Taking taylor expansion of (pow a 1/3) in a 1.149 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log a))) in a 1.149 * [taylor]: Taking taylor expansion of (* 1/3 (log a)) in a 1.149 * [taylor]: Taking taylor expansion of 1/3 in a 1.149 * [taylor]: Taking taylor expansion of (log a) in a 1.149 * [taylor]: Taking taylor expansion of a in a 1.200 * [approximate]: Taking taylor expansion of (pow (/ 1 a) 1/3) in (a) around 0 1.200 * [taylor]: Taking taylor expansion of (pow (/ 1 a) 1/3) in a 1.200 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 a)))) in a 1.200 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 a))) in a 1.200 * [taylor]: Taking taylor expansion of 1/3 in a 1.200 * [taylor]: Taking taylor expansion of (log (/ 1 a)) in a 1.200 * [taylor]: Taking taylor expansion of (/ 1 a) in a 1.200 * [taylor]: Taking taylor expansion of a in a 1.201 * [taylor]: Taking taylor expansion of (pow (/ 1 a) 1/3) in a 1.201 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 a)))) in a 1.201 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 a))) in a 1.201 * [taylor]: Taking taylor expansion of 1/3 in a 1.201 * [taylor]: Taking taylor expansion of (log (/ 1 a)) in a 1.201 * [taylor]: Taking taylor expansion of (/ 1 a) in a 1.201 * [taylor]: Taking taylor expansion of a in a 1.252 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 a) 1/3)) in (a) around 0 1.252 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 a) 1/3)) in a 1.252 * [taylor]: Taking taylor expansion of (cbrt -1) in a 1.252 * [taylor]: Taking taylor expansion of -1 in a 1.253 * [taylor]: Taking taylor expansion of (pow (/ 1 a) 1/3) in a 1.253 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 a)))) in a 1.253 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 a))) in a 1.253 * [taylor]: Taking taylor expansion of 1/3 in a 1.253 * [taylor]: Taking taylor expansion of (log (/ 1 a)) in a 1.253 * [taylor]: Taking taylor expansion of (/ 1 a) in a 1.253 * [taylor]: Taking taylor expansion of a in a 1.254 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 a) 1/3)) in a 1.254 * [taylor]: Taking taylor expansion of (cbrt -1) in a 1.254 * [taylor]: Taking taylor expansion of -1 in a 1.255 * [taylor]: Taking taylor expansion of (pow (/ 1 a) 1/3) in a 1.255 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 a)))) in a 1.255 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 a))) in a 1.255 * [taylor]: Taking taylor expansion of 1/3 in a 1.255 * [taylor]: Taking taylor expansion of (log (/ 1 a)) in a 1.255 * [taylor]: Taking taylor expansion of (/ 1 a) in a 1.255 * [taylor]: Taking taylor expansion of a in a 1.318 * * * [progress]: simplifying candidates 1.319 * [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)) 1.319 * [simplify]: Sending expressions to egg_math: (expm1 (sqrt (acos h0))) (log1p (sqrt (acos h0))) (log (sqrt (acos h0))) (exp (sqrt (acos h0))) (* (cbrt (sqrt (acos h0))) (cbrt (sqrt (acos h0)))) (cbrt (sqrt (acos h0))) (* (* (sqrt (acos h0)) (sqrt (acos h0))) (sqrt (acos h0))) (sqrt (* (cbrt (acos h0)) (cbrt (acos h0)))) (sqrt (cbrt (acos h0))) (sqrt (sqrt (acos h0))) (sqrt (sqrt (acos h0))) (sqrt 1) (sqrt (acos h0)) (/ 1 2) (sqrt (sqrt (acos h0))) (sqrt (sqrt (acos h0))) (expm1 (sqrt (acos h0))) (log1p (sqrt (acos h0))) (log (sqrt (acos h0))) (exp (sqrt (acos h0))) (* (cbrt (sqrt (acos h0))) (cbrt (sqrt (acos h0)))) (cbrt (sqrt (acos h0))) (* (* (sqrt (acos h0)) (sqrt (acos h0))) (sqrt (acos h0))) (sqrt (* (cbrt (acos h0)) (cbrt (acos h0)))) (sqrt (cbrt (acos h0))) (sqrt (sqrt (acos h0))) (sqrt (sqrt (acos h0))) (sqrt 1) (sqrt (acos h0)) (/ 1 2) (sqrt (sqrt (acos h0))) (sqrt (sqrt (acos h0))) (expm1 (cbrt h0)) (log1p (cbrt h0)) (log (cbrt h0)) (exp (cbrt h0)) (cbrt (* (cbrt h0) (cbrt h0))) (cbrt (cbrt h0)) (cbrt (sqrt h0)) (cbrt (sqrt h0)) (cbrt 1) (cbrt h0) (* (cbrt (cbrt h0)) (cbrt (cbrt h0))) (cbrt (cbrt h0)) (* (* (cbrt h0) (cbrt h0)) (cbrt h0)) (sqrt (cbrt h0)) (sqrt (cbrt h0)) (expm1 (cbrt h0)) (log1p (cbrt h0)) (log (cbrt h0)) (exp (cbrt h0)) (cbrt (* (cbrt h0) (cbrt h0))) (cbrt (cbrt h0)) (cbrt (sqrt h0)) (cbrt (sqrt h0)) (cbrt 1) (cbrt h0) (* (cbrt (cbrt h0)) (cbrt (cbrt h0))) (cbrt (cbrt h0)) (* (* (cbrt h0) (cbrt h0)) (cbrt h0)) (sqrt (cbrt h0)) (sqrt (cbrt h0)) (sqrt (acos h0)) (sqrt (acos h0)) (sqrt (acos h0)) (sqrt (acos h0)) (sqrt (acos h0)) (sqrt (acos h0)) (pow h0 1/3) (pow (/ 1 h0) -1/3) (* (pow (* -1 h0) 1/3) (cbrt -1)) (pow h0 1/3) (pow (/ 1 h0) -1/3) (* (pow (* -1 h0) 1/3) (cbrt -1)) 1.322 * * [simplify]: iteration 0 : 61 enodes (cost 192 ) 1.323 * * [simplify]: iteration 1 : 104 enodes (cost 184 ) 1.326 * * [simplify]: iteration 2 : 218 enodes (cost 180 ) 1.330 * * [simplify]: iteration 3 : 725 enodes (cost 180 ) 1.351 * * [simplify]: iteration 4 : 4173 enodes (cost 180 ) 1.444 * * [simplify]: iteration 5 : 5001 enodes (cost 180 ) 1.445 * [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))) (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))) (pow (sqrt (acos a)) 3) (fabs (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) (pow a 1/3) (* (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 (* (cbrt a) (cbrt a))) (cbrt (cbrt a)) (cbrt (sqrt a)) (cbrt (sqrt a)) (cbrt 1) (pow a 1/3) (* (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)) (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)) 1.445 * * * [progress]: adding candidates to table 1.608 * [progress]: [Phase 3 of 3] Extracting. 1.608 * * [regime]: Finding splitpoints for: (# # # # # # # # # #) 1.609 * * * [regime-changes]: Trying 2 branch expressions: ((/ a (- (acos a))) a) 1.610 * * * * [regimes]: Trying to branch on (/ a (- (acos a))) from (# # # # # # # # # #) 1.645 * * * * [regimes]: Trying to branch on a from (# # # # # # # # # #) 1.672 * * * [regime]: Found split indices: #