10.162 * [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))) 0.022 * * [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 0.028 * * * [progress]: generating rewritten candidates 0.028 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.041 * * * [progress]: generating series expansions 0.041 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.041 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.041 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.041 * [taylor]: Taking taylor expansion of -1 in a 0.041 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.041 * [taylor]: Taking taylor expansion of a in a 0.041 * [taylor]: Taking taylor expansion of (acos a) in a 0.041 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.041 * [taylor]: Taking taylor expansion of -1 in a 0.041 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.041 * [taylor]: Taking taylor expansion of a in a 0.041 * [taylor]: Taking taylor expansion of (acos a) in a 0.048 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.049 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.049 * [taylor]: Taking taylor expansion of -1 in a 0.049 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.049 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.049 * [taylor]: Taking taylor expansion of a in a 0.049 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.049 * [taylor]: Taking taylor expansion of -1 in a 0.049 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.049 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.049 * [taylor]: Taking taylor expansion of a in a 0.055 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 0.055 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.055 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.055 * [taylor]: Taking taylor expansion of a in a 0.055 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.056 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.056 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.056 * [taylor]: Taking taylor expansion of a in a 0.056 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.065 * * * [progress]: simplifying candidates 0.066 * [simplify]: Simplifying using # : (expm1 (/ a (- (acos a)))) (log1p (/ a (- (acos a)))) (- (log a) (log (- (acos a)))) (log (/ a (- (acos a)))) (exp (/ a (- (acos a)))) (/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a)))) (* (cbrt (/ a (- (acos a)))) (cbrt (/ a (- (acos a))))) (cbrt (/ a (- (acos a)))) (* (* (/ a (- (acos a))) (/ a (- (acos a)))) (/ a (- (acos a)))) (sqrt (/ a (- (acos a)))) (sqrt (/ a (- (acos a)))) (- a) (- (- (acos a))) (/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ (cbrt a) (cbrt (- (acos a)))) (/ (* (cbrt a) (cbrt a)) (sqrt (- (acos a)))) (/ (cbrt a) (sqrt (- (acos a)))) (/ (* (cbrt a) (cbrt a)) 1) (/ (cbrt a) (- (acos a))) (/ (* (cbrt a) (cbrt a)) -1) (/ (cbrt a) (acos a)) (/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (cbrt a) (cbrt (acos a))) (/ (* (cbrt a) (cbrt a)) (- (sqrt (acos a)))) (/ (cbrt a) (sqrt (acos a))) (/ (* (cbrt a) (cbrt a)) (- 1)) (/ (cbrt a) (acos a)) (/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (cbrt a) (- (cbrt (acos a)))) (/ (* (cbrt a) (cbrt a)) (sqrt (acos a))) (/ (cbrt a) (- (sqrt (acos a)))) (/ (* (cbrt a) (cbrt a)) 1) (/ (cbrt a) (- (acos a))) (/ (sqrt a) (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ (sqrt a) (cbrt (- (acos a)))) (/ (sqrt a) (sqrt (- (acos a)))) (/ (sqrt a) (sqrt (- (acos a)))) (/ (sqrt a) 1) (/ (sqrt a) (- (acos a))) (/ (sqrt a) -1) (/ (sqrt a) (acos a)) (/ (sqrt a) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt a) (cbrt (acos a))) (/ (sqrt a) (- (sqrt (acos a)))) (/ (sqrt a) (sqrt (acos a))) (/ (sqrt a) (- 1)) (/ (sqrt a) (acos a)) (/ (sqrt a) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (sqrt a) (- (cbrt (acos a)))) (/ (sqrt a) (sqrt (acos a))) (/ (sqrt a) (- (sqrt (acos a)))) (/ (sqrt a) 1) (/ (sqrt a) (- (acos a))) (/ 1 (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ a (cbrt (- (acos a)))) (/ 1 (sqrt (- (acos a)))) (/ a (sqrt (- (acos a)))) (/ 1 1) (/ a (- (acos a))) (/ 1 -1) (/ a (acos a)) (/ 1 (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ a (cbrt (acos a))) (/ 1 (- (sqrt (acos a)))) (/ a (sqrt (acos a))) (/ 1 (- 1)) (/ a (acos a)) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ a (- (cbrt (acos a)))) (/ 1 (sqrt (acos a))) (/ a (- (sqrt (acos a)))) (/ 1 1) (/ a (- (acos a))) (/ 1 (- (acos a))) (/ (- (acos a)) a) (/ a (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ a (sqrt (- (acos a)))) (/ a 1) (/ a -1) (/ a (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ a (- (sqrt (acos a)))) (/ a (- 1)) (/ a (* (cbrt (acos a)) (cbrt (acos a)))) (/ a (sqrt (acos a))) (/ a 1) (/ (- (acos a)) (cbrt a)) (/ (- (acos a)) (sqrt a)) (/ (- (acos a)) a) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) 0.066 * [simplify]: 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))) 0.070 * * [simplify]: iteration 0 : 166 enodes (cost 384 ) 0.074 * * [simplify]: iteration 1 : 493 enodes (cost 372 ) 0.081 * * [simplify]: iteration 2 : 1442 enodes (cost 367 ) 0.101 * * [simplify]: iteration 3 : 3704 enodes (cost 366 ) 0.158 * * [simplify]: iteration 4 : 5002 enodes (cost 366 ) 0.160 * [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))) 0.161 * * * [progress]: adding candidates to table 0.272 * * [progress]: iteration 2 / 4 0.272 * * * [progress]: picking best candidate 0.287 * * * * [pick]: Picked # 0.287 * * * [progress]: localizing error 0.292 * * * [progress]: generating rewritten candidates 0.292 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.307 * * * * [progress]: [ 2 / 2 ] rewriting at (2 2) 0.326 * * * [progress]: generating series expansions 0.326 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.326 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.326 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.326 * [taylor]: Taking taylor expansion of -1 in a 0.326 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.326 * [taylor]: Taking taylor expansion of a in a 0.326 * [taylor]: Taking taylor expansion of (acos a) in a 0.326 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.326 * [taylor]: Taking taylor expansion of -1 in a 0.326 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.326 * [taylor]: Taking taylor expansion of a in a 0.326 * [taylor]: Taking taylor expansion of (acos a) in a 0.333 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.333 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.333 * [taylor]: Taking taylor expansion of -1 in a 0.333 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.333 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.333 * [taylor]: Taking taylor expansion of a in a 0.333 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.333 * [taylor]: Taking taylor expansion of -1 in a 0.333 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.333 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.334 * [taylor]: Taking taylor expansion of a in a 0.344 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 0.344 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.344 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.344 * [taylor]: Taking taylor expansion of a in a 0.344 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.345 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.345 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.345 * [taylor]: Taking taylor expansion of a in a 0.345 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.353 * * * * [progress]: [ 2 / 2 ] generating series at (2 2) 0.353 * [approximate]: Taking taylor expansion of (* -1 (/ (acos a) a)) in (a) around 0 0.353 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.353 * [taylor]: Taking taylor expansion of -1 in a 0.353 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.353 * [taylor]: Taking taylor expansion of (acos a) in a 0.354 * [taylor]: Taking taylor expansion of a in a 0.354 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 0.354 * [taylor]: Taking taylor expansion of -1 in a 0.354 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 0.354 * [taylor]: Taking taylor expansion of (acos a) in a 0.354 * [taylor]: Taking taylor expansion of a in a 0.367 * [approximate]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.367 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 0.367 * [taylor]: Taking taylor expansion of -1 in a 0.367 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.367 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.367 * [taylor]: Taking taylor expansion of a in a 0.367 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 0.367 * [taylor]: Taking taylor expansion of -1 in a 0.367 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.367 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.367 * [taylor]: Taking taylor expansion of a in a 0.378 * [approximate]: Taking taylor expansion of (* a (acos (/ -1 a))) in (a) around 0 0.378 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.378 * [taylor]: Taking taylor expansion of a in a 0.378 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.378 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.378 * [taylor]: Taking taylor expansion of a in a 0.378 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.385 * * * [progress]: simplifying candidates 0.388 * [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)) 0.398 * * [simplify]: iteration 0 : 663 enodes (cost 1934 ) 0.411 * * [simplify]: iteration 1 : 3064 enodes (cost 1717 ) 0.448 * * [simplify]: iteration 2 : 5001 enodes (cost 1525 ) 0.455 * [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) 0.457 * * * [progress]: adding candidates to table 0.747 * * [progress]: iteration 3 / 4 0.747 * * * [progress]: picking best candidate 0.773 * * * * [pick]: Picked # 0.774 * * * [progress]: localizing error 0.779 * * * [progress]: generating rewritten candidates 0.779 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.804 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 0.816 * * * [progress]: generating series expansions 0.816 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.816 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.816 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.816 * [taylor]: Taking taylor expansion of -1 in a 0.816 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.816 * [taylor]: Taking taylor expansion of a in a 0.816 * [taylor]: Taking taylor expansion of (acos a) in a 0.816 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.816 * [taylor]: Taking taylor expansion of -1 in a 0.816 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.816 * [taylor]: Taking taylor expansion of a in a 0.816 * [taylor]: Taking taylor expansion of (acos a) in a 0.829 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.829 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.829 * [taylor]: Taking taylor expansion of -1 in a 0.829 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.829 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.829 * [taylor]: Taking taylor expansion of a in a 0.829 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.829 * [taylor]: Taking taylor expansion of -1 in a 0.829 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.829 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.829 * [taylor]: Taking taylor expansion of a in a 0.835 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 0.835 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.835 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.835 * [taylor]: Taking taylor expansion of a in a 0.836 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.836 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.836 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.836 * [taylor]: Taking taylor expansion of a in a 0.836 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.845 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 0.845 * [approximate]: Taking taylor expansion of (/ -1 (acos a)) in (a) around 0 0.845 * [taylor]: Taking taylor expansion of (/ -1 (acos a)) in a 0.845 * [taylor]: Taking taylor expansion of -1 in a 0.845 * [taylor]: Taking taylor expansion of (acos a) in a 0.845 * [taylor]: Taking taylor expansion of (/ -1 (acos a)) in a 0.845 * [taylor]: Taking taylor expansion of -1 in a 0.845 * [taylor]: Taking taylor expansion of (acos a) in a 0.846 * [approximate]: Taking taylor expansion of (/ -1 (acos (/ 1 a))) in (a) around 0 0.846 * [taylor]: Taking taylor expansion of (/ -1 (acos (/ 1 a))) in a 0.846 * [taylor]: Taking taylor expansion of -1 in a 0.846 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.846 * [taylor]: Taking taylor expansion of (/ -1 (acos (/ 1 a))) in a 0.846 * [taylor]: Taking taylor expansion of -1 in a 0.846 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.848 * [approximate]: Taking taylor expansion of (/ -1 (acos (/ -1 a))) in (a) around 0 0.848 * [taylor]: Taking taylor expansion of (/ -1 (acos (/ -1 a))) in a 0.848 * [taylor]: Taking taylor expansion of -1 in a 0.848 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.848 * [taylor]: Taking taylor expansion of (/ -1 (acos (/ -1 a))) in a 0.848 * [taylor]: Taking taylor expansion of -1 in a 0.848 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.850 * * * [progress]: simplifying candidates 0.852 * [simplify]: Simplifying using # : (expm1 (* (/ 1 (- (acos a))) a)) (log1p (* (/ 1 (- (acos a))) a)) (* (/ 1 (- (acos a))) a) (+ (- (log (- (acos a)))) (log a)) (+ (- 0 (log (- (acos a)))) (log a)) (+ (- (log 1) (log (- (acos a)))) (log a)) (+ (log (/ 1 (- (acos a)))) (log a)) (log (* (/ 1 (- (acos a))) a)) (exp (* (/ 1 (- (acos a))) a)) (* (/ (* (* 1 1) 1) (* (* (- (acos a)) (- (acos a))) (- (acos a)))) (* (* a a) a)) (* (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* a 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)) (* (sqrt (/ 1 (- (acos a)))) (sqrt a)) (* (sqrt (/ 1 (- (acos a)))) (sqrt a)) (* (/ (sqrt 1) (sqrt (- (acos a)))) (sqrt a)) (* (/ (sqrt 1) (sqrt (- (acos a)))) (sqrt a)) (* (/ 1 (sqrt (- (acos a)))) (sqrt a)) (* (/ 1 (sqrt (- (acos a)))) (sqrt a)) (* (/ 1 (- (acos a))) (* (cbrt a) (cbrt a))) (* (/ 1 (- (acos a))) (sqrt a)) (* (/ 1 (- (acos a))) 1) (* (cbrt (/ 1 (- (acos a)))) a) (* (sqrt (/ 1 (- (acos a)))) a) (* (/ (cbrt 1) (cbrt (- (acos a)))) a) (* (/ (cbrt 1) (sqrt (- (acos a)))) a) (* (/ (cbrt 1) (- (acos a))) a) (* (/ (cbrt 1) (acos a)) a) (* (/ (cbrt 1) (cbrt (acos a))) a) (* (/ (cbrt 1) (sqrt (acos a))) a) (* (/ (cbrt 1) (acos a)) a) (* (/ (cbrt 1) (- (cbrt (acos a)))) a) (* (/ (cbrt 1) (- (sqrt (acos a)))) a) (* (/ (cbrt 1) (- (acos a))) a) (* (/ (sqrt 1) (cbrt (- (acos a)))) a) (* (/ (sqrt 1) (sqrt (- (acos a)))) a) (* (/ (sqrt 1) (- (acos a))) a) (* (/ (sqrt 1) (acos a)) a) (* (/ (sqrt 1) (cbrt (acos a))) a) (* (/ (sqrt 1) (sqrt (acos a))) a) (* (/ (sqrt 1) (acos a)) a) (* (/ (sqrt 1) (- (cbrt (acos a)))) a) (* (/ (sqrt 1) (- (sqrt (acos a)))) a) (* (/ (sqrt 1) (- (acos a))) a) (* (/ 1 (cbrt (- (acos a)))) a) (* (/ 1 (sqrt (- (acos a)))) a) (* (/ 1 (- (acos a))) a) (* (/ 1 (acos a)) a) (* (/ 1 (cbrt (acos a))) a) (* (/ 1 (sqrt (acos a))) a) (* (/ 1 (acos a)) a) (* (/ 1 (- (cbrt (acos a)))) a) (* (/ 1 (- (sqrt (acos a)))) a) (* (/ 1 (- (acos a))) a) (* (/ 1 (- (acos a))) a) (* (/ 1 (- (acos a))) a) (* 1 a) (expm1 (/ 1 (- (acos a)))) (log1p (/ 1 (- (acos a)))) (- 1) (- (log (- (acos a)))) (- 0 (log (- (acos a)))) (- (log 1) (log (- (acos a)))) (log (/ 1 (- (acos a)))) (exp (/ 1 (- (acos a)))) (/ (* (* 1 1) 1) (* (* (- (acos a)) (- (acos a))) (- (acos a)))) (* (cbrt (/ 1 (- (acos a)))) (cbrt (/ 1 (- (acos a))))) (cbrt (/ 1 (- (acos a)))) (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (sqrt (/ 1 (- (acos a)))) (sqrt (/ 1 (- (acos a)))) (- 1) (- (- (acos a))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ (cbrt 1) (cbrt (- (acos a)))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (- (acos a)))) (/ (cbrt 1) (sqrt (- (acos a)))) (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (- (acos a))) (/ (* (cbrt 1) (cbrt 1)) -1) (/ (cbrt 1) (acos a)) (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (cbrt 1) (cbrt (acos a))) (/ (* (cbrt 1) (cbrt 1)) (- (sqrt (acos a)))) (/ (cbrt 1) (sqrt (acos a))) (/ (* (cbrt 1) (cbrt 1)) (- 1)) (/ (cbrt 1) (acos a)) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (cbrt 1) (- (cbrt (acos a)))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (acos a))) (/ (cbrt 1) (- (sqrt (acos a)))) (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (- (acos a))) (/ (sqrt 1) (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ (sqrt 1) (cbrt (- (acos a)))) (/ (sqrt 1) (sqrt (- (acos a)))) (/ (sqrt 1) (sqrt (- (acos a)))) (/ (sqrt 1) 1) (/ (sqrt 1) (- (acos a))) (/ (sqrt 1) -1) (/ (sqrt 1) (acos a)) (/ (sqrt 1) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt 1) (cbrt (acos a))) (/ (sqrt 1) (- (sqrt (acos a)))) (/ (sqrt 1) (sqrt (acos a))) (/ (sqrt 1) (- 1)) (/ (sqrt 1) (acos a)) (/ (sqrt 1) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (sqrt 1) (- (cbrt (acos a)))) (/ (sqrt 1) (sqrt (acos a))) (/ (sqrt 1) (- (sqrt (acos a)))) (/ (sqrt 1) 1) (/ (sqrt 1) (- (acos a))) (/ 1 (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ 1 (cbrt (- (acos a)))) (/ 1 (sqrt (- (acos a)))) (/ 1 (sqrt (- (acos a)))) (/ 1 1) (/ 1 (- (acos a))) (/ 1 -1) (/ 1 (acos a)) (/ 1 (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ 1 (cbrt (acos a))) (/ 1 (- (sqrt (acos a)))) (/ 1 (sqrt (acos a))) (/ 1 (- 1)) (/ 1 (acos a)) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ 1 (- (cbrt (acos a)))) (/ 1 (sqrt (acos a))) (/ 1 (- (sqrt (acos a)))) (/ 1 1) (/ 1 (- (acos a))) (/ 1 (- (acos a))) (/ (- (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) (/ (- (acos a)) (cbrt 1)) (/ (- (acos a)) (sqrt 1)) (/ (- (acos a)) 1) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) (/ -1 (acos a)) (/ -1 (acos a)) (/ -1 (acos a)) 0.852 * [simplify]: Sending expressions to egg_math: (expm1 (* (/ 1 (- (acos h0))) h0)) (log1p (* (/ 1 (- (acos h0))) h0)) (* (/ 1 (- (acos h0))) h0) (+ (- (log (- (acos h0)))) (log h0)) (+ (- 0 (log (- (acos h0)))) (log h0)) (+ (- (log 1) (log (- (acos h0)))) (log h0)) (+ (log (/ 1 (- (acos h0)))) (log h0)) (log (* (/ 1 (- (acos h0))) h0)) (exp (* (/ 1 (- (acos h0))) h0)) (* (/ (* (* 1 1) 1) (* (* (- (acos h0)) (- (acos h0))) (- (acos h0)))) (* (* h0 h0) h0)) (* (* (* (/ 1 (- (acos h0))) (/ 1 (- (acos h0)))) (/ 1 (- (acos h0)))) (* (* h0 h0) h0)) (* (cbrt (* (/ 1 (- (acos h0))) h0)) (cbrt (* (/ 1 (- (acos h0))) h0))) (cbrt (* (/ 1 (- (acos h0))) h0)) (* (* (* (/ 1 (- (acos h0))) h0) (* (/ 1 (- (acos h0))) h0)) (* (/ 1 (- (acos h0))) h0)) (sqrt (* (/ 1 (- (acos h0))) h0)) (sqrt (* (/ 1 (- (acos h0))) h0)) (* (sqrt (/ 1 (- (acos h0)))) (sqrt h0)) (* (sqrt (/ 1 (- (acos h0)))) (sqrt h0)) (* (/ (sqrt 1) (sqrt (- (acos h0)))) (sqrt h0)) (* (/ (sqrt 1) (sqrt (- (acos h0)))) (sqrt h0)) (* (/ 1 (sqrt (- (acos h0)))) (sqrt h0)) (* (/ 1 (sqrt (- (acos h0)))) (sqrt h0)) (* (/ 1 (- (acos h0))) (* (cbrt h0) (cbrt h0))) (* (/ 1 (- (acos h0))) (sqrt h0)) (* (/ 1 (- (acos h0))) 1) (* (cbrt (/ 1 (- (acos h0)))) h0) (* (sqrt (/ 1 (- (acos h0)))) h0) (* (/ (cbrt 1) (cbrt (- (acos h0)))) h0) (* (/ (cbrt 1) (sqrt (- (acos h0)))) h0) (* (/ (cbrt 1) (- (acos h0))) h0) (* (/ (cbrt 1) (acos h0)) h0) (* (/ (cbrt 1) (cbrt (acos h0))) h0) (* (/ (cbrt 1) (sqrt (acos h0))) h0) (* (/ (cbrt 1) (acos h0)) h0) (* (/ (cbrt 1) (- (cbrt (acos h0)))) h0) (* (/ (cbrt 1) (- (sqrt (acos h0)))) h0) (* (/ (cbrt 1) (- (acos h0))) h0) (* (/ (sqrt 1) (cbrt (- (acos h0)))) h0) (* (/ (sqrt 1) (sqrt (- (acos h0)))) h0) (* (/ (sqrt 1) (- (acos h0))) h0) (* (/ (sqrt 1) (acos h0)) h0) (* (/ (sqrt 1) (cbrt (acos h0))) h0) (* (/ (sqrt 1) (sqrt (acos h0))) h0) (* (/ (sqrt 1) (acos h0)) h0) (* (/ (sqrt 1) (- (cbrt (acos h0)))) h0) (* (/ (sqrt 1) (- (sqrt (acos h0)))) h0) (* (/ (sqrt 1) (- (acos h0))) h0) (* (/ 1 (cbrt (- (acos h0)))) h0) (* (/ 1 (sqrt (- (acos h0)))) h0) (* (/ 1 (- (acos h0))) h0) (* (/ 1 (acos h0)) h0) (* (/ 1 (cbrt (acos h0))) h0) (* (/ 1 (sqrt (acos h0))) h0) (* (/ 1 (acos h0)) h0) (* (/ 1 (- (cbrt (acos h0)))) h0) (* (/ 1 (- (sqrt (acos h0)))) h0) (* (/ 1 (- (acos h0))) h0) (* (/ 1 (- (acos h0))) h0) (* (/ 1 (- (acos h0))) h0) (* 1 h0) (expm1 (/ 1 (- (acos h0)))) (log1p (/ 1 (- (acos h0)))) (- 1) (- (log (- (acos h0)))) (- 0 (log (- (acos h0)))) (- (log 1) (log (- (acos h0)))) (log (/ 1 (- (acos h0)))) (exp (/ 1 (- (acos h0)))) (/ (* (* 1 1) 1) (* (* (- (acos h0)) (- (acos h0))) (- (acos h0)))) (* (cbrt (/ 1 (- (acos h0)))) (cbrt (/ 1 (- (acos h0))))) (cbrt (/ 1 (- (acos h0)))) (* (* (/ 1 (- (acos h0))) (/ 1 (- (acos h0)))) (/ 1 (- (acos h0)))) (sqrt (/ 1 (- (acos h0)))) (sqrt (/ 1 (- (acos h0)))) (- 1) (- (- (acos h0))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (- (acos h0))) (cbrt (- (acos h0))))) (/ (cbrt 1) (cbrt (- (acos h0)))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (- (acos h0)))) (/ (cbrt 1) (sqrt (- (acos h0)))) (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (- (acos h0))) (/ (* (cbrt 1) (cbrt 1)) -1) (/ (cbrt 1) (acos h0)) (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos h0)) (cbrt (acos h0))))) (/ (cbrt 1) (cbrt (acos h0))) (/ (* (cbrt 1) (cbrt 1)) (- (sqrt (acos h0)))) (/ (cbrt 1) (sqrt (acos h0))) (/ (* (cbrt 1) (cbrt 1)) (- 1)) (/ (cbrt 1) (acos h0)) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (acos h0)) (cbrt (acos h0)))) (/ (cbrt 1) (- (cbrt (acos h0)))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (acos h0))) (/ (cbrt 1) (- (sqrt (acos h0)))) (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (- (acos h0))) (/ (sqrt 1) (* (cbrt (- (acos h0))) (cbrt (- (acos h0))))) (/ (sqrt 1) (cbrt (- (acos h0)))) (/ (sqrt 1) (sqrt (- (acos h0)))) (/ (sqrt 1) (sqrt (- (acos h0)))) (/ (sqrt 1) 1) (/ (sqrt 1) (- (acos h0))) (/ (sqrt 1) -1) (/ (sqrt 1) (acos h0)) (/ (sqrt 1) (- (* (cbrt (acos h0)) (cbrt (acos h0))))) (/ (sqrt 1) (cbrt (acos h0))) (/ (sqrt 1) (- (sqrt (acos h0)))) (/ (sqrt 1) (sqrt (acos h0))) (/ (sqrt 1) (- 1)) (/ (sqrt 1) (acos h0)) (/ (sqrt 1) (* (cbrt (acos h0)) (cbrt (acos h0)))) (/ (sqrt 1) (- (cbrt (acos h0)))) (/ (sqrt 1) (sqrt (acos h0))) (/ (sqrt 1) (- (sqrt (acos h0)))) (/ (sqrt 1) 1) (/ (sqrt 1) (- (acos h0))) (/ 1 (* (cbrt (- (acos h0))) (cbrt (- (acos h0))))) (/ 1 (cbrt (- (acos h0)))) (/ 1 (sqrt (- (acos h0)))) (/ 1 (sqrt (- (acos h0)))) (/ 1 1) (/ 1 (- (acos h0))) (/ 1 -1) (/ 1 (acos h0)) (/ 1 (- (* (cbrt (acos h0)) (cbrt (acos h0))))) (/ 1 (cbrt (acos h0))) (/ 1 (- (sqrt (acos h0)))) (/ 1 (sqrt (acos h0))) (/ 1 (- 1)) (/ 1 (acos h0)) (/ 1 (* (cbrt (acos h0)) (cbrt (acos h0)))) (/ 1 (- (cbrt (acos h0)))) (/ 1 (sqrt (acos h0))) (/ 1 (- (sqrt (acos h0)))) (/ 1 1) (/ 1 (- (acos h0))) (/ 1 (- (acos h0))) (/ (- (acos h0)) 1) (/ 1 (* (cbrt (- (acos h0))) (cbrt (- (acos h0))))) (/ 1 (sqrt (- (acos h0)))) (/ 1 1) (/ 1 -1) (/ 1 (- (* (cbrt (acos h0)) (cbrt (acos h0))))) (/ 1 (- (sqrt (acos h0)))) (/ 1 (- 1)) (/ 1 (* (cbrt (acos h0)) (cbrt (acos h0)))) (/ 1 (sqrt (acos h0))) (/ 1 1) (/ (- (acos h0)) (cbrt 1)) (/ (- (acos h0)) (sqrt 1)) (/ (- (acos h0)) 1) (* -1 (/ h0 (acos h0))) (* -1 (/ h0 (acos h0))) (* -1 (/ h0 (acos h0))) (/ -1 (acos h0)) (/ -1 (acos h0)) (/ -1 (acos h0)) 0.857 * * [simplify]: iteration 0 : 302 enodes (cost 704 ) 0.864 * * [simplify]: iteration 1 : 1221 enodes (cost 623 ) 0.881 * * [simplify]: iteration 2 : 3187 enodes (cost 538 ) 0.908 * * [simplify]: iteration 3 : 5001 enodes (cost 535 ) 0.912 * [simplify]: Simplified to: (expm1 (* (/ 1 (- (acos a))) a)) (log1p (* (/ 1 (- (acos a))) a)) (/ a (- (acos 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))) (pow (/ a (- (acos a))) 3) (pow (/ a (- (acos a))) 3) (* (cbrt (* (/ 1 (- (acos a))) a)) (cbrt (* (/ 1 (- (acos a))) a))) (cbrt (* (/ 1 (- (acos a))) a)) (pow (/ a (- (acos a))) 3) (sqrt (* (/ 1 (- (acos a))) a)) (sqrt (* (/ 1 (- (acos a))) a)) (* (sqrt (/ 1 (- (acos a)))) (sqrt a)) (* (sqrt (/ 1 (- (acos a)))) (sqrt a)) (/ (sqrt a) (sqrt (- (acos a)))) (/ (sqrt a) (sqrt (- (acos a)))) (/ (sqrt a) (sqrt (- (acos a)))) (/ (sqrt a) (sqrt (- (acos a)))) (/ (* (cbrt a) (cbrt a)) (- (acos a))) (/ (sqrt a) (- (acos a))) (/ -1 (acos a)) (* (cbrt (/ 1 (- (acos a)))) a) (* (sqrt (/ 1 (- (acos a)))) 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 (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 (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 (expm1 (/ 1 (- (acos a)))) (log1p (/ 1 (- (acos a)))) -1 (log (/ 1 (- (acos a)))) (log (/ 1 (- (acos a)))) (log (/ 1 (- (acos a)))) (log (/ 1 (- (acos a)))) (exp (/ 1 (- (acos a)))) (/ -1 (pow (acos a) 3)) (* (cbrt (/ 1 (- (acos a)))) (cbrt (/ 1 (- (acos a))))) (cbrt (/ 1 (- (acos a)))) (/ -1 (pow (acos a) 3)) (sqrt (/ 1 (- (acos a)))) (sqrt (/ 1 (- (acos a)))) -1 (acos a) (/ 1 (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ 1 (cbrt (- (acos a)))) (/ 1 (sqrt (- (acos a)))) (/ 1 (sqrt (- (acos a)))) 1 (/ -1 (acos a)) -1 (/ 1 (acos a)) (/ 1 (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ 1 (cbrt (acos a))) (/ 1 (- (sqrt (acos a)))) (/ 1 (sqrt (acos a))) -1 (/ 1 (acos a)) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ 1 (- (cbrt (acos a)))) (/ 1 (sqrt (acos a))) (/ 1 (- (sqrt (acos a)))) 1 (/ -1 (acos a)) (/ 1 (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ 1 (cbrt (- (acos a)))) (/ 1 (sqrt (- (acos a)))) (/ 1 (sqrt (- (acos a)))) 1 (/ -1 (acos a)) -1 (/ 1 (acos a)) (/ 1 (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ 1 (cbrt (acos a))) (/ 1 (- (sqrt (acos a)))) (/ 1 (sqrt (acos a))) -1 (/ 1 (acos a)) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ 1 (- (cbrt (acos a)))) (/ 1 (sqrt (acos a))) (/ 1 (- (sqrt (acos a)))) 1 (/ -1 (acos a)) (/ 1 (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ 1 (cbrt (- (acos a)))) (/ 1 (sqrt (- (acos a)))) (/ 1 (sqrt (- (acos a)))) 1 (/ -1 (acos a)) -1 (/ 1 (acos a)) (/ 1 (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ 1 (cbrt (acos a))) (/ 1 (- (sqrt (acos a)))) (/ 1 (sqrt (acos a))) -1 (/ 1 (acos a)) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ 1 (- (cbrt (acos a)))) (/ 1 (sqrt (acos a))) (/ 1 (- (sqrt (acos a)))) 1 (/ -1 (acos a)) (/ -1 (acos a)) (- (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 (* (cbrt (acos a)) (cbrt (acos a)))) (/ 1 (sqrt (acos a))) 1 (- (acos a)) (- (acos a)) (- (acos a)) (/ a (- (acos a))) (/ a (- (acos a))) (/ a (- (acos a))) (/ -1 (acos a)) (/ -1 (acos a)) (/ -1 (acos a)) 0.912 * * * [progress]: adding candidates to table 1.098 * * [progress]: iteration 4 / 4 1.099 * * * [progress]: picking best candidate 1.115 * * * * [pick]: Picked # 1.116 * * * [progress]: localizing error 1.122 * * * [progress]: generating rewritten candidates 1.122 * * * * [progress]: [ 1 / 2 ] rewriting at (2 2) 1.141 * * * * [progress]: [ 2 / 2 ] rewriting at (2) 1.169 * * * [progress]: generating series expansions 1.169 * * * * [progress]: [ 1 / 2 ] generating series at (2 2) 1.169 * [approximate]: Taking taylor expansion of (* -1 (/ (acos a) a)) in (a) around 0 1.169 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 1.169 * [taylor]: Taking taylor expansion of -1 in a 1.169 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 1.169 * [taylor]: Taking taylor expansion of (acos a) in a 1.169 * [taylor]: Taking taylor expansion of a in a 1.169 * [taylor]: Taking taylor expansion of (* -1 (/ (acos a) a)) in a 1.169 * [taylor]: Taking taylor expansion of -1 in a 1.169 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 1.170 * [taylor]: Taking taylor expansion of (acos a) in a 1.170 * [taylor]: Taking taylor expansion of a in a 1.183 * [approximate]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in (a) around 0 1.183 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 1.183 * [taylor]: Taking taylor expansion of -1 in a 1.183 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 1.183 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 1.183 * [taylor]: Taking taylor expansion of a in a 1.183 * [taylor]: Taking taylor expansion of (* -1 (* (acos (/ 1 a)) a)) in a 1.183 * [taylor]: Taking taylor expansion of -1 in a 1.183 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 1.183 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 1.183 * [taylor]: Taking taylor expansion of a in a 1.194 * [approximate]: Taking taylor expansion of (* a (acos (/ -1 a))) in (a) around 0 1.194 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 1.194 * [taylor]: Taking taylor expansion of a in a 1.194 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 1.194 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 1.194 * [taylor]: Taking taylor expansion of a in a 1.194 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 1.201 * * * * [progress]: [ 2 / 2 ] generating series at (2) 1.201 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 1.201 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 1.201 * [taylor]: Taking taylor expansion of -1 in a 1.201 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 1.201 * [taylor]: Taking taylor expansion of a in a 1.201 * [taylor]: Taking taylor expansion of (acos a) in a 1.201 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 1.201 * [taylor]: Taking taylor expansion of -1 in a 1.201 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 1.201 * [taylor]: Taking taylor expansion of a in a 1.201 * [taylor]: Taking taylor expansion of (acos a) in a 1.208 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 1.208 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 1.208 * [taylor]: Taking taylor expansion of -1 in a 1.208 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 1.208 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 1.208 * [taylor]: Taking taylor expansion of a in a 1.209 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 1.209 * [taylor]: Taking taylor expansion of -1 in a 1.209 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 1.209 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 1.209 * [taylor]: Taking taylor expansion of a in a 1.215 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 1.215 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 1.215 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 1.215 * [taylor]: Taking taylor expansion of a in a 1.215 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 1.216 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 1.216 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 1.216 * [taylor]: Taking taylor expansion of a in a 1.216 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 1.224 * * * [progress]: simplifying candidates 1.226 * [simplify]: Simplifying using # : (expm1 (* (- (acos a)) (/ 1 a))) (log1p (* (- (acos a)) (/ 1 a))) (* (- (acos a)) (/ 1 a)) (+ (log (- (acos a))) (- (log a))) (+ (log (- (acos a))) (- 0 (log a))) (+ (log (- (acos a))) (- (log 1) (log a))) (+ (log (- (acos a))) (log (/ 1 a))) (log (* (- (acos a)) (/ 1 a))) (exp (* (- (acos a)) (/ 1 a))) (* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (/ (* (* 1 1) 1) (* (* a a) a))) (* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a))) (* (cbrt (* (- (acos a)) (/ 1 a))) (cbrt (* (- (acos a)) (/ 1 a)))) (cbrt (* (- (acos a)) (/ 1 a))) (* (* (* (- (acos a)) (/ 1 a)) (* (- (acos a)) (/ 1 a))) (* (- (acos a)) (/ 1 a))) (sqrt (* (- (acos a)) (/ 1 a))) (sqrt (* (- (acos a)) (/ 1 a))) (* (sqrt (- (acos a))) (sqrt (/ 1 a))) (* (sqrt (- (acos a))) (sqrt (/ 1 a))) (* (sqrt (- (acos a))) (/ (sqrt 1) (sqrt a))) (* (sqrt (- (acos a))) (/ (sqrt 1) (sqrt a))) (* (sqrt (- (acos a))) (/ 1 (sqrt a))) (* (sqrt (- (acos a))) (/ 1 (sqrt a))) (* (acos a) (/ 1 a)) (* (- (acos a)) (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))) (* (- (acos a)) (sqrt (/ 1 a))) (* (- (acos a)) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a)))) (* (- (acos a)) (/ (* (cbrt 1) (cbrt 1)) (sqrt a))) (* (- (acos a)) (/ (* (cbrt 1) (cbrt 1)) 1)) (* (- (acos a)) (/ (sqrt 1) (* (cbrt a) (cbrt a)))) (* (- (acos a)) (/ (sqrt 1) (sqrt a))) (* (- (acos a)) (/ (sqrt 1) 1)) (* (- (acos a)) (/ 1 (* (cbrt a) (cbrt a)))) (* (- (acos a)) (/ 1 (sqrt a))) (* (- (acos a)) (/ 1 1)) (* (- (acos a)) 1) (* (- (acos a)) 1) (* (cbrt (- (acos a))) (/ 1 a)) (* (sqrt (- (acos a))) (/ 1 a)) (* (- (acos a)) (/ 1 a)) (* (acos a) (/ 1 a)) (* (cbrt (acos a)) (/ 1 a)) (* (sqrt (acos a)) (/ 1 a)) (* (acos a) (/ 1 a)) (* (- (cbrt (acos a))) (/ 1 a)) (* (- (sqrt (acos a))) (/ 1 a)) (* (- (acos a)) (/ 1 a)) (* (- (acos a)) 1) (expm1 (/ 1 (* (- (acos a)) (/ 1 a)))) (log1p (/ 1 (* (- (acos a)) (/ 1 a)))) (- 1) (- 1) (- (+ (log (- (acos a))) (- (log a)))) (- (+ (log (- (acos a))) (- 0 (log a)))) (- (+ (log (- (acos a))) (- (log 1) (log a)))) (- (+ (log (- (acos a))) (log (/ 1 a)))) (- (log (* (- (acos a)) (/ 1 a)))) (- 0 (+ (log (- (acos a))) (- (log a)))) (- 0 (+ (log (- (acos a))) (- 0 (log a)))) (- 0 (+ (log (- (acos a))) (- (log 1) (log a)))) (- 0 (+ (log (- (acos a))) (log (/ 1 a)))) (- 0 (log (* (- (acos a)) (/ 1 a)))) (- (log 1) (+ (log (- (acos a))) (- (log a)))) (- (log 1) (+ (log (- (acos a))) (- 0 (log a)))) (- (log 1) (+ (log (- (acos a))) (- (log 1) (log a)))) (- (log 1) (+ (log (- (acos a))) (log (/ 1 a)))) (- (log 1) (log (* (- (acos a)) (/ 1 a)))) (log (/ 1 (* (- (acos a)) (/ 1 a)))) (exp (/ 1 (* (- (acos a)) (/ 1 a)))) (/ (* (* 1 1) 1) (* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (/ (* (* 1 1) 1) (* (* a a) a)))) (/ (* (* 1 1) 1) (* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))) (/ (* (* 1 1) 1) (* (* (* (- (acos a)) (/ 1 a)) (* (- (acos a)) (/ 1 a))) (* (- (acos a)) (/ 1 a)))) (* (cbrt (/ 1 (* (- (acos a)) (/ 1 a)))) (cbrt (/ 1 (* (- (acos a)) (/ 1 a))))) (cbrt (/ 1 (* (- (acos a)) (/ 1 a)))) (* (* (/ 1 (* (- (acos a)) (/ 1 a))) (/ 1 (* (- (acos a)) (/ 1 a)))) (/ 1 (* (- (acos a)) (/ 1 a)))) (sqrt (/ 1 (* (- (acos a)) (/ 1 a)))) (sqrt (/ 1 (* (- (acos a)) (/ 1 a)))) (- 1) (- (* (- (acos a)) (/ 1 a))) (/ (* (cbrt 1) (cbrt 1)) (- (acos a))) (/ (cbrt 1) (/ 1 a)) (/ (sqrt 1) (- (acos a))) (/ (sqrt 1) (/ 1 a)) (/ 1 (- (acos a))) (/ 1 (/ 1 a)) (/ 1 (* (- (acos a)) (/ 1 a))) (/ (* (- (acos a)) (/ 1 a)) 1) (/ 1 (- (acos a))) (/ (* (- (acos a)) (/ 1 a)) (cbrt 1)) (/ (* (- (acos a)) (/ 1 a)) (sqrt 1)) (/ (* (- (acos a)) (/ 1 a)) 1) (/ 1 (- (acos a))) (/ 1 (* (- (acos a)) 1)) (* -1 (/ (acos a) a)) (* -1 (/ (acos a) a)) (* -1 (/ (acos a) a)) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) (* -1 (/ a (acos a))) 1.226 * [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))) 1.231 * * [simplify]: iteration 0 : 355 enodes (cost 529 ) 1.239 * * [simplify]: iteration 1 : 1644 enodes (cost 425 ) 1.265 * * [simplify]: iteration 2 : 5001 enodes (cost 401 ) 1.267 * [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))) 1.268 * * * [progress]: adding candidates to table 1.402 * [progress]: [Phase 3 of 3] Extracting. 1.402 * * [regime]: Finding splitpoints for: (# # # # # # # # #) 1.403 * * * [regime-changes]: Trying 2 branch expressions: ((/ a (- (acos a))) a) 1.403 * * * * [regimes]: Trying to branch on (/ a (- (acos a))) from (# # # # # # # # #) 1.437 * * * * [regimes]: Trying to branch on a from (# # # # # # # # #) 1.467 * * * [regime]: Found split indices: #