90.098 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.033 * * * [progress]: [2/2] Setting up program. 0.036 * [progress]: [Phase 2 of 3] Improving. 0.036 * [simplify]: Simplifying: (/ a (- (acos a))) 0.036 * * [simplify]: Extracting # 0 : cost 0 0.036 * * [simplify]: Extracting # 1 : cost 0 0.036 * * [simplify]: Extracting # 2 : cost 0 0.036 * * [simplify]: Extracting # 3 : cost 0 0.037 * * [simplify]: Extracting # 4 : cost 0 0.037 * * [simplify]: iteration 0 : 4 enodes (cost 5 ) 0.038 * * [simplify]: Extracting # 0 : cost 0 0.038 * * [simplify]: iteration done: 4 enodes (cost 5 ) 0.038 * [simplify]: Simplified to: (/ a (- (acos a))) 0.038 * * [progress]: iteration 1 / 4 0.038 * * * [progress]: picking best candidate 0.041 * * * * [pick]: Picked # 0.041 * * * [progress]: localizing error 0.051 * * * [progress]: generating rewritten candidates 0.051 * * * * [progress]: [ 1 / 1 ] rewriting at (2) 0.061 * * * [progress]: generating series expansions 0.061 * * * * [progress]: [ 1 / 1 ] generating series at (2) 0.061 * [backup-simplify]: Simplify (/ a (- (acos a))) into (* -1 (/ a (acos a))) 0.061 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 0.061 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.061 * [taylor]: Taking taylor expansion of -1 in a 0.061 * [backup-simplify]: Simplify -1 into -1 0.061 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.061 * [taylor]: Taking taylor expansion of a in a 0.061 * [backup-simplify]: Simplify 0 into 0 0.061 * [backup-simplify]: Simplify 1 into 1 0.061 * [taylor]: Taking taylor expansion of (acos a) in a 0.063 * [backup-simplify]: Simplify (acos a) into (acos a) 0.063 * [backup-simplify]: Simplify (/ 1 (acos a)) into (/ 1 (acos a)) 0.063 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 0.063 * [taylor]: Taking taylor expansion of -1 in a 0.063 * [backup-simplify]: Simplify -1 into -1 0.063 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 0.063 * [taylor]: Taking taylor expansion of a in a 0.063 * [backup-simplify]: Simplify 0 into 0 0.063 * [backup-simplify]: Simplify 1 into 1 0.063 * [taylor]: Taking taylor expansion of (acos a) in a 0.063 * [backup-simplify]: Simplify (acos a) into (acos a) 0.063 * [backup-simplify]: Simplify (/ 1 (acos a)) into (/ 1 (acos a)) 0.063 * [backup-simplify]: Simplify (* -1 (/ 1 (acos a))) into (/ -1 (acos a)) 0.063 * [backup-simplify]: Simplify (/ -1 (acos a)) into (/ -1 (acos a)) 0.063 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))))) into 0 0.064 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 (/ 1 (acos a)))) into 0 0.064 * [backup-simplify]: Simplify 0 into 0 0.064 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 0.065 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (/ 1 (acos a))))) into 0 0.065 * [backup-simplify]: Simplify 0 into 0 0.065 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 0.066 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 (acos a)))))) into 0 0.066 * [backup-simplify]: Simplify 0 into 0 0.067 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 0.068 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 (acos a))))))) into 0 0.068 * [backup-simplify]: Simplify 0 into 0 0.068 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 0.070 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 (acos a)))))))) into 0 0.070 * [backup-simplify]: Simplify 0 into 0 0.070 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 0.072 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 (acos a))))))))) into 0 0.072 * [backup-simplify]: Simplify 0 into 0 0.072 * [backup-simplify]: Simplify (* (/ -1 (acos a)) a) into (* -1 (/ a (acos a))) 0.072 * [backup-simplify]: Simplify (/ (/ 1 a) (- (acos (/ 1 a)))) into (/ -1 (* (acos (/ 1 a)) a)) 0.072 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 0.072 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.073 * [taylor]: Taking taylor expansion of -1 in a 0.073 * [backup-simplify]: Simplify -1 into -1 0.073 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.073 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.073 * [backup-simplify]: Simplify (acos (/ 1 a)) into (acos (/ 1 a)) 0.073 * [taylor]: Taking taylor expansion of a in a 0.073 * [backup-simplify]: Simplify 0 into 0 0.073 * [backup-simplify]: Simplify 1 into 1 0.073 * [backup-simplify]: Simplify (* (acos (/ 1 a)) 0) into 0 0.073 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 1) (* 0 0)) into (acos (/ 1 a)) 0.073 * [backup-simplify]: Simplify (/ -1 (acos (/ 1 a))) into (/ -1 (acos (/ 1 a))) 0.073 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 0.073 * [taylor]: Taking taylor expansion of -1 in a 0.073 * [backup-simplify]: Simplify -1 into -1 0.073 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 0.073 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 0.073 * [backup-simplify]: Simplify (acos (/ 1 a)) into (acos (/ 1 a)) 0.074 * [taylor]: Taking taylor expansion of a in a 0.074 * [backup-simplify]: Simplify 0 into 0 0.074 * [backup-simplify]: Simplify 1 into 1 0.074 * [backup-simplify]: Simplify (* (acos (/ 1 a)) 0) into 0 0.074 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 1) (* 0 0)) into (acos (/ 1 a)) 0.074 * [backup-simplify]: Simplify (/ -1 (acos (/ 1 a))) into (/ -1 (acos (/ 1 a))) 0.074 * [backup-simplify]: Simplify (/ -1 (acos (/ 1 a))) into (/ -1 (acos (/ 1 a))) 0.075 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 1) (* 0 0))) into 0 0.075 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))))) into 0 0.075 * [backup-simplify]: Simplify 0 into 0 0.076 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 0.076 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 0.076 * [backup-simplify]: Simplify 0 into 0 0.077 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 0.077 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 0.077 * [backup-simplify]: Simplify 0 into 0 0.078 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 0.078 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 0.078 * [backup-simplify]: Simplify 0 into 0 0.079 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 0.080 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 0.080 * [backup-simplify]: Simplify 0 into 0 0.081 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))))) into 0 0.082 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 0.082 * [backup-simplify]: Simplify 0 into 0 0.082 * [backup-simplify]: Simplify (* (/ -1 (acos (/ 1 (/ 1 a)))) (/ 1 (/ 1 a))) into (* -1 (/ a (acos a))) 0.082 * [backup-simplify]: Simplify (/ (/ 1 (- a)) (- (acos (/ 1 (- a))))) into (/ 1 (* a (acos (/ -1 a)))) 0.082 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 0.082 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.082 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.082 * [taylor]: Taking taylor expansion of a in a 0.082 * [backup-simplify]: Simplify 0 into 0 0.082 * [backup-simplify]: Simplify 1 into 1 0.082 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.082 * [backup-simplify]: Simplify (acos (/ -1 a)) into (acos (/ -1 a)) 0.082 * [backup-simplify]: Simplify (* 0 (acos (/ -1 a))) into 0 0.083 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 (acos (/ -1 a)))) into (acos (/ -1 a)) 0.083 * [backup-simplify]: Simplify (/ 1 (acos (/ -1 a))) into (/ 1 (acos (/ -1 a))) 0.083 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 0.083 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 0.083 * [taylor]: Taking taylor expansion of a in a 0.083 * [backup-simplify]: Simplify 0 into 0 0.083 * [backup-simplify]: Simplify 1 into 1 0.083 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 0.083 * [backup-simplify]: Simplify (acos (/ -1 a)) into (acos (/ -1 a)) 0.083 * [backup-simplify]: Simplify (* 0 (acos (/ -1 a))) into 0 0.083 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 (acos (/ -1 a)))) into (acos (/ -1 a)) 0.083 * [backup-simplify]: Simplify (/ 1 (acos (/ -1 a))) into (/ 1 (acos (/ -1 a))) 0.084 * [backup-simplify]: Simplify (/ 1 (acos (/ -1 a))) into (/ 1 (acos (/ -1 a))) 0.084 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (acos (/ -1 a))))) into 0 0.084 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))))) into 0 0.084 * [backup-simplify]: Simplify 0 into 0 0.085 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (acos (/ -1 a)))))) into 0 0.086 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 0.086 * [backup-simplify]: Simplify 0 into 0 0.087 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (acos (/ -1 a))))))) into 0 0.087 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 0.087 * [backup-simplify]: Simplify 0 into 0 0.088 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (acos (/ -1 a)))))))) into 0 0.089 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 0.089 * [backup-simplify]: Simplify 0 into 0 0.091 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (acos (/ -1 a))))))))) into 0 0.091 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 0.091 * [backup-simplify]: Simplify 0 into 0 0.094 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (acos (/ -1 a)))))))))) into 0 0.095 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 0.095 * [backup-simplify]: Simplify 0 into 0 0.095 * [backup-simplify]: Simplify (* (/ 1 (acos (/ -1 (/ 1 (- a))))) (/ 1 (/ 1 (- a)))) into (* -1 (/ a (acos a))) 0.096 * * * [progress]: simplifying candidates 0.097 * [simplify]: Simplifying: (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))) 0.100 * * [simplify]: Extracting # 0 : cost 0 0.100 * * [simplify]: Extracting # 1 : cost 0 0.100 * * [simplify]: Extracting # 2 : cost 0 0.101 * * [simplify]: Extracting # 3 : cost 0 0.101 * * [simplify]: Extracting # 4 : cost 0 0.101 * * [simplify]: iteration 0 : 96 enodes (cost 613 ) 0.142 * * [simplify]: Extracting # 0 : cost 0 0.142 * * [simplify]: Extracting # 1 : cost 0 0.142 * * [simplify]: Extracting # 2 : cost 0 0.142 * * [simplify]: Extracting # 3 : cost 0 0.143 * * [simplify]: iteration 1 : 166 enodes (cost 581 ) 0.195 * * [simplify]: Extracting # 0 : cost 0 0.196 * * [simplify]: Extracting # 1 : cost 0 0.197 * * [simplify]: Extracting # 2 : cost 0 0.197 * * [simplify]: Extracting # 3 : cost 0 0.198 * * [simplify]: Extracting # 4 : cost 0 0.199 * * [simplify]: iteration 2 : 333 enodes (cost 563 ) 0.321 * * [simplify]: Extracting # 0 : cost 0 0.323 * * [simplify]: Extracting # 1 : cost 0 0.324 * * [simplify]: Extracting # 2 : cost 0 0.325 * * [simplify]: Extracting # 3 : cost 0 0.326 * * [simplify]: Extracting # 4 : cost 0 0.327 * * [simplify]: iteration 3 : 587 enodes (cost 563 ) 0.607 * * [simplify]: Extracting # 0 : cost 0 0.608 * * [simplify]: Extracting # 1 : cost 0 0.609 * * [simplify]: Extracting # 2 : cost 0 0.610 * * [simplify]: Extracting # 3 : cost 0 0.611 * * [simplify]: Extracting # 4 : cost 0 0.612 * * [simplify]: iteration 4 : 1105 enodes (cost 563 ) 1.922 * * [simplify]: Extracting # 0 : cost 0 1.925 * * [simplify]: Extracting # 1 : cost 0 1.927 * * [simplify]: Extracting # 2 : cost 0 1.929 * * [simplify]: Extracting # 3 : cost 0 1.931 * * [simplify]: Extracting # 4 : cost 0 1.938 * * [simplify]: iteration 5 : 2150 enodes (cost 558 ) 4.811 * * [simplify]: Extracting # 0 : cost 0 4.816 * * [simplify]: Extracting # 1 : cost 0 4.821 * * [simplify]: Extracting # 2 : cost 0 4.826 * * [simplify]: Extracting # 3 : cost 0 4.839 * * [simplify]: Extracting # 4 : cost 0 4.848 * * [simplify]: iteration done: 5001 enodes (cost 558 ) 4.849 * [simplify]: Simplified to: (expm1 (/ a (- (acos a)))) (log1p (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (exp (/ a (- (acos a)))) (pow (/ a (- (acos a))) 3) (* (cbrt (/ a (- (acos a)))) (cbrt (/ a (- (acos a))))) (cbrt (/ a (- (acos a)))) (pow (/ a (- (acos a))) 3) (sqrt (/ a (- (acos a)))) (sqrt (/ a (- (acos a)))) (- a) (acos a) (/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ (cbrt a) (cbrt (- (acos a)))) (/ (* (cbrt a) (cbrt a)) (sqrt (- (acos a)))) (/ (cbrt a) (sqrt (- (acos a)))) (* (cbrt a) (cbrt a)) (/ (cbrt a) (- (acos a))) (/ (* (cbrt a) (cbrt a)) -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 (/ a (- (acos a))) -1 (/ a (acos a)) (/ (/ -1 (cbrt (acos a))) (cbrt (acos a))) (/ a (cbrt (acos a))) (/ -1 (sqrt (acos a))) (/ a (sqrt (acos a))) -1 (/ a (acos a)) (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ a (- (cbrt (acos a)))) (/ 1 (sqrt (acos a))) (/ a (- (sqrt (acos a)))) 1 (/ a (- (acos a))) (/ -1 (acos a)) (- (/ (acos a) a)) (/ a (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ a (sqrt (- (acos a)))) a (- a) (/ a (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ a (- (sqrt (acos a)))) (- a) (/ a (* (cbrt (acos a)) (cbrt (acos a)))) (/ a (sqrt (acos a))) a (/ (- (acos a)) (cbrt a)) (/ (- (acos a)) (sqrt a)) (- (/ (acos a) a)) (/ a (- (acos a))) (/ a (- (acos a))) (/ a (- (acos a))) 4.850 * * * [progress]: adding candidates to table 5.029 * * [progress]: iteration 2 / 4 5.029 * * * [progress]: picking best candidate 5.054 * * * * [pick]: Picked # 5.054 * * * [progress]: localizing error 5.073 * * * [progress]: generating rewritten candidates 5.073 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 5.093 * * * * [progress]: [ 2 / 2 ] rewriting at (2 2 1) 5.108 * * * [progress]: generating series expansions 5.108 * * * * [progress]: [ 1 / 2 ] generating series at (2) 5.108 * [backup-simplify]: Simplify (/ 1 (- (/ (acos a) a))) into (* -1 (/ a (acos a))) 5.108 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 5.108 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 5.108 * [taylor]: Taking taylor expansion of -1 in a 5.108 * [backup-simplify]: Simplify -1 into -1 5.108 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 5.108 * [taylor]: Taking taylor expansion of a in a 5.108 * [backup-simplify]: Simplify 0 into 0 5.108 * [backup-simplify]: Simplify 1 into 1 5.108 * [taylor]: Taking taylor expansion of (acos a) in a 5.108 * [backup-simplify]: Simplify (acos a) into (acos a) 5.108 * [backup-simplify]: Simplify (/ 1 (acos a)) into (/ 1 (acos a)) 5.108 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 5.108 * [taylor]: Taking taylor expansion of -1 in a 5.108 * [backup-simplify]: Simplify -1 into -1 5.108 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 5.108 * [taylor]: Taking taylor expansion of a in a 5.108 * [backup-simplify]: Simplify 0 into 0 5.109 * [backup-simplify]: Simplify 1 into 1 5.109 * [taylor]: Taking taylor expansion of (acos a) in a 5.109 * [backup-simplify]: Simplify (acos a) into (acos a) 5.109 * [backup-simplify]: Simplify (/ 1 (acos a)) into (/ 1 (acos a)) 5.109 * [backup-simplify]: Simplify (* -1 (/ 1 (acos a))) into (/ -1 (acos a)) 5.109 * [backup-simplify]: Simplify (/ -1 (acos a)) into (/ -1 (acos a)) 5.109 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))))) into 0 5.110 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 (/ 1 (acos a)))) into 0 5.110 * [backup-simplify]: Simplify 0 into 0 5.110 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 5.111 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (/ 1 (acos a))))) into 0 5.111 * [backup-simplify]: Simplify 0 into 0 5.111 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 5.112 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 (acos a)))))) into 0 5.112 * [backup-simplify]: Simplify 0 into 0 5.112 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 5.113 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 (acos a))))))) into 0 5.113 * [backup-simplify]: Simplify 0 into 0 5.114 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 5.115 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 (acos a)))))))) into 0 5.115 * [backup-simplify]: Simplify 0 into 0 5.115 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 5.117 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 (acos a))))))))) into 0 5.117 * [backup-simplify]: Simplify 0 into 0 5.117 * [backup-simplify]: Simplify (* (/ -1 (acos a)) a) into (* -1 (/ a (acos a))) 5.117 * [backup-simplify]: Simplify (/ 1 (- (/ (acos (/ 1 a)) (/ 1 a)))) into (/ -1 (* (acos (/ 1 a)) a)) 5.117 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 5.117 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 5.117 * [taylor]: Taking taylor expansion of -1 in a 5.117 * [backup-simplify]: Simplify -1 into -1 5.117 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 5.117 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 5.117 * [backup-simplify]: Simplify (acos (/ 1 a)) into (acos (/ 1 a)) 5.117 * [taylor]: Taking taylor expansion of a in a 5.117 * [backup-simplify]: Simplify 0 into 0 5.117 * [backup-simplify]: Simplify 1 into 1 5.118 * [backup-simplify]: Simplify (* (acos (/ 1 a)) 0) into 0 5.118 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 1) (* 0 0)) into (acos (/ 1 a)) 5.118 * [backup-simplify]: Simplify (/ -1 (acos (/ 1 a))) into (/ -1 (acos (/ 1 a))) 5.118 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 5.118 * [taylor]: Taking taylor expansion of -1 in a 5.118 * [backup-simplify]: Simplify -1 into -1 5.118 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 5.118 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 5.118 * [backup-simplify]: Simplify (acos (/ 1 a)) into (acos (/ 1 a)) 5.118 * [taylor]: Taking taylor expansion of a in a 5.118 * [backup-simplify]: Simplify 0 into 0 5.118 * [backup-simplify]: Simplify 1 into 1 5.118 * [backup-simplify]: Simplify (* (acos (/ 1 a)) 0) into 0 5.119 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 1) (* 0 0)) into (acos (/ 1 a)) 5.119 * [backup-simplify]: Simplify (/ -1 (acos (/ 1 a))) into (/ -1 (acos (/ 1 a))) 5.119 * [backup-simplify]: Simplify (/ -1 (acos (/ 1 a))) into (/ -1 (acos (/ 1 a))) 5.120 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 1) (* 0 0))) into 0 5.120 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))))) into 0 5.120 * [backup-simplify]: Simplify 0 into 0 5.120 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 5.121 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 5.121 * [backup-simplify]: Simplify 0 into 0 5.121 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 5.122 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 5.122 * [backup-simplify]: Simplify 0 into 0 5.123 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 5.123 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 5.123 * [backup-simplify]: Simplify 0 into 0 5.124 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 5.125 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 5.125 * [backup-simplify]: Simplify 0 into 0 5.126 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))))) into 0 5.126 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 5.127 * [backup-simplify]: Simplify 0 into 0 5.127 * [backup-simplify]: Simplify (* (/ -1 (acos (/ 1 (/ 1 a)))) (/ 1 (/ 1 a))) into (* -1 (/ a (acos a))) 5.127 * [backup-simplify]: Simplify (/ 1 (- (/ (acos (/ 1 (- a))) (/ 1 (- a))))) into (/ 1 (* a (acos (/ -1 a)))) 5.127 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 5.127 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 5.127 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 5.127 * [taylor]: Taking taylor expansion of a in a 5.127 * [backup-simplify]: Simplify 0 into 0 5.127 * [backup-simplify]: Simplify 1 into 1 5.127 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 5.127 * [backup-simplify]: Simplify (acos (/ -1 a)) into (acos (/ -1 a)) 5.127 * [backup-simplify]: Simplify (* 0 (acos (/ -1 a))) into 0 5.128 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 (acos (/ -1 a)))) into (acos (/ -1 a)) 5.128 * [backup-simplify]: Simplify (/ 1 (acos (/ -1 a))) into (/ 1 (acos (/ -1 a))) 5.128 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 5.128 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 5.128 * [taylor]: Taking taylor expansion of a in a 5.128 * [backup-simplify]: Simplify 0 into 0 5.128 * [backup-simplify]: Simplify 1 into 1 5.128 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 5.128 * [backup-simplify]: Simplify (acos (/ -1 a)) into (acos (/ -1 a)) 5.128 * [backup-simplify]: Simplify (* 0 (acos (/ -1 a))) into 0 5.128 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 (acos (/ -1 a)))) into (acos (/ -1 a)) 5.129 * [backup-simplify]: Simplify (/ 1 (acos (/ -1 a))) into (/ 1 (acos (/ -1 a))) 5.129 * [backup-simplify]: Simplify (/ 1 (acos (/ -1 a))) into (/ 1 (acos (/ -1 a))) 5.129 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (acos (/ -1 a))))) into 0 5.130 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))))) into 0 5.130 * [backup-simplify]: Simplify 0 into 0 5.130 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (acos (/ -1 a)))))) into 0 5.131 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 5.131 * [backup-simplify]: Simplify 0 into 0 5.132 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (acos (/ -1 a))))))) into 0 5.132 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 5.132 * [backup-simplify]: Simplify 0 into 0 5.134 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (acos (/ -1 a)))))))) into 0 5.134 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 5.134 * [backup-simplify]: Simplify 0 into 0 5.136 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (acos (/ -1 a))))))))) into 0 5.136 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 5.136 * [backup-simplify]: Simplify 0 into 0 5.138 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (acos (/ -1 a)))))))))) into 0 5.138 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 5.138 * [backup-simplify]: Simplify 0 into 0 5.139 * [backup-simplify]: Simplify (* (/ 1 (acos (/ -1 (/ 1 (- a))))) (/ 1 (/ 1 (- a)))) into (* -1 (/ a (acos a))) 5.139 * * * * [progress]: [ 2 / 2 ] generating series at (2 2 1) 5.139 * [backup-simplify]: Simplify (/ (acos a) a) into (/ (acos a) a) 5.139 * [approximate]: Taking taylor expansion of (/ (acos a) a) in (a) around 0 5.139 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 5.139 * [taylor]: Taking taylor expansion of (acos a) in a 5.139 * [backup-simplify]: Simplify (acos a) into (acos a) 5.139 * [taylor]: Taking taylor expansion of a in a 5.139 * [backup-simplify]: Simplify 0 into 0 5.139 * [backup-simplify]: Simplify 1 into 1 5.139 * [backup-simplify]: Simplify (/ (acos a) 1) into (acos a) 5.139 * [taylor]: Taking taylor expansion of (/ (acos a) a) in a 5.139 * [taylor]: Taking taylor expansion of (acos a) in a 5.139 * [backup-simplify]: Simplify (acos a) into (acos a) 5.139 * [taylor]: Taking taylor expansion of a in a 5.139 * [backup-simplify]: Simplify 0 into 0 5.139 * [backup-simplify]: Simplify 1 into 1 5.139 * [backup-simplify]: Simplify (/ (acos a) 1) into (acos a) 5.139 * [backup-simplify]: Simplify (acos a) into (acos a) 5.140 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (acos a) (/ 0 1)))) into 0 5.140 * [backup-simplify]: Simplify 0 into 0 5.141 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (acos a) (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.141 * [backup-simplify]: Simplify 0 into 0 5.142 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (acos a) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.142 * [backup-simplify]: Simplify 0 into 0 5.144 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (acos a) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.144 * [backup-simplify]: Simplify 0 into 0 5.146 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (acos a) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.146 * [backup-simplify]: Simplify 0 into 0 5.148 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (acos a) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.148 * [backup-simplify]: Simplify 0 into 0 5.149 * [backup-simplify]: Simplify (* (acos a) (/ 1 a)) into (/ (acos a) a) 5.149 * [backup-simplify]: Simplify (/ (acos (/ 1 a)) (/ 1 a)) into (* (acos (/ 1 a)) a) 5.149 * [approximate]: Taking taylor expansion of (* (acos (/ 1 a)) a) in (a) around 0 5.149 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 5.149 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 5.149 * [backup-simplify]: Simplify (acos (/ 1 a)) into (acos (/ 1 a)) 5.149 * [taylor]: Taking taylor expansion of a in a 5.149 * [backup-simplify]: Simplify 0 into 0 5.149 * [backup-simplify]: Simplify 1 into 1 5.149 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 5.149 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 5.149 * [backup-simplify]: Simplify (acos (/ 1 a)) into (acos (/ 1 a)) 5.149 * [taylor]: Taking taylor expansion of a in a 5.149 * [backup-simplify]: Simplify 0 into 0 5.149 * [backup-simplify]: Simplify 1 into 1 5.149 * [backup-simplify]: Simplify (* (acos (/ 1 a)) 0) into 0 5.149 * [backup-simplify]: Simplify 0 into 0 5.150 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 1) (* 0 0)) into (acos (/ 1 a)) 5.150 * [backup-simplify]: Simplify (acos (/ 1 a)) into (acos (/ 1 a)) 5.150 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 1) (* 0 0))) into 0 5.151 * [backup-simplify]: Simplify 0 into 0 5.151 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 5.151 * [backup-simplify]: Simplify 0 into 0 5.152 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 5.152 * [backup-simplify]: Simplify 0 into 0 5.153 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 5.153 * [backup-simplify]: Simplify 0 into 0 5.154 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 5.154 * [backup-simplify]: Simplify 0 into 0 5.156 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))))) into 0 5.156 * [backup-simplify]: Simplify 0 into 0 5.156 * [backup-simplify]: Simplify (* (acos (/ 1 (/ 1 a))) (/ 1 a)) into (/ (acos a) a) 5.156 * [backup-simplify]: Simplify (/ (acos (/ 1 (- a))) (/ 1 (- a))) into (* -1 (* a (acos (/ -1 a)))) 5.156 * [approximate]: Taking taylor expansion of (* -1 (* a (acos (/ -1 a)))) in (a) around 0 5.156 * [taylor]: Taking taylor expansion of (* -1 (* a (acos (/ -1 a)))) in a 5.156 * [taylor]: Taking taylor expansion of -1 in a 5.156 * [backup-simplify]: Simplify -1 into -1 5.156 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 5.156 * [taylor]: Taking taylor expansion of a in a 5.156 * [backup-simplify]: Simplify 0 into 0 5.156 * [backup-simplify]: Simplify 1 into 1 5.156 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 5.156 * [backup-simplify]: Simplify (acos (/ -1 a)) into (acos (/ -1 a)) 5.156 * [taylor]: Taking taylor expansion of (* -1 (* a (acos (/ -1 a)))) in a 5.156 * [taylor]: Taking taylor expansion of -1 in a 5.156 * [backup-simplify]: Simplify -1 into -1 5.156 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 5.156 * [taylor]: Taking taylor expansion of a in a 5.156 * [backup-simplify]: Simplify 0 into 0 5.156 * [backup-simplify]: Simplify 1 into 1 5.156 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 5.156 * [backup-simplify]: Simplify (acos (/ -1 a)) into (acos (/ -1 a)) 5.157 * [backup-simplify]: Simplify (* 0 (acos (/ -1 a))) into 0 5.157 * [backup-simplify]: Simplify (* -1 0) into 0 5.157 * [backup-simplify]: Simplify 0 into 0 5.158 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 (acos (/ -1 a)))) into (acos (/ -1 a)) 5.158 * [backup-simplify]: Simplify (+ (* -1 (acos (/ -1 a))) (* 0 0)) into (- (acos (/ -1 a))) 5.158 * [backup-simplify]: Simplify (- (acos (/ -1 a))) into (- (acos (/ -1 a))) 5.159 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (acos (/ -1 a))))) into 0 5.159 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 (acos (/ -1 a))) (* 0 0))) into 0 5.159 * [backup-simplify]: Simplify 0 into 0 5.160 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (acos (/ -1 a)))))) into 0 5.161 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 (acos (/ -1 a))) (* 0 0)))) into 0 5.161 * [backup-simplify]: Simplify 0 into 0 5.162 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (acos (/ -1 a))))))) into 0 5.163 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 (acos (/ -1 a))) (* 0 0))))) into 0 5.163 * [backup-simplify]: Simplify 0 into 0 5.170 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (acos (/ -1 a)))))))) into 0 5.171 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 (acos (/ -1 a))) (* 0 0)))))) into 0 5.171 * [backup-simplify]: Simplify 0 into 0 5.173 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (acos (/ -1 a))))))))) into 0 5.174 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 (acos (/ -1 a))) (* 0 0))))))) into 0 5.175 * [backup-simplify]: Simplify 0 into 0 5.176 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (acos (/ -1 a)))))))))) into 0 5.178 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 (acos (/ -1 a))) (* 0 0)))))))) into 0 5.178 * [backup-simplify]: Simplify 0 into 0 5.178 * [backup-simplify]: Simplify (* (- (acos (/ -1 (/ 1 (- a))))) (/ 1 (- a))) into (/ (acos a) a) 5.178 * * * [progress]: simplifying candidates 5.181 * [simplify]: Simplifying: (expm1 (/ 1 (- (/ (acos a) a)))) (log1p (/ 1 (- (/ (acos a) a)))) (- 1) (- (log (- (/ (acos a) a)))) (- 0 (log (- (/ (acos a) a)))) (- (log 1) (log (- (/ (acos a) a)))) (log (/ 1 (- (/ (acos a) a)))) (exp (/ 1 (- (/ (acos 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)) 1) (/ (cbrt 1) (- (/ (acos a) a))) (/ (* (cbrt 1) (cbrt 1)) -1) (/ (cbrt 1) (/ (acos a) a)) (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (/ (acos a) a)) (cbrt (/ (acos a) a))))) (/ (cbrt 1) (cbrt (/ (acos a) a))) (/ (* 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(/ a (acos a))) (* -1 (/ a (acos a))) (/ (acos a) a) (/ (acos a) a) (/ (acos a) a) 5.185 * * [simplify]: Extracting # 0 : cost 0 5.186 * * [simplify]: Extracting # 1 : cost 0 5.186 * * [simplify]: Extracting # 2 : cost 0 5.186 * * [simplify]: Extracting # 3 : cost 0 5.187 * * [simplify]: Extracting # 4 : cost 0 5.187 * * [simplify]: Extracting # 5 : cost 0 5.187 * * [simplify]: Extracting # 6 : cost 0 5.188 * * [simplify]: iteration 0 : 265 enodes (cost 2409 ) 5.332 * * [simplify]: Extracting # 0 : cost 0 5.335 * * [simplify]: Extracting # 1 : cost 0 5.336 * * [simplify]: Extracting # 2 : cost 0 5.336 * * [simplify]: iteration 1 : 472 enodes (cost 2004 ) 5.475 * * [simplify]: Extracting # 0 : cost 0 5.476 * * [simplify]: Extracting # 1 : cost 0 5.476 * * [simplify]: Extracting # 2 : cost 0 5.477 * * [simplify]: Extracting # 3 : cost 0 5.478 * * [simplify]: iteration 2 : 774 enodes (cost 1861 ) 5.828 * * [simplify]: Extracting # 0 : cost 0 5.829 * * [simplify]: Extracting # 1 : cost 0 5.831 * * [simplify]: Extracting # 2 : cost 0 5.832 * * [simplify]: Extracting # 3 : cost 0 5.833 * * [simplify]: Extracting # 4 : cost 0 5.834 * * [simplify]: iteration 3 : 1510 enodes (cost 1711 ) 7.741 * * [simplify]: Extracting # 0 : cost 0 7.744 * * [simplify]: Extracting # 1 : cost 0 7.747 * * [simplify]: Extracting # 2 : cost 0 7.751 * * [simplify]: Extracting # 3 : cost 0 7.755 * * [simplify]: Extracting # 4 : cost 0 7.759 * * [simplify]: iteration 4 : 2755 enodes (cost 1711 ) 12.032 * * [simplify]: Extracting # 0 : cost 0 12.038 * * [simplify]: Extracting # 1 : cost 0 12.041 * * [simplify]: Extracting # 2 : cost 0 12.045 * * [simplify]: Extracting # 3 : cost 0 12.051 * * [simplify]: Extracting # 4 : cost 0 12.061 * * [simplify]: iteration done: 5000 enodes (cost 1711 ) 12.063 * [simplify]: Simplified to: (expm1 (/ a (- (acos a)))) (log1p (/ a (- (acos a)))) -1 (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (log (/ a (- (acos a)))) (exp (/ a (- (acos 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a)))) 1 (- (/ a (acos a))) -1 (/ a (acos 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))))) (/ (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)))) (/ (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))) (/ (cbrt a) (acos a)) (- (sqrt a)) (/ (sqrt a) (acos a)) -1 (/ a (acos a)) -1 (/ a (acos 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)))) (/ (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))) (/ (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)) (/ (cbrt a) (- (acos a))) (sqrt a) (/ (sqrt a) (- (acos a))) 1 (- (/ a (acos a))) 1 (- (/ a (acos 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)))) 1 (- (/ a (acos a))) -1 (/ a (acos 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))))) (/ (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)))) (/ (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))) (/ (cbrt a) (acos a)) (- (sqrt a)) (/ (sqrt a) (acos a)) -1 (/ a (acos a)) -1 (/ a (acos 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)))) (/ (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))) (/ (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)) (/ (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)))) 1 -1 (/ 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 (/ 1 (- (acos 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 (/ 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) (/ (/ PI 2) a) (/ (asin a) a) (/ (* (cbrt (acos a)) (/ (cbrt (acos a)) (cbrt a))) (cbrt a)) (/ (cbrt (acos a)) (cbrt a)) (/ (cbrt (acos a)) (/ (sqrt a) (cbrt (acos a)))) (/ (cbrt (acos a)) (sqrt a)) (* (cbrt (acos a)) (cbrt (acos a))) (/ (cbrt (acos a)) a) (/ (/ (sqrt (acos a)) (cbrt a)) (cbrt a)) (/ (sqrt (acos a)) (cbrt a)) (/ (sqrt (acos a)) (sqrt a)) (/ (sqrt (acos a)) (sqrt a)) (sqrt (acos a)) (/ (sqrt (acos a)) a) (/ (/ 1 (cbrt a)) (cbrt a)) (/ (acos a) (cbrt a)) (/ 1 (sqrt a)) (/ (acos a) (sqrt a)) 1 (/ (acos a) a) (/ 1 a) (/ a (acos 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 (acos a))) (- (/ a (acos a))) (/ (acos a) a) (/ (acos a) a) (/ (acos a) a) 12.065 * * * [progress]: adding candidates to table 12.443 * * [progress]: iteration 3 / 4 12.443 * * * [progress]: picking best candidate 12.478 * * * * [pick]: Picked # 12.478 * * * [progress]: localizing error 12.501 * * * [progress]: generating rewritten candidates 12.501 * * * * [progress]: [ 1 / 3 ] rewriting at (2) 12.776 * * * * [progress]: [ 2 / 3 ] rewriting at (2 2 1 1) 12.796 * * * * [progress]: [ 3 / 3 ] rewriting at (2 2 1) 13.049 * * * [progress]: generating series expansions 13.050 * * * * [progress]: [ 1 / 3 ] generating series at (2) 13.050 * [backup-simplify]: Simplify (/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a)))) into (/ 1 (- (/ (asin a) a) (* 1/2 (/ PI a)))) 13.050 * [approximate]: Taking taylor expansion of (/ 1 (- (/ (asin a) a) (* 1/2 (/ PI a)))) in (a) around 0 13.050 * [taylor]: Taking taylor expansion of (/ 1 (- (/ (asin a) a) (* 1/2 (/ PI a)))) in a 13.051 * [taylor]: Taking taylor expansion of (- (/ (asin a) a) (* 1/2 (/ PI a))) in a 13.051 * [taylor]: Taking taylor expansion of (/ (asin a) a) in a 13.051 * [taylor]: Taking taylor expansion of (asin a) in a 13.051 * [backup-simplify]: Simplify (asin a) into (asin a) 13.051 * [taylor]: Taking taylor expansion of a in a 13.051 * [backup-simplify]: Simplify 0 into 0 13.051 * [backup-simplify]: Simplify 1 into 1 13.051 * [backup-simplify]: Simplify (/ (asin a) 1) into (asin a) 13.051 * [taylor]: Taking taylor expansion of (* 1/2 (/ PI a)) in a 13.051 * [taylor]: Taking taylor expansion of 1/2 in a 13.051 * [backup-simplify]: Simplify 1/2 into 1/2 13.051 * [taylor]: Taking taylor expansion of (/ PI a) in a 13.051 * [taylor]: Taking taylor expansion of PI in a 13.051 * [backup-simplify]: Simplify PI into PI 13.051 * [taylor]: Taking taylor expansion of a in a 13.051 * [backup-simplify]: Simplify 0 into 0 13.051 * [backup-simplify]: Simplify 1 into 1 13.051 * [backup-simplify]: Simplify (/ PI 1) into PI 13.052 * [backup-simplify]: Simplify (* 1/2 PI) into (* 1/2 PI) 13.052 * [backup-simplify]: Simplify (- (* 1/2 PI)) into (- (* 1/2 PI)) 13.053 * [backup-simplify]: Simplify (+ (asin a) (- (* 1/2 PI))) into (- (asin a) (* 1/2 PI)) 13.053 * [backup-simplify]: Simplify (/ 1 (- (asin a) (* 1/2 PI))) into (/ 1 (- (asin a) (* 1/2 PI))) 13.054 * [taylor]: Taking taylor expansion of (/ 1 (- (/ (asin a) a) (* 1/2 (/ PI a)))) in a 13.054 * [taylor]: Taking taylor expansion of (- (/ (asin a) a) (* 1/2 (/ PI a))) in a 13.054 * [taylor]: Taking taylor expansion of (/ (asin a) a) in a 13.054 * [taylor]: Taking taylor expansion of (asin a) in a 13.054 * [backup-simplify]: Simplify (asin a) into (asin a) 13.054 * [taylor]: Taking taylor expansion of a in a 13.054 * [backup-simplify]: Simplify 0 into 0 13.054 * [backup-simplify]: Simplify 1 into 1 13.054 * [backup-simplify]: Simplify (/ (asin a) 1) into (asin a) 13.054 * [taylor]: Taking taylor expansion of (* 1/2 (/ PI a)) in a 13.054 * [taylor]: Taking taylor expansion of 1/2 in a 13.054 * [backup-simplify]: Simplify 1/2 into 1/2 13.054 * [taylor]: Taking taylor expansion of (/ PI a) in a 13.054 * [taylor]: Taking taylor expansion of PI in a 13.054 * [backup-simplify]: Simplify PI into PI 13.054 * [taylor]: Taking taylor expansion of a in a 13.054 * [backup-simplify]: Simplify 0 into 0 13.054 * [backup-simplify]: Simplify 1 into 1 13.054 * [backup-simplify]: Simplify (/ PI 1) into PI 13.055 * [backup-simplify]: Simplify (* 1/2 PI) into (* 1/2 PI) 13.055 * [backup-simplify]: Simplify (- (* 1/2 PI)) into (- (* 1/2 PI)) 13.068 * [backup-simplify]: Simplify (+ (asin a) (- (* 1/2 PI))) into (- (asin a) (* 1/2 PI)) 13.069 * [backup-simplify]: Simplify (/ 1 (- (asin a) (* 1/2 PI))) into (/ 1 (- (asin a) (* 1/2 PI))) 13.070 * [backup-simplify]: Simplify (/ 1 (- (asin a) (* 1/2 PI))) into (/ 1 (- (asin a) (* 1/2 PI))) 13.071 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (asin a) (/ 0 1)))) into 0 13.072 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.073 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 PI)) into 0 13.074 * [backup-simplify]: Simplify (- 0) into 0 13.074 * [backup-simplify]: Simplify (+ 0 0) into 0 13.076 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (asin a) (* 1/2 PI))) (/ 0 (- (asin a) (* 1/2 PI)))))) into 0 13.076 * [backup-simplify]: Simplify 0 into 0 13.077 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (asin a) (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.079 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.080 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 PI))) into 0 13.080 * [backup-simplify]: Simplify (- 0) into 0 13.081 * [backup-simplify]: Simplify (+ 0 0) into 0 13.083 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (asin a) (* 1/2 PI))) (/ 0 (- (asin a) (* 1/2 PI)))) (* 0 (/ 0 (- (asin a) (* 1/2 PI)))))) into 0 13.083 * [backup-simplify]: Simplify 0 into 0 13.085 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (asin a) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.086 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.088 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.088 * [backup-simplify]: Simplify (- 0) into 0 13.088 * [backup-simplify]: Simplify (+ 0 0) into 0 13.090 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (asin a) (* 1/2 PI))) (/ 0 (- (asin a) (* 1/2 PI)))) (* 0 (/ 0 (- (asin a) (* 1/2 PI)))) (* 0 (/ 0 (- (asin a) (* 1/2 PI)))))) into 0 13.090 * [backup-simplify]: Simplify 0 into 0 13.091 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (asin a) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.092 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.093 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.093 * [backup-simplify]: Simplify (- 0) into 0 13.094 * [backup-simplify]: Simplify (+ 0 0) into 0 13.096 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (asin a) (* 1/2 PI))) (/ 0 (- (asin a) (* 1/2 PI)))) (* 0 (/ 0 (- (asin a) (* 1/2 PI)))) (* 0 (/ 0 (- (asin a) (* 1/2 PI)))) (* 0 (/ 0 (- (asin a) (* 1/2 PI)))))) into 0 13.096 * [backup-simplify]: Simplify 0 into 0 13.098 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (asin a) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.098 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.099 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.100 * [backup-simplify]: Simplify (- 0) into 0 13.100 * [backup-simplify]: Simplify (+ 0 0) into 0 13.102 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (asin a) (* 1/2 PI))) (/ 0 (- (asin a) (* 1/2 PI)))) (* 0 (/ 0 (- (asin a) (* 1/2 PI)))) (* 0 (/ 0 (- (asin a) (* 1/2 PI)))) (* 0 (/ 0 (- (asin a) (* 1/2 PI)))) (* 0 (/ 0 (- (asin a) (* 1/2 PI)))))) into 0 13.102 * [backup-simplify]: Simplify 0 into 0 13.104 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (asin a) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.105 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.106 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.107 * [backup-simplify]: Simplify (- 0) into 0 13.107 * [backup-simplify]: Simplify (+ 0 0) into 0 13.109 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (asin a) (* 1/2 PI))) (/ 0 (- (asin a) (* 1/2 PI)))) (* 0 (/ 0 (- (asin a) (* 1/2 PI)))) (* 0 (/ 0 (- (asin a) (* 1/2 PI)))) (* 0 (/ 0 (- (asin a) (* 1/2 PI)))) (* 0 (/ 0 (- (asin a) (* 1/2 PI)))) (* 0 (/ 0 (- (asin a) (* 1/2 PI)))))) into 0 13.110 * [backup-simplify]: Simplify 0 into 0 13.110 * [backup-simplify]: Simplify (* (/ 1 (- (asin a) (* 1/2 PI))) a) into (/ a (- (asin a) (* 1/2 PI))) 13.111 * [backup-simplify]: Simplify (/ 1 (- (- (/ (/ PI 2) (/ 1 a)) (/ (asin (/ 1 a)) (/ 1 a))))) into (/ 1 (- (* a (asin (/ 1 a))) (* 1/2 (* a PI)))) 13.111 * [approximate]: Taking taylor expansion of (/ 1 (- (* a (asin (/ 1 a))) (* 1/2 (* a PI)))) in (a) around 0 13.111 * [taylor]: Taking taylor expansion of (/ 1 (- (* a (asin (/ 1 a))) (* 1/2 (* a PI)))) in a 13.111 * [taylor]: Taking taylor expansion of (- (* a (asin (/ 1 a))) (* 1/2 (* a PI))) in a 13.111 * [taylor]: Taking taylor expansion of (* a (asin (/ 1 a))) in a 13.111 * [taylor]: Taking taylor expansion of a in a 13.111 * [backup-simplify]: Simplify 0 into 0 13.111 * [backup-simplify]: Simplify 1 into 1 13.111 * [taylor]: Taking taylor expansion of (asin (/ 1 a)) in a 13.111 * [backup-simplify]: Simplify (asin (/ 1 a)) into (asin (/ 1 a)) 13.111 * [taylor]: Taking taylor expansion of (* 1/2 (* a PI)) in a 13.111 * [taylor]: Taking taylor expansion of 1/2 in a 13.111 * [backup-simplify]: Simplify 1/2 into 1/2 13.111 * [taylor]: Taking taylor expansion of (* a PI) in a 13.111 * [taylor]: Taking taylor expansion of a in a 13.111 * [backup-simplify]: Simplify 0 into 0 13.111 * [backup-simplify]: Simplify 1 into 1 13.111 * [taylor]: Taking taylor expansion of PI in a 13.111 * [backup-simplify]: Simplify PI into PI 13.111 * [backup-simplify]: Simplify (* 0 (asin (/ 1 a))) into 0 13.112 * [backup-simplify]: Simplify (* 0 PI) into 0 13.112 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.112 * [backup-simplify]: Simplify (- 0) into 0 13.112 * [backup-simplify]: Simplify (+ 0 0) into 0 13.113 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 (asin (/ 1 a)))) into (asin (/ 1 a)) 13.114 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.115 * [backup-simplify]: Simplify (+ (* 1/2 PI) (* 0 0)) into (* 1/2 PI) 13.116 * [backup-simplify]: Simplify (- (* 1/2 PI)) into (- (* 1/2 PI)) 13.116 * [backup-simplify]: Simplify (+ (asin (/ 1 a)) (- (* 1/2 PI))) into (- (asin (/ 1 a)) (* 1/2 PI)) 13.117 * [backup-simplify]: Simplify (/ 1 (- (asin (/ 1 a)) (* 1/2 PI))) into (/ 1 (- (asin (/ 1 a)) (* 1/2 PI))) 13.117 * [taylor]: Taking taylor expansion of (/ 1 (- (* a (asin (/ 1 a))) (* 1/2 (* a PI)))) in a 13.117 * [taylor]: Taking taylor expansion of (- (* a (asin (/ 1 a))) (* 1/2 (* a PI))) in a 13.117 * [taylor]: Taking taylor expansion of (* a (asin (/ 1 a))) in a 13.117 * [taylor]: Taking taylor expansion of a in a 13.117 * [backup-simplify]: Simplify 0 into 0 13.117 * [backup-simplify]: Simplify 1 into 1 13.117 * [taylor]: Taking taylor expansion of (asin (/ 1 a)) in a 13.117 * [backup-simplify]: Simplify (asin (/ 1 a)) into (asin (/ 1 a)) 13.117 * [taylor]: Taking taylor expansion of (* 1/2 (* a PI)) in a 13.117 * [taylor]: Taking taylor expansion of 1/2 in a 13.117 * [backup-simplify]: Simplify 1/2 into 1/2 13.117 * [taylor]: Taking taylor expansion of (* a PI) in a 13.117 * [taylor]: Taking taylor expansion of a in a 13.117 * [backup-simplify]: Simplify 0 into 0 13.117 * [backup-simplify]: Simplify 1 into 1 13.117 * [taylor]: Taking taylor expansion of PI in a 13.117 * [backup-simplify]: Simplify PI into PI 13.117 * [backup-simplify]: Simplify (* 0 (asin (/ 1 a))) into 0 13.118 * [backup-simplify]: Simplify (* 0 PI) into 0 13.118 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.118 * [backup-simplify]: Simplify (- 0) into 0 13.118 * [backup-simplify]: Simplify (+ 0 0) into 0 13.119 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 (asin (/ 1 a)))) into (asin (/ 1 a)) 13.120 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.122 * [backup-simplify]: Simplify (+ (* 1/2 PI) (* 0 0)) into (* 1/2 PI) 13.123 * [backup-simplify]: Simplify (- (* 1/2 PI)) into (- (* 1/2 PI)) 13.124 * [backup-simplify]: Simplify (+ (asin (/ 1 a)) (- (* 1/2 PI))) into (- (asin (/ 1 a)) (* 1/2 PI)) 13.125 * [backup-simplify]: Simplify (/ 1 (- (asin (/ 1 a)) (* 1/2 PI))) into (/ 1 (- (asin (/ 1 a)) (* 1/2 PI))) 13.126 * [backup-simplify]: Simplify (/ 1 (- (asin (/ 1 a)) (* 1/2 PI))) into (/ 1 (- (asin (/ 1 a)) (* 1/2 PI))) 13.127 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (asin (/ 1 a))))) into 0 13.129 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.130 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 PI) (* 0 0))) into 0 13.130 * [backup-simplify]: Simplify (- 0) into 0 13.131 * [backup-simplify]: Simplify (+ 0 0) into 0 13.133 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (asin (/ 1 a)) (* 1/2 PI))) (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))))) into 0 13.133 * [backup-simplify]: Simplify 0 into 0 13.134 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (asin (/ 1 a)))))) into 0 13.136 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.137 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.138 * [backup-simplify]: Simplify (- 0) into 0 13.138 * [backup-simplify]: Simplify (+ 0 0) into 0 13.140 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (asin (/ 1 a)) (* 1/2 PI))) (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))) (* 0 (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))))) into 0 13.141 * [backup-simplify]: Simplify 0 into 0 13.142 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (asin (/ 1 a))))))) into 0 13.144 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.146 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 13.146 * [backup-simplify]: Simplify (- 0) into 0 13.147 * [backup-simplify]: Simplify (+ 0 0) into 0 13.150 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (asin (/ 1 a)) (* 1/2 PI))) (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))) (* 0 (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))) (* 0 (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))))) into 0 13.150 * [backup-simplify]: Simplify 0 into 0 13.152 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (asin (/ 1 a)))))))) into 0 13.154 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.156 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 13.156 * [backup-simplify]: Simplify (- 0) into 0 13.157 * [backup-simplify]: Simplify (+ 0 0) into 0 13.160 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (asin (/ 1 a)) (* 1/2 PI))) (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))) (* 0 (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))) (* 0 (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))) (* 0 (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))))) into 0 13.160 * [backup-simplify]: Simplify 0 into 0 13.163 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (asin (/ 1 a))))))))) into 0 13.165 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.166 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 13.166 * [backup-simplify]: Simplify (- 0) into 0 13.166 * [backup-simplify]: Simplify (+ 0 0) into 0 13.169 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (asin (/ 1 a)) (* 1/2 PI))) (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))) (* 0 (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))) (* 0 (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))) (* 0 (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))) (* 0 (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))))) into 0 13.169 * [backup-simplify]: Simplify 0 into 0 13.170 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (asin (/ 1 a)))))))))) into 0 13.172 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 13.173 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 13.173 * [backup-simplify]: Simplify (- 0) into 0 13.173 * [backup-simplify]: Simplify (+ 0 0) into 0 13.176 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (asin (/ 1 a)) (* 1/2 PI))) (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))) (* 0 (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))) (* 0 (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))) (* 0 (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))) (* 0 (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))) (* 0 (/ 0 (- (asin (/ 1 a)) (* 1/2 PI)))))) into 0 13.177 * [backup-simplify]: Simplify 0 into 0 13.177 * [backup-simplify]: Simplify (* (/ 1 (- (asin (/ 1 (/ 1 a))) (* 1/2 PI))) (/ 1 (/ 1 a))) into (/ a (- (asin a) (* 1/2 PI))) 13.178 * [backup-simplify]: Simplify (/ 1 (- (- (/ (/ PI 2) (/ 1 (- a))) (/ (asin (/ 1 (- a))) (/ 1 (- a)))))) into (/ 1 (- (* 1/2 (* a PI)) (* a (asin (/ -1 a))))) 13.178 * [approximate]: Taking taylor expansion of (/ 1 (- (* 1/2 (* a PI)) (* a (asin (/ -1 a))))) in (a) around 0 13.178 * [taylor]: Taking taylor expansion of (/ 1 (- (* 1/2 (* a PI)) (* a (asin (/ -1 a))))) in a 13.178 * [taylor]: Taking taylor expansion of (- (* 1/2 (* a PI)) (* a (asin (/ -1 a)))) in a 13.178 * [taylor]: Taking taylor expansion of (* 1/2 (* a PI)) in a 13.178 * [taylor]: Taking taylor expansion of 1/2 in a 13.178 * [backup-simplify]: Simplify 1/2 into 1/2 13.178 * [taylor]: Taking taylor expansion of (* a PI) in a 13.178 * [taylor]: Taking taylor expansion of a in a 13.178 * [backup-simplify]: Simplify 0 into 0 13.178 * [backup-simplify]: Simplify 1 into 1 13.178 * [taylor]: Taking taylor expansion of PI in a 13.178 * [backup-simplify]: Simplify PI into PI 13.178 * [taylor]: Taking taylor expansion of (* a (asin (/ -1 a))) in a 13.178 * [taylor]: Taking taylor expansion of a in a 13.178 * [backup-simplify]: Simplify 0 into 0 13.178 * [backup-simplify]: Simplify 1 into 1 13.178 * [taylor]: Taking taylor expansion of (asin (/ -1 a)) in a 13.178 * [backup-simplify]: Simplify (asin (/ -1 a)) into (asin (/ -1 a)) 13.179 * [backup-simplify]: Simplify (* 0 PI) into 0 13.179 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.179 * [backup-simplify]: Simplify (* 0 (asin (/ -1 a))) into 0 13.179 * [backup-simplify]: Simplify (- 0) into 0 13.179 * [backup-simplify]: Simplify (+ 0 0) into 0 13.180 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.181 * [backup-simplify]: Simplify (+ (* 1/2 PI) (* 0 0)) into (* 1/2 PI) 13.182 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 (asin (/ -1 a)))) into (asin (/ -1 a)) 13.182 * [backup-simplify]: Simplify (- (asin (/ -1 a))) into (- (asin (/ -1 a))) 13.182 * [backup-simplify]: Simplify (+ (* 1/2 PI) (- (asin (/ -1 a)))) into (- (* 1/2 PI) (asin (/ -1 a))) 13.183 * [backup-simplify]: Simplify (/ 1 (- (* 1/2 PI) (asin (/ -1 a)))) into (/ 1 (- (* 1/2 PI) (asin (/ -1 a)))) 13.183 * [taylor]: Taking taylor expansion of (/ 1 (- (* 1/2 (* a PI)) (* a (asin (/ -1 a))))) in a 13.183 * [taylor]: Taking taylor expansion of (- (* 1/2 (* a PI)) (* a (asin (/ -1 a)))) in a 13.183 * [taylor]: Taking taylor expansion of (* 1/2 (* a PI)) in a 13.183 * [taylor]: Taking taylor expansion of 1/2 in a 13.183 * [backup-simplify]: Simplify 1/2 into 1/2 13.183 * [taylor]: Taking taylor expansion of (* a PI) in a 13.183 * [taylor]: Taking taylor expansion of a in a 13.183 * [backup-simplify]: Simplify 0 into 0 13.183 * [backup-simplify]: Simplify 1 into 1 13.183 * [taylor]: Taking taylor expansion of PI in a 13.183 * [backup-simplify]: Simplify PI into PI 13.183 * [taylor]: Taking taylor expansion of (* a (asin (/ -1 a))) in a 13.183 * [taylor]: Taking taylor expansion of a in a 13.183 * [backup-simplify]: Simplify 0 into 0 13.183 * [backup-simplify]: Simplify 1 into 1 13.183 * [taylor]: Taking taylor expansion of (asin (/ -1 a)) in a 13.183 * [backup-simplify]: Simplify (asin (/ -1 a)) into (asin (/ -1 a)) 13.183 * [backup-simplify]: Simplify (* 0 PI) into 0 13.184 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.184 * [backup-simplify]: Simplify (* 0 (asin (/ -1 a))) into 0 13.184 * [backup-simplify]: Simplify (- 0) into 0 13.184 * [backup-simplify]: Simplify (+ 0 0) into 0 13.185 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.186 * [backup-simplify]: Simplify (+ (* 1/2 PI) (* 0 0)) into (* 1/2 PI) 13.187 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 (asin (/ -1 a)))) into (asin (/ -1 a)) 13.187 * [backup-simplify]: Simplify (- (asin (/ -1 a))) into (- (asin (/ -1 a))) 13.187 * [backup-simplify]: Simplify (+ (* 1/2 PI) (- (asin (/ -1 a)))) into (- (* 1/2 PI) (asin (/ -1 a))) 13.188 * [backup-simplify]: Simplify (/ 1 (- (* 1/2 PI) (asin (/ -1 a)))) into (/ 1 (- (* 1/2 PI) (asin (/ -1 a)))) 13.188 * [backup-simplify]: Simplify (/ 1 (- (* 1/2 PI) (asin (/ -1 a)))) into (/ 1 (- (* 1/2 PI) (asin (/ -1 a)))) 13.189 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.189 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 PI) (* 0 0))) into 0 13.190 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (asin (/ -1 a))))) into 0 13.190 * [backup-simplify]: Simplify (- 0) into 0 13.191 * [backup-simplify]: Simplify (+ 0 0) into 0 13.191 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (* 1/2 PI) (asin (/ -1 a)))) (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))))) into 0 13.191 * [backup-simplify]: Simplify 0 into 0 13.192 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.196 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.198 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (asin (/ -1 a)))))) into 0 13.198 * [backup-simplify]: Simplify (- 0) into 0 13.199 * [backup-simplify]: Simplify (+ 0 0) into 0 13.201 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (* 1/2 PI) (asin (/ -1 a)))) (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))) (* 0 (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))))) into 0 13.201 * [backup-simplify]: Simplify 0 into 0 13.202 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.204 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 13.206 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (asin (/ -1 a))))))) into 0 13.206 * [backup-simplify]: Simplify (- 0) into 0 13.207 * [backup-simplify]: Simplify (+ 0 0) into 0 13.209 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (* 1/2 PI) (asin (/ -1 a)))) (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))) (* 0 (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))) (* 0 (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))))) into 0 13.209 * [backup-simplify]: Simplify 0 into 0 13.210 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.211 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 13.212 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (asin (/ -1 a)))))))) into 0 13.212 * [backup-simplify]: Simplify (- 0) into 0 13.213 * [backup-simplify]: Simplify (+ 0 0) into 0 13.215 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (* 1/2 PI) (asin (/ -1 a)))) (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))) (* 0 (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))) (* 0 (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))) (* 0 (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))))) into 0 13.215 * [backup-simplify]: Simplify 0 into 0 13.216 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.217 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 13.218 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (asin (/ -1 a))))))))) into 0 13.219 * [backup-simplify]: Simplify (- 0) into 0 13.219 * [backup-simplify]: Simplify (+ 0 0) into 0 13.221 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (* 1/2 PI) (asin (/ -1 a)))) (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))) (* 0 (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))) (* 0 (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))) (* 0 (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))) (* 0 (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))))) into 0 13.221 * [backup-simplify]: Simplify 0 into 0 13.223 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 13.224 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 13.226 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (asin (/ -1 a)))))))))) into 0 13.226 * [backup-simplify]: Simplify (- 0) into 0 13.226 * [backup-simplify]: Simplify (+ 0 0) into 0 13.229 * [backup-simplify]: Simplify (- (+ (* (/ 1 (- (* 1/2 PI) (asin (/ -1 a)))) (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))) (* 0 (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))) (* 0 (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))) (* 0 (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))) (* 0 (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))) (* 0 (/ 0 (- (* 1/2 PI) (asin (/ -1 a))))))) into 0 13.229 * [backup-simplify]: Simplify 0 into 0 13.230 * [backup-simplify]: Simplify (* (/ 1 (- (* 1/2 PI) (asin (/ -1 (/ 1 (- a)))))) (/ 1 (/ 1 (- a)))) into (* -1 (/ a (- (* 1/2 PI) (asin a)))) 13.230 * * * * [progress]: [ 2 / 3 ] generating series at (2 2 1 1) 13.230 * [backup-simplify]: Simplify (/ (/ PI 2) a) into (* 1/2 (/ PI a)) 13.230 * [approximate]: Taking taylor expansion of (* 1/2 (/ PI a)) in (a) around 0 13.230 * [taylor]: Taking taylor expansion of (* 1/2 (/ PI a)) in a 13.230 * [taylor]: Taking taylor expansion of 1/2 in a 13.230 * [backup-simplify]: Simplify 1/2 into 1/2 13.230 * [taylor]: Taking taylor expansion of (/ PI a) in a 13.230 * [taylor]: Taking taylor expansion of PI in a 13.230 * [backup-simplify]: Simplify PI into PI 13.230 * [taylor]: Taking taylor expansion of a in a 13.230 * [backup-simplify]: Simplify 0 into 0 13.230 * [backup-simplify]: Simplify 1 into 1 13.231 * [backup-simplify]: Simplify (/ PI 1) into PI 13.231 * [taylor]: Taking taylor expansion of (* 1/2 (/ PI a)) in a 13.231 * [taylor]: Taking taylor expansion of 1/2 in a 13.231 * [backup-simplify]: Simplify 1/2 into 1/2 13.231 * [taylor]: Taking taylor expansion of (/ PI a) in a 13.231 * [taylor]: Taking taylor expansion of PI in a 13.231 * [backup-simplify]: Simplify PI into PI 13.231 * [taylor]: Taking taylor expansion of a in a 13.231 * [backup-simplify]: Simplify 0 into 0 13.231 * [backup-simplify]: Simplify 1 into 1 13.231 * [backup-simplify]: Simplify (/ PI 1) into PI 13.232 * [backup-simplify]: Simplify (* 1/2 PI) into (* 1/2 PI) 13.232 * [backup-simplify]: Simplify (* 1/2 PI) into (* 1/2 PI) 13.233 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.233 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 PI)) into 0 13.233 * [backup-simplify]: Simplify 0 into 0 13.234 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.234 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 PI))) into 0 13.234 * [backup-simplify]: Simplify 0 into 0 13.235 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.236 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.236 * [backup-simplify]: Simplify 0 into 0 13.237 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.238 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.238 * [backup-simplify]: Simplify 0 into 0 13.238 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.240 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.240 * [backup-simplify]: Simplify 0 into 0 13.241 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.243 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.243 * [backup-simplify]: Simplify 0 into 0 13.244 * [backup-simplify]: Simplify (* (* 1/2 PI) (/ 1 a)) into (* 1/2 (/ PI a)) 13.244 * [backup-simplify]: Simplify (/ (/ PI 2) (/ 1 a)) into (* 1/2 (* a PI)) 13.244 * [approximate]: Taking taylor expansion of (* 1/2 (* a PI)) in (a) around 0 13.244 * [taylor]: Taking taylor expansion of (* 1/2 (* a PI)) in a 13.244 * [taylor]: Taking taylor expansion of 1/2 in a 13.244 * [backup-simplify]: Simplify 1/2 into 1/2 13.244 * [taylor]: Taking taylor expansion of (* a PI) in a 13.245 * [taylor]: Taking taylor expansion of a in a 13.245 * [backup-simplify]: Simplify 0 into 0 13.245 * [backup-simplify]: Simplify 1 into 1 13.245 * [taylor]: Taking taylor expansion of PI in a 13.245 * [backup-simplify]: Simplify PI into PI 13.245 * [taylor]: Taking taylor expansion of (* 1/2 (* a PI)) in a 13.245 * [taylor]: Taking taylor expansion of 1/2 in a 13.245 * [backup-simplify]: Simplify 1/2 into 1/2 13.245 * [taylor]: Taking taylor expansion of (* a PI) in a 13.245 * [taylor]: Taking taylor expansion of a in a 13.245 * [backup-simplify]: Simplify 0 into 0 13.245 * [backup-simplify]: Simplify 1 into 1 13.245 * [taylor]: Taking taylor expansion of PI in a 13.245 * [backup-simplify]: Simplify PI into PI 13.246 * [backup-simplify]: Simplify (* 0 PI) into 0 13.246 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.246 * [backup-simplify]: Simplify 0 into 0 13.248 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.250 * [backup-simplify]: Simplify (+ (* 1/2 PI) (* 0 0)) into (* 1/2 PI) 13.250 * [backup-simplify]: Simplify (* 1/2 PI) into (* 1/2 PI) 13.251 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.253 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 PI) (* 0 0))) into 0 13.253 * [backup-simplify]: Simplify 0 into 0 13.254 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.256 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.256 * [backup-simplify]: Simplify 0 into 0 13.257 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.259 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 13.259 * [backup-simplify]: Simplify 0 into 0 13.260 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.262 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 13.262 * [backup-simplify]: Simplify 0 into 0 13.264 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.266 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 13.266 * [backup-simplify]: Simplify 0 into 0 13.268 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 13.270 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 13.270 * [backup-simplify]: Simplify 0 into 0 13.271 * [backup-simplify]: Simplify (* (* 1/2 PI) (/ 1 a)) into (* 1/2 (/ PI a)) 13.272 * [backup-simplify]: Simplify (/ (/ PI 2) (/ 1 (- a))) into (* -1/2 (* a PI)) 13.272 * [approximate]: Taking taylor expansion of (* -1/2 (* a PI)) in (a) around 0 13.272 * [taylor]: Taking taylor expansion of (* -1/2 (* a PI)) in a 13.272 * [taylor]: Taking taylor expansion of -1/2 in a 13.272 * [backup-simplify]: Simplify -1/2 into -1/2 13.272 * [taylor]: Taking taylor expansion of (* a PI) in a 13.272 * [taylor]: Taking taylor expansion of a in a 13.272 * [backup-simplify]: Simplify 0 into 0 13.272 * [backup-simplify]: Simplify 1 into 1 13.272 * [taylor]: Taking taylor expansion of PI in a 13.272 * [backup-simplify]: Simplify PI into PI 13.272 * [taylor]: Taking taylor expansion of (* -1/2 (* a PI)) in a 13.272 * [taylor]: Taking taylor expansion of -1/2 in a 13.272 * [backup-simplify]: Simplify -1/2 into -1/2 13.272 * [taylor]: Taking taylor expansion of (* a PI) in a 13.272 * [taylor]: Taking taylor expansion of a in a 13.272 * [backup-simplify]: Simplify 0 into 0 13.272 * [backup-simplify]: Simplify 1 into 1 13.272 * [taylor]: Taking taylor expansion of PI in a 13.272 * [backup-simplify]: Simplify PI into PI 13.273 * [backup-simplify]: Simplify (* 0 PI) into 0 13.273 * [backup-simplify]: Simplify (* -1/2 0) into 0 13.273 * [backup-simplify]: Simplify 0 into 0 13.275 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.276 * [backup-simplify]: Simplify (+ (* -1/2 PI) (* 0 0)) into (- (* 1/2 PI)) 13.277 * [backup-simplify]: Simplify (- (* 1/2 PI)) into (- (* 1/2 PI)) 13.278 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.278 * [backup-simplify]: Simplify (+ (* -1/2 0) (+ (* 0 PI) (* 0 0))) into 0 13.278 * [backup-simplify]: Simplify 0 into 0 13.279 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.280 * [backup-simplify]: Simplify (+ (* -1/2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.280 * [backup-simplify]: Simplify 0 into 0 13.280 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.281 * [backup-simplify]: Simplify (+ (* -1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 13.281 * [backup-simplify]: Simplify 0 into 0 13.282 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.283 * [backup-simplify]: Simplify (+ (* -1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 13.283 * [backup-simplify]: Simplify 0 into 0 13.284 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.285 * [backup-simplify]: Simplify (+ (* -1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 13.285 * [backup-simplify]: Simplify 0 into 0 13.286 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 13.287 * [backup-simplify]: Simplify (+ (* -1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 13.287 * [backup-simplify]: Simplify 0 into 0 13.288 * [backup-simplify]: Simplify (* (- (* 1/2 PI)) (/ 1 (- a))) into (* 1/2 (/ PI a)) 13.288 * * * * [progress]: [ 3 / 3 ] generating series at (2 2 1) 13.289 * [backup-simplify]: Simplify (- (/ (/ PI 2) a) (/ (asin a) a)) into (- (* 1/2 (/ PI a)) (/ (asin a) a)) 13.289 * [approximate]: Taking taylor expansion of (- (* 1/2 (/ PI a)) (/ (asin a) a)) in (a) around 0 13.289 * [taylor]: Taking taylor expansion of (- (* 1/2 (/ PI a)) (/ (asin a) a)) in a 13.289 * [taylor]: Taking taylor expansion of (* 1/2 (/ PI a)) in a 13.289 * [taylor]: Taking taylor expansion of 1/2 in a 13.289 * [backup-simplify]: Simplify 1/2 into 1/2 13.289 * [taylor]: Taking taylor expansion of (/ PI a) in a 13.289 * [taylor]: Taking taylor expansion of PI in a 13.289 * [backup-simplify]: Simplify PI into PI 13.289 * [taylor]: Taking taylor expansion of a in a 13.289 * [backup-simplify]: Simplify 0 into 0 13.289 * [backup-simplify]: Simplify 1 into 1 13.289 * [backup-simplify]: Simplify (/ PI 1) into PI 13.289 * [taylor]: Taking taylor expansion of (/ (asin a) a) in a 13.289 * [taylor]: Taking taylor expansion of (asin a) in a 13.289 * [backup-simplify]: Simplify (asin a) into (asin a) 13.289 * [taylor]: Taking taylor expansion of a in a 13.289 * [backup-simplify]: Simplify 0 into 0 13.289 * [backup-simplify]: Simplify 1 into 1 13.289 * [backup-simplify]: Simplify (/ (asin a) 1) into (asin a) 13.289 * [taylor]: Taking taylor expansion of (- (* 1/2 (/ PI a)) (/ (asin a) a)) in a 13.289 * [taylor]: Taking taylor expansion of (* 1/2 (/ PI a)) in a 13.289 * [taylor]: Taking taylor expansion of 1/2 in a 13.289 * [backup-simplify]: Simplify 1/2 into 1/2 13.289 * [taylor]: Taking taylor expansion of (/ PI a) in a 13.290 * [taylor]: Taking taylor expansion of PI in a 13.290 * [backup-simplify]: Simplify PI into PI 13.290 * [taylor]: Taking taylor expansion of a in a 13.290 * [backup-simplify]: Simplify 0 into 0 13.290 * [backup-simplify]: Simplify 1 into 1 13.290 * [backup-simplify]: Simplify (/ PI 1) into PI 13.290 * [taylor]: Taking taylor expansion of (/ (asin a) a) in a 13.290 * [taylor]: Taking taylor expansion of (asin a) in a 13.290 * [backup-simplify]: Simplify (asin a) into (asin a) 13.290 * [taylor]: Taking taylor expansion of a in a 13.290 * [backup-simplify]: Simplify 0 into 0 13.290 * [backup-simplify]: Simplify 1 into 1 13.290 * [backup-simplify]: Simplify (/ (asin a) 1) into (asin a) 13.290 * [backup-simplify]: Simplify (* 1/2 PI) into (* 1/2 PI) 13.291 * [backup-simplify]: Simplify (- (asin a)) into (- (asin a)) 13.291 * [backup-simplify]: Simplify (+ (* 1/2 PI) (- (asin a))) into (- (* 1/2 PI) (asin a)) 13.291 * [backup-simplify]: Simplify (- (* 1/2 PI) (asin a)) into (- (* 1/2 PI) (asin a)) 13.292 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.292 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 PI)) into 0 13.293 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (asin a) (/ 0 1)))) into 0 13.293 * [backup-simplify]: Simplify (- 0) into 0 13.293 * [backup-simplify]: Simplify (+ 0 0) into 0 13.293 * [backup-simplify]: Simplify 0 into 0 13.294 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.295 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 PI))) into 0 13.295 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (asin a) (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.296 * [backup-simplify]: Simplify (- 0) into 0 13.296 * [backup-simplify]: Simplify (+ 0 0) into 0 13.296 * [backup-simplify]: Simplify 0 into 0 13.297 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.297 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.298 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (asin a) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.299 * [backup-simplify]: Simplify (- 0) into 0 13.299 * [backup-simplify]: Simplify (+ 0 0) into 0 13.299 * [backup-simplify]: Simplify 0 into 0 13.300 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.300 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.302 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (asin a) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.302 * [backup-simplify]: Simplify (- 0) into 0 13.302 * [backup-simplify]: Simplify (+ 0 0) into 0 13.302 * [backup-simplify]: Simplify 0 into 0 13.303 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.304 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.307 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (asin a) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.307 * [backup-simplify]: Simplify (- 0) into 0 13.308 * [backup-simplify]: Simplify (+ 0 0) into 0 13.308 * [backup-simplify]: Simplify 0 into 0 13.309 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.311 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.319 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (asin a) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.319 * [backup-simplify]: Simplify (- 0) into 0 13.320 * [backup-simplify]: Simplify (+ 0 0) into 0 13.320 * [backup-simplify]: Simplify 0 into 0 13.321 * [backup-simplify]: Simplify (* (- (* 1/2 PI) (asin a)) (/ 1 a)) into (/ (- (* 1/2 PI) (asin a)) a) 13.321 * [backup-simplify]: Simplify (- (/ (/ PI 2) (/ 1 a)) (/ (asin (/ 1 a)) (/ 1 a))) into (- (* 1/2 (* a PI)) (* a (asin (/ 1 a)))) 13.321 * [approximate]: Taking taylor expansion of (- (* 1/2 (* a PI)) (* a (asin (/ 1 a)))) in (a) around 0 13.322 * [taylor]: Taking taylor expansion of (- (* 1/2 (* a PI)) (* a (asin (/ 1 a)))) in a 13.322 * [taylor]: Taking taylor expansion of (* 1/2 (* a PI)) in a 13.322 * [taylor]: Taking taylor expansion of 1/2 in a 13.322 * [backup-simplify]: Simplify 1/2 into 1/2 13.322 * [taylor]: Taking taylor expansion of (* a PI) in a 13.322 * [taylor]: Taking taylor expansion of a in a 13.322 * [backup-simplify]: Simplify 0 into 0 13.322 * [backup-simplify]: Simplify 1 into 1 13.322 * [taylor]: Taking taylor expansion of PI in a 13.322 * [backup-simplify]: Simplify PI into PI 13.322 * [taylor]: Taking taylor expansion of (* a (asin (/ 1 a))) in a 13.322 * [taylor]: Taking taylor expansion of a in a 13.322 * [backup-simplify]: Simplify 0 into 0 13.322 * [backup-simplify]: Simplify 1 into 1 13.322 * [taylor]: Taking taylor expansion of (asin (/ 1 a)) in a 13.322 * [backup-simplify]: Simplify (asin (/ 1 a)) into (asin (/ 1 a)) 13.322 * [taylor]: Taking taylor expansion of (- (* 1/2 (* a PI)) (* a (asin (/ 1 a)))) in a 13.322 * [taylor]: Taking taylor expansion of (* 1/2 (* a PI)) in a 13.322 * [taylor]: Taking taylor expansion of 1/2 in a 13.322 * [backup-simplify]: Simplify 1/2 into 1/2 13.322 * [taylor]: Taking taylor expansion of (* a PI) in a 13.322 * [taylor]: Taking taylor expansion of a in a 13.322 * [backup-simplify]: Simplify 0 into 0 13.322 * [backup-simplify]: Simplify 1 into 1 13.322 * [taylor]: Taking taylor expansion of PI in a 13.322 * [backup-simplify]: Simplify PI into PI 13.322 * [taylor]: Taking taylor expansion of (* a (asin (/ 1 a))) in a 13.322 * [taylor]: Taking taylor expansion of a in a 13.322 * [backup-simplify]: Simplify 0 into 0 13.322 * [backup-simplify]: Simplify 1 into 1 13.323 * [taylor]: Taking taylor expansion of (asin (/ 1 a)) in a 13.323 * [backup-simplify]: Simplify (asin (/ 1 a)) into (asin (/ 1 a)) 13.323 * [backup-simplify]: Simplify (* 0 PI) into 0 13.324 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.324 * [backup-simplify]: Simplify (* 0 (asin (/ 1 a))) into 0 13.324 * [backup-simplify]: Simplify (- 0) into 0 13.325 * [backup-simplify]: Simplify (+ 0 0) into 0 13.325 * [backup-simplify]: Simplify 0 into 0 13.327 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.329 * [backup-simplify]: Simplify (+ (* 1/2 PI) (* 0 0)) into (* 1/2 PI) 13.330 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 (asin (/ 1 a)))) into (asin (/ 1 a)) 13.330 * [backup-simplify]: Simplify (- (asin (/ 1 a))) into (- (asin (/ 1 a))) 13.330 * [backup-simplify]: Simplify (+ (* 1/2 PI) (- (asin (/ 1 a)))) into (- (* 1/2 PI) (asin (/ 1 a))) 13.331 * [backup-simplify]: Simplify (- (* 1/2 PI) (asin (/ 1 a))) into (- (* 1/2 PI) (asin (/ 1 a))) 13.333 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.334 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 PI) (* 0 0))) into 0 13.335 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (asin (/ 1 a))))) into 0 13.336 * [backup-simplify]: Simplify (- 0) into 0 13.336 * [backup-simplify]: Simplify (+ 0 0) into 0 13.336 * [backup-simplify]: Simplify 0 into 0 13.337 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.339 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.340 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (asin (/ 1 a)))))) into 0 13.341 * [backup-simplify]: Simplify (- 0) into 0 13.341 * [backup-simplify]: Simplify (+ 0 0) into 0 13.341 * [backup-simplify]: Simplify 0 into 0 13.343 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.344 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 13.346 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (asin (/ 1 a))))))) into 0 13.347 * [backup-simplify]: Simplify (- 0) into 0 13.347 * [backup-simplify]: Simplify (+ 0 0) into 0 13.347 * [backup-simplify]: Simplify 0 into 0 13.348 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.349 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 13.351 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (asin (/ 1 a)))))))) into 0 13.351 * [backup-simplify]: Simplify (- 0) into 0 13.351 * [backup-simplify]: Simplify (+ 0 0) into 0 13.351 * [backup-simplify]: Simplify 0 into 0 13.353 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.354 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 13.355 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (asin (/ 1 a))))))))) into 0 13.356 * [backup-simplify]: Simplify (- 0) into 0 13.356 * [backup-simplify]: Simplify (+ 0 0) into 0 13.356 * [backup-simplify]: Simplify 0 into 0 13.357 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 13.358 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 13.360 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (asin (/ 1 a)))))))))) into 0 13.360 * [backup-simplify]: Simplify (- 0) into 0 13.361 * [backup-simplify]: Simplify (+ 0 0) into 0 13.361 * [backup-simplify]: Simplify 0 into 0 13.361 * [backup-simplify]: Simplify (* (- (* 1/2 PI) (asin (/ 1 (/ 1 a)))) (/ 1 a)) into (/ (- (* 1/2 PI) (asin a)) a) 13.362 * [backup-simplify]: Simplify (- (/ (/ PI 2) (/ 1 (- a))) (/ (asin (/ 1 (- a))) (/ 1 (- a)))) into (- (* a (asin (/ -1 a))) (* 1/2 (* a PI))) 13.362 * [approximate]: Taking taylor expansion of (- (* a (asin (/ -1 a))) (* 1/2 (* a PI))) in (a) around 0 13.362 * [taylor]: Taking taylor expansion of (- (* a (asin (/ -1 a))) (* 1/2 (* a PI))) in a 13.362 * [taylor]: Taking taylor expansion of (* a (asin (/ -1 a))) in a 13.362 * [taylor]: Taking taylor expansion of a in a 13.362 * [backup-simplify]: Simplify 0 into 0 13.362 * [backup-simplify]: Simplify 1 into 1 13.362 * [taylor]: Taking taylor expansion of (asin (/ -1 a)) in a 13.362 * [backup-simplify]: Simplify (asin (/ -1 a)) into (asin (/ -1 a)) 13.362 * [taylor]: Taking taylor expansion of (* 1/2 (* a PI)) in a 13.362 * [taylor]: Taking taylor expansion of 1/2 in a 13.362 * [backup-simplify]: Simplify 1/2 into 1/2 13.362 * [taylor]: Taking taylor expansion of (* a PI) in a 13.362 * [taylor]: Taking taylor expansion of a in a 13.362 * [backup-simplify]: Simplify 0 into 0 13.362 * [backup-simplify]: Simplify 1 into 1 13.362 * [taylor]: Taking taylor expansion of PI in a 13.362 * [backup-simplify]: Simplify PI into PI 13.362 * [taylor]: Taking taylor expansion of (- (* a (asin (/ -1 a))) (* 1/2 (* a PI))) in a 13.362 * [taylor]: Taking taylor expansion of (* a (asin (/ -1 a))) in a 13.362 * [taylor]: Taking taylor expansion of a in a 13.362 * [backup-simplify]: Simplify 0 into 0 13.362 * [backup-simplify]: Simplify 1 into 1 13.362 * [taylor]: Taking taylor expansion of (asin (/ -1 a)) in a 13.362 * [backup-simplify]: Simplify (asin (/ -1 a)) into (asin (/ -1 a)) 13.362 * [taylor]: Taking taylor expansion of (* 1/2 (* a PI)) in a 13.362 * [taylor]: Taking taylor expansion of 1/2 in a 13.362 * [backup-simplify]: Simplify 1/2 into 1/2 13.362 * [taylor]: Taking taylor expansion of (* a PI) in a 13.362 * [taylor]: Taking taylor expansion of a in a 13.362 * [backup-simplify]: Simplify 0 into 0 13.362 * [backup-simplify]: Simplify 1 into 1 13.362 * [taylor]: Taking taylor expansion of PI in a 13.362 * [backup-simplify]: Simplify PI into PI 13.362 * [backup-simplify]: Simplify (* 0 (asin (/ -1 a))) into 0 13.363 * [backup-simplify]: Simplify (* 0 PI) into 0 13.363 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.363 * [backup-simplify]: Simplify (- 0) into 0 13.364 * [backup-simplify]: Simplify (+ 0 0) into 0 13.364 * [backup-simplify]: Simplify 0 into 0 13.364 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 (asin (/ -1 a)))) into (asin (/ -1 a)) 13.365 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.366 * [backup-simplify]: Simplify (+ (* 1/2 PI) (* 0 0)) into (* 1/2 PI) 13.367 * [backup-simplify]: Simplify (- (* 1/2 PI)) into (- (* 1/2 PI)) 13.368 * [backup-simplify]: Simplify (+ (asin (/ -1 a)) (- (* 1/2 PI))) into (- (asin (/ -1 a)) (* 1/2 PI)) 13.368 * [backup-simplify]: Simplify (- (asin (/ -1 a)) (* 1/2 PI)) into (- (asin (/ -1 a)) (* 1/2 PI)) 13.369 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (asin (/ -1 a))))) into 0 13.369 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.370 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 PI) (* 0 0))) into 0 13.370 * [backup-simplify]: Simplify (- 0) into 0 13.370 * [backup-simplify]: Simplify (+ 0 0) into 0 13.370 * [backup-simplify]: Simplify 0 into 0 13.371 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (asin (/ -1 a)))))) into 0 13.372 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.373 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.373 * [backup-simplify]: Simplify (- 0) into 0 13.373 * [backup-simplify]: Simplify (+ 0 0) into 0 13.373 * [backup-simplify]: Simplify 0 into 0 13.374 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (asin (/ -1 a))))))) into 0 13.375 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.376 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 13.377 * [backup-simplify]: Simplify (- 0) into 0 13.377 * [backup-simplify]: Simplify (+ 0 0) into 0 13.377 * [backup-simplify]: Simplify 0 into 0 13.378 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (asin (/ -1 a)))))))) into 0 13.379 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.380 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 13.381 * [backup-simplify]: Simplify (- 0) into 0 13.381 * [backup-simplify]: Simplify (+ 0 0) into 0 13.381 * [backup-simplify]: Simplify 0 into 0 13.383 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (asin (/ -1 a))))))))) into 0 13.385 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.387 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 13.388 * [backup-simplify]: Simplify (- 0) into 0 13.388 * [backup-simplify]: Simplify (+ 0 0) into 0 13.389 * [backup-simplify]: Simplify 0 into 0 13.391 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (asin (/ -1 a)))))))))) into 0 13.393 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 13.395 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 13.396 * [backup-simplify]: Simplify (- 0) into 0 13.396 * [backup-simplify]: Simplify (+ 0 0) into 0 13.396 * [backup-simplify]: Simplify 0 into 0 13.397 * [backup-simplify]: Simplify (* (- (asin (/ -1 (/ 1 (- a)))) (* 1/2 PI)) (/ 1 (- a))) into (* -1 (/ (- (asin a) (* 1/2 PI)) a)) 13.397 * * * [progress]: simplifying candidates 13.445 * [simplify]: Simplifying: (expm1 (/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))) (log1p (/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))) (- 1) (- (log (- (- (/ (/ PI 2) a) (/ (asin a) a))))) (- 0 (log (- (- (/ (/ PI 2) a) (/ (asin a) a))))) (- (log 1) (log (- (- (/ (/ PI 2) a) (/ (asin a) a))))) (log (/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))) (exp (/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))) (/ (* (* 1 1) 1) (* (* (- (- (/ (/ PI 2) a) (/ (asin a) a))) (- (- (/ (/ PI 2) a) (/ (asin a) a)))) (- (- (/ (/ PI 2) a) (/ (asin a) a))))) (* (cbrt (/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))) (cbrt (/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a)))))) (cbrt (/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))) (* (* (/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a)))) (/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))) (/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))) (sqrt (/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))) (sqrt (/ 1 (- (- (/ (/ PI 2) a) (/ (asin a) a))))) (- 1) (- (- (- (/ (/ PI 2) a) (/ (asin a) a)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (- (- (/ (/ PI 2) a) (/ (asin a) a)))) (cbrt (- (- (/ (/ PI 2) a) (/ (asin a) a)))))) (/ (cbrt 1) (cbrt (- (- (/ (/ PI 2) a) (/ (asin a) a))))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (- (- (/ (/ PI 2) a) (/ (asin a) a))))) (/ (cbrt 1) (sqrt (- (- (/ (/ PI 2) a) (/ (asin a) a))))) (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (- (- (/ (/ PI 2) a) (/ (asin a) a)))) (/ (* (cbrt 1) (cbrt 1)) -1) (/ (cbrt 1) (- (/ (/ PI 2) a) (/ (asin a) a))) (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (- (/ (/ PI 2) a) (/ (asin a) a))) (cbrt (- (/ (/ PI 2) a) (/ (asin a) a)))))) (/ (cbrt 1) (cbrt (- (/ (/ PI 2) a) (/ (asin a) a)))) (/ (* (cbrt 1) (cbrt 1)) (- (sqrt (- (/ (/ PI 2) a) (/ (asin a) a))))) (/ (cbrt 1) (sqrt (- (/ (/ PI 2) a) (/ 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(sqrt a))) (+ (/ (/ (sqrt PI) (sqrt 2)) (sqrt a)) (sqrt (/ (asin a) a))) (- (/ (/ (sqrt PI) (sqrt 2)) (sqrt a)) (sqrt (/ (asin a) a))) (+ (/ (/ (sqrt PI) (sqrt 2)) (sqrt a)) (/ (sqrt (asin a)) (sqrt a))) (- (/ (/ (sqrt PI) (sqrt 2)) (sqrt a)) (/ (sqrt (asin a)) (sqrt a))) (- (/ (/ PI 2) (cbrt a)) (/ (asin a) (cbrt a))) (- (/ (/ PI 2) (sqrt a)) (/ (asin a) (sqrt a))) (- (/ (/ PI 2) a) (/ (asin a) a)) (- (/ (/ PI 2) a) (/ (asin a) a)) (- (/ PI 2) (asin a)) (- (/ (/ PI 2) a) (/ (/ PI 2) a)) (- (/ (asin a) a)) (/ a (- (asin a) (* 1/2 PI))) (/ a (- (asin a) (* 1/2 PI))) (* -1 (/ a (- (* 1/2 PI) (asin a)))) (* 1/2 (/ PI a)) (* 1/2 (/ PI a)) (* 1/2 (/ PI a)) (/ (- (* 1/2 PI) (asin a)) a) (/ (- (* 1/2 PI) (asin a)) a) (* -1 (/ (- (asin a) (* 1/2 PI)) a)) 13.546 * * [simplify]: Extracting # 0 : cost 0 13.551 * * [simplify]: Extracting # 1 : cost 0 13.556 * * [simplify]: Extracting # 2 : cost 0 13.562 * * [simplify]: Extracting # 3 : cost 0 13.573 * * [simplify]: Extracting # 4 : cost 0 13.576 * * [simplify]: Extracting # 5 : cost 0 13.578 * * [simplify]: Extracting # 6 : cost 0 13.581 * * [simplify]: Extracting # 7 : cost 0 13.584 * * [simplify]: Extracting # 8 : cost 0 13.587 * * [simplify]: iteration 0 : 1053 enodes (cost 36471 ) 14.074 * * [simplify]: Extracting # 0 : cost 0 14.082 * * [simplify]: Extracting # 1 : cost 0 14.085 * * [simplify]: Extracting # 2 : cost 0 14.089 * * [simplify]: Extracting # 3 : cost 0 14.096 * * [simplify]: Extracting # 4 : cost 0 14.100 * * [simplify]: iteration 1 : 2133 enodes (cost 31850 ) 15.042 * * [simplify]: Extracting # 0 : cost 0 15.050 * * [simplify]: Extracting # 1 : cost 0 15.059 * * [simplify]: Extracting # 2 : cost 0 15.067 * * [simplify]: Extracting # 3 : cost 0 15.076 * * [simplify]: Extracting # 4 : cost 0 15.087 * * [simplify]: iteration 2 : 4149 enodes (cost 24003 ) 16.379 * * [simplify]: Extracting # 0 : cost 0 16.390 * * [simplify]: Extracting # 1 : cost 0 16.401 * * [simplify]: Extracting # 2 : cost 0 16.409 * * 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(/ (pow (cbrt (asin a)) 3) (sqrt a)) (sqrt a)) (/ (- (/ (pow (cbrt (asin a)) 3) (sqrt a))) (sqrt a))) (fma (/ PI 2) (/ 1 a) (- (/ (pow (cbrt (asin a)) 3) a))) (+ (- (/ (pow (cbrt (asin a)) 3) a)) (/ (pow (cbrt (asin a)) 3) a)) (- (* (/ PI 2) (/ 1 a)) (/ (/ (asin a) (cbrt a)) (* (cbrt a) (cbrt a)))) (* (/ 1 (* (cbrt a) (cbrt a))) (+ (- (/ (asin a) (cbrt a))) (/ (asin a) (cbrt a)))) (fma (/ PI 2) (/ 1 a) (/ (- (/ (asin a) (sqrt a))) (sqrt a))) (* (/ (asin a) (sqrt a)) (+ (/ -1 (sqrt a)) (/ 1 (sqrt a)))) (- (* (/ PI 2) (/ 1 a)) (/ (asin a) a)) (* (/ (asin a) a) 0) (- (* (/ PI 2) (/ 1 a)) (/ (/ (asin a) (cbrt a)) (* (cbrt a) (cbrt a)))) (* (/ 1 (* (cbrt a) (cbrt a))) (+ (- (/ (asin a) (cbrt a))) (/ (asin a) (cbrt a)))) (fma (/ PI 2) (/ 1 a) (/ (- (/ (asin a) (sqrt a))) (sqrt a))) (* (/ (asin a) (sqrt a)) (+ (/ -1 (sqrt a)) (/ 1 (sqrt a)))) (- (* (/ PI 2) (/ 1 a)) (/ (asin a) a)) (* (/ (asin a) a) 0) (- (* (/ PI 2) (/ 1 a)) (/ (asin a) a)) (* (/ (asin a) a) 0) (- (* (/ PI 2) (/ 1 a)) (/ (asin a) a)) (* (/ (asin a) a) 0) (expm1 (/ (- (* 1/2 PI) (asin a)) a)) (log1p (/ (- (* 1/2 PI) (asin a)) a)) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (/ (- (asin a)) a) (exp (/ (- (* 1/2 PI) (asin a)) a)) (log (/ (- (* 1/2 PI) (asin a)) a)) (exp (/ (- (* 1/2 PI) (asin a)) a)) (* (cbrt (/ (- (* 1/2 PI) (asin a)) a)) (cbrt (/ (- (* 1/2 PI) (asin a)) a))) (cbrt (/ (- (* 1/2 PI) (asin a)) a)) (pow (/ (- (* 1/2 PI) (asin a)) a) 3) (sqrt (/ (- (* 1/2 PI) (asin a)) a)) (sqrt (/ (- (* 1/2 PI) (asin a)) a)) (- (/ PI 2) (asin a)) (- (* (/ PI 2) a) (* a (asin a))) (* a a) (- (pow (/ (/ PI 2) a) 3) (pow (/ (asin a) a) 3)) (fma (/ (asin a) a) (fma 1/2 (/ PI a) (/ (asin a) a)) (/ (* (/ PI 2) (/ PI 2)) (* a a))) (/ (- (asin a)) a) (* (/ (- (* 1/2 PI) (asin a)) a) (fma 1/2 (/ PI a) (/ (asin a) a))) (fma 1/2 (/ PI a) (/ (asin a) a)) (+ (sqrt (/ (asin a) a)) (sqrt (/ (/ PI 2) a))) (- (sqrt (/ (/ PI 2) a)) (sqrt (/ (asin a) a))) (+ (/ (sqrt (asin a)) (sqrt a)) (sqrt (/ (/ PI 2) a))) (- (sqrt (/ (/ PI 2) a)) (/ (sqrt (asin a)) (sqrt a))) (+ (/ (sqrt (/ PI 2)) (sqrt a)) (sqrt (/ (asin a) a))) (- (/ (sqrt (/ PI 2)) (sqrt a)) (sqrt (/ (asin a) a))) (+ (/ (sqrt (asin a)) (sqrt a)) (/ (sqrt (/ PI 2)) (sqrt a))) (- (/ (sqrt (/ PI 2)) (sqrt a)) (/ (sqrt (asin a)) (sqrt a))) (+ (sqrt (/ (asin a) a)) (/ (/ (sqrt PI) (sqrt 2)) (sqrt a))) (- (/ (/ (sqrt PI) (sqrt 2)) (sqrt a)) (sqrt (/ (asin a) a))) (+ (/ (/ (sqrt PI) (sqrt 2)) (sqrt a)) (/ (sqrt (asin a)) (sqrt a))) (- (/ (/ (sqrt PI) (sqrt 2)) (sqrt a)) (/ (sqrt (asin a)) (sqrt a))) (- (/ (/ PI 2) (cbrt a)) (/ (asin a) (cbrt a))) (- (/ (/ PI 2) (sqrt a)) (/ (asin a) (sqrt a))) (/ (- (* 1/2 PI) (asin a)) a) (/ (- (* 1/2 PI) (asin a)) a) (- (/ PI 2) (asin a)) 0 (/ (- (asin a)) a) (/ a (fma -1/2 PI (asin a))) (/ a (fma -1/2 PI (asin a))) (- (/ a (- (* 1/2 PI) (asin a)))) (/ (/ PI 2) a) (/ (/ PI 2) a) (/ (/ PI 2) a) (/ (- (* 1/2 PI) (asin a)) a) (/ (- (* 1/2 PI) (asin a)) a) (- (/ (fma -1/2 PI (asin a)) a)) 16.430 * * * [progress]: adding candidates to table 18.908 * * [progress]: iteration 4 / 4 18.908 * * * [progress]: picking best candidate 18.941 * * * * [pick]: Picked # 18.941 * * * [progress]: localizing error 18.957 * * * [progress]: generating rewritten candidates 18.957 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 19.002 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 19.043 * * * [progress]: generating series expansions 19.043 * * * * [progress]: [ 1 / 2 ] generating series at (2) 19.043 * [backup-simplify]: Simplify (/ (/ 1 (acos a)) (- (/ 1 a))) into (* -1 (/ a (acos a))) 19.043 * [approximate]: Taking taylor expansion of (* -1 (/ a (acos a))) in (a) around 0 19.043 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 19.043 * [taylor]: Taking taylor expansion of -1 in a 19.043 * [backup-simplify]: Simplify -1 into -1 19.043 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 19.043 * [taylor]: Taking taylor expansion of a in a 19.043 * [backup-simplify]: Simplify 0 into 0 19.043 * [backup-simplify]: Simplify 1 into 1 19.043 * [taylor]: Taking taylor expansion of (acos a) in a 19.043 * [backup-simplify]: Simplify (acos a) into (acos a) 19.043 * [backup-simplify]: Simplify (/ 1 (acos a)) into (/ 1 (acos a)) 19.044 * [taylor]: Taking taylor expansion of (* -1 (/ a (acos a))) in a 19.044 * [taylor]: Taking taylor expansion of -1 in a 19.044 * [backup-simplify]: Simplify -1 into -1 19.044 * [taylor]: Taking taylor expansion of (/ a (acos a)) in a 19.044 * [taylor]: Taking taylor expansion of a in a 19.044 * [backup-simplify]: Simplify 0 into 0 19.044 * [backup-simplify]: Simplify 1 into 1 19.044 * [taylor]: Taking taylor expansion of (acos a) in a 19.044 * [backup-simplify]: Simplify (acos a) into (acos a) 19.044 * [backup-simplify]: Simplify (/ 1 (acos a)) into (/ 1 (acos a)) 19.044 * [backup-simplify]: Simplify (* -1 (/ 1 (acos a))) into (/ -1 (acos a)) 19.044 * [backup-simplify]: Simplify (/ -1 (acos a)) into (/ -1 (acos a)) 19.044 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))))) into 0 19.045 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 (/ 1 (acos a)))) into 0 19.045 * [backup-simplify]: Simplify 0 into 0 19.045 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 19.046 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 (/ 1 (acos a))))) into 0 19.046 * [backup-simplify]: Simplify 0 into 0 19.046 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 19.047 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 (acos a)))))) into 0 19.047 * [backup-simplify]: Simplify 0 into 0 19.047 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 19.048 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 (acos a))))))) into 0 19.048 * [backup-simplify]: Simplify 0 into 0 19.049 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 19.051 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 (acos a)))))))) into 0 19.051 * [backup-simplify]: Simplify 0 into 0 19.052 * [backup-simplify]: Simplify (- (/ 0 (acos a)) (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 19.055 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 (acos a))))))))) into 0 19.055 * [backup-simplify]: Simplify 0 into 0 19.055 * [backup-simplify]: Simplify (* (/ -1 (acos a)) a) into (* -1 (/ a (acos a))) 19.055 * [backup-simplify]: Simplify (/ (/ 1 (acos (/ 1 a))) (- (/ 1 (/ 1 a)))) into (/ -1 (* (acos (/ 1 a)) a)) 19.055 * [approximate]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in (a) around 0 19.056 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 19.056 * [taylor]: Taking taylor expansion of -1 in a 19.056 * [backup-simplify]: Simplify -1 into -1 19.056 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 19.056 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 19.056 * [backup-simplify]: Simplify (acos (/ 1 a)) into (acos (/ 1 a)) 19.056 * [taylor]: Taking taylor expansion of a in a 19.056 * [backup-simplify]: Simplify 0 into 0 19.056 * [backup-simplify]: Simplify 1 into 1 19.056 * [backup-simplify]: Simplify (* (acos (/ 1 a)) 0) into 0 19.057 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 1) (* 0 0)) into (acos (/ 1 a)) 19.057 * [backup-simplify]: Simplify (/ -1 (acos (/ 1 a))) into (/ -1 (acos (/ 1 a))) 19.057 * [taylor]: Taking taylor expansion of (/ -1 (* (acos (/ 1 a)) a)) in a 19.057 * [taylor]: Taking taylor expansion of -1 in a 19.057 * [backup-simplify]: Simplify -1 into -1 19.057 * [taylor]: Taking taylor expansion of (* (acos (/ 1 a)) a) in a 19.057 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 19.057 * [backup-simplify]: Simplify (acos (/ 1 a)) into (acos (/ 1 a)) 19.057 * [taylor]: Taking taylor expansion of a in a 19.057 * [backup-simplify]: Simplify 0 into 0 19.057 * [backup-simplify]: Simplify 1 into 1 19.057 * [backup-simplify]: Simplify (* (acos (/ 1 a)) 0) into 0 19.058 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 1) (* 0 0)) into (acos (/ 1 a)) 19.059 * [backup-simplify]: Simplify (/ -1 (acos (/ 1 a))) into (/ -1 (acos (/ 1 a))) 19.059 * [backup-simplify]: Simplify (/ -1 (acos (/ 1 a))) into (/ -1 (acos (/ 1 a))) 19.060 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 1) (* 0 0))) into 0 19.060 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))))) into 0 19.060 * [backup-simplify]: Simplify 0 into 0 19.072 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 19.073 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 19.073 * [backup-simplify]: Simplify 0 into 0 19.074 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 19.074 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 19.074 * [backup-simplify]: Simplify 0 into 0 19.075 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))) into 0 19.076 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 19.076 * [backup-simplify]: Simplify 0 into 0 19.077 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))))) into 0 19.077 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 19.077 * [backup-simplify]: Simplify 0 into 0 19.078 * [backup-simplify]: Simplify (+ (* (acos (/ 1 a)) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))))))) into 0 19.079 * [backup-simplify]: Simplify (- (/ 0 (acos (/ 1 a))) (+ (* (/ -1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 19.079 * [backup-simplify]: Simplify 0 into 0 19.079 * [backup-simplify]: Simplify (* (/ -1 (acos (/ 1 (/ 1 a)))) (/ 1 (/ 1 a))) into (* -1 (/ a (acos a))) 19.079 * [backup-simplify]: Simplify (/ (/ 1 (acos (/ 1 (- a)))) (- (/ 1 (/ 1 (- a))))) into (/ 1 (* a (acos (/ -1 a)))) 19.079 * [approximate]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in (a) around 0 19.079 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 19.079 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 19.079 * [taylor]: Taking taylor expansion of a in a 19.079 * [backup-simplify]: Simplify 0 into 0 19.079 * [backup-simplify]: Simplify 1 into 1 19.079 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 19.079 * [backup-simplify]: Simplify (acos (/ -1 a)) into (acos (/ -1 a)) 19.079 * [backup-simplify]: Simplify (* 0 (acos (/ -1 a))) into 0 19.080 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 (acos (/ -1 a)))) into (acos (/ -1 a)) 19.080 * [backup-simplify]: Simplify (/ 1 (acos (/ -1 a))) into (/ 1 (acos (/ -1 a))) 19.080 * [taylor]: Taking taylor expansion of (/ 1 (* a (acos (/ -1 a)))) in a 19.080 * [taylor]: Taking taylor expansion of (* a (acos (/ -1 a))) in a 19.080 * [taylor]: Taking taylor expansion of a in a 19.080 * [backup-simplify]: Simplify 0 into 0 19.080 * [backup-simplify]: Simplify 1 into 1 19.080 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 19.080 * [backup-simplify]: Simplify (acos (/ -1 a)) into (acos (/ -1 a)) 19.080 * [backup-simplify]: Simplify (* 0 (acos (/ -1 a))) into 0 19.081 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 (acos (/ -1 a)))) into (acos (/ -1 a)) 19.081 * [backup-simplify]: Simplify (/ 1 (acos (/ -1 a))) into (/ 1 (acos (/ -1 a))) 19.081 * [backup-simplify]: Simplify (/ 1 (acos (/ -1 a))) into (/ 1 (acos (/ -1 a))) 19.081 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 (acos (/ -1 a))))) into 0 19.082 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))))) into 0 19.082 * [backup-simplify]: Simplify 0 into 0 19.082 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 (acos (/ -1 a)))))) into 0 19.083 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 19.083 * [backup-simplify]: Simplify 0 into 0 19.084 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 (acos (/ -1 a))))))) into 0 19.084 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 19.084 * [backup-simplify]: Simplify 0 into 0 19.085 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (acos (/ -1 a)))))))) into 0 19.086 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 19.086 * [backup-simplify]: Simplify 0 into 0 19.087 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (acos (/ -1 a))))))))) into 0 19.088 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 19.088 * [backup-simplify]: Simplify 0 into 0 19.089 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (acos (/ -1 a)))))))))) into 0 19.090 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 19.090 * [backup-simplify]: Simplify 0 into 0 19.090 * [backup-simplify]: Simplify (* (/ 1 (acos (/ -1 (/ 1 (- a))))) (/ 1 (/ 1 (- a)))) into (* -1 (/ a (acos a))) 19.090 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 19.090 * [backup-simplify]: Simplify (/ 1 (acos a)) into (/ 1 (acos a)) 19.090 * [approximate]: Taking taylor expansion of (/ 1 (acos a)) in (a) around 0 19.090 * [taylor]: Taking taylor expansion of (/ 1 (acos a)) in a 19.090 * [taylor]: Taking taylor expansion of (acos a) in a 19.090 * [backup-simplify]: Simplify (acos a) into (acos a) 19.090 * [backup-simplify]: Simplify (/ 1 (acos a)) into (/ 1 (acos a)) 19.090 * [taylor]: Taking taylor expansion of (/ 1 (acos a)) in a 19.090 * [taylor]: Taking taylor expansion of (acos a) in a 19.090 * [backup-simplify]: Simplify (acos a) into (acos a) 19.090 * [backup-simplify]: Simplify (/ 1 (acos a)) into (/ 1 (acos a)) 19.091 * [backup-simplify]: Simplify (/ 1 (acos a)) into (/ 1 (acos a)) 19.091 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos a)) (/ 0 (acos a))))) into 0 19.091 * [backup-simplify]: Simplify 0 into 0 19.091 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 19.091 * [backup-simplify]: Simplify 0 into 0 19.091 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 19.091 * [backup-simplify]: Simplify 0 into 0 19.091 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 19.091 * [backup-simplify]: Simplify 0 into 0 19.092 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 19.092 * [backup-simplify]: Simplify 0 into 0 19.092 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos a)) (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))) (* 0 (/ 0 (acos a))))) into 0 19.092 * [backup-simplify]: Simplify 0 into 0 19.092 * [backup-simplify]: Simplify (/ 1 (acos a)) into (/ 1 (acos a)) 19.092 * [backup-simplify]: Simplify (/ 1 (acos (/ 1 a))) into (/ 1 (acos (/ 1 a))) 19.092 * [approximate]: Taking taylor expansion of (/ 1 (acos (/ 1 a))) in (a) around 0 19.092 * [taylor]: Taking taylor expansion of (/ 1 (acos (/ 1 a))) in a 19.092 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 19.092 * [backup-simplify]: Simplify (acos (/ 1 a)) into (acos (/ 1 a)) 19.092 * [backup-simplify]: Simplify (/ 1 (acos (/ 1 a))) into (/ 1 (acos (/ 1 a))) 19.092 * [taylor]: Taking taylor expansion of (/ 1 (acos (/ 1 a))) in a 19.092 * [taylor]: Taking taylor expansion of (acos (/ 1 a)) in a 19.093 * [backup-simplify]: Simplify (acos (/ 1 a)) into (acos (/ 1 a)) 19.093 * [backup-simplify]: Simplify (/ 1 (acos (/ 1 a))) into (/ 1 (acos (/ 1 a))) 19.093 * [backup-simplify]: Simplify (/ 1 (acos (/ 1 a))) into (/ 1 (acos (/ 1 a))) 19.093 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))))) into 0 19.093 * [backup-simplify]: Simplify 0 into 0 19.093 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 19.093 * [backup-simplify]: Simplify 0 into 0 19.093 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 19.093 * [backup-simplify]: Simplify 0 into 0 19.094 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 19.094 * [backup-simplify]: Simplify 0 into 0 19.094 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 19.094 * [backup-simplify]: Simplify 0 into 0 19.095 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ 1 a))) (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))) (* 0 (/ 0 (acos (/ 1 a)))))) into 0 19.095 * [backup-simplify]: Simplify 0 into 0 19.095 * [backup-simplify]: Simplify (/ 1 (acos (/ 1 (/ 1 a)))) into (/ 1 (acos a)) 19.095 * [backup-simplify]: Simplify (/ 1 (acos (/ 1 (- a)))) into (/ 1 (acos (/ -1 a))) 19.095 * [approximate]: Taking taylor expansion of (/ 1 (acos (/ -1 a))) in (a) around 0 19.095 * [taylor]: Taking taylor expansion of (/ 1 (acos (/ -1 a))) in a 19.095 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 19.095 * [backup-simplify]: Simplify (acos (/ -1 a)) into (acos (/ -1 a)) 19.095 * [backup-simplify]: Simplify (/ 1 (acos (/ -1 a))) into (/ 1 (acos (/ -1 a))) 19.095 * [taylor]: Taking taylor expansion of (/ 1 (acos (/ -1 a))) in a 19.095 * [taylor]: Taking taylor expansion of (acos (/ -1 a)) in a 19.095 * [backup-simplify]: Simplify (acos (/ -1 a)) into (acos (/ -1 a)) 19.095 * [backup-simplify]: Simplify (/ 1 (acos (/ -1 a))) into (/ 1 (acos (/ -1 a))) 19.095 * [backup-simplify]: Simplify (/ 1 (acos (/ -1 a))) into (/ 1 (acos (/ -1 a))) 19.095 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))))) into 0 19.095 * [backup-simplify]: Simplify 0 into 0 19.096 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 19.096 * [backup-simplify]: Simplify 0 into 0 19.096 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 19.096 * [backup-simplify]: Simplify 0 into 0 19.096 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 19.096 * [backup-simplify]: Simplify 0 into 0 19.097 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 19.097 * [backup-simplify]: Simplify 0 into 0 19.097 * [backup-simplify]: Simplify (- (+ (* (/ 1 (acos (/ -1 a))) (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))) (* 0 (/ 0 (acos (/ -1 a)))))) into 0 19.097 * [backup-simplify]: Simplify 0 into 0 19.097 * [backup-simplify]: Simplify (/ 1 (acos (/ -1 (/ 1 (- a))))) into (/ 1 (acos a)) 19.098 * * * 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# 5 : cost 0 19.142 * * [simplify]: Extracting # 6 : cost 0 19.154 * * [simplify]: iteration 0 : 713 enodes (cost 10319 ) 19.854 * * [simplify]: Extracting # 0 : cost 0 19.857 * * [simplify]: Extracting # 1 : cost 0 19.858 * * [simplify]: Extracting # 2 : cost 0 19.859 * * [simplify]: Extracting # 3 : cost 0 19.861 * * [simplify]: iteration 1 : 1737 enodes (cost 7603 ) 20.185 * * [simplify]: Extracting # 0 : cost 0 20.187 * * [simplify]: Extracting # 1 : cost 0 20.189 * * [simplify]: Extracting # 2 : cost 0 20.191 * * [simplify]: Extracting # 3 : cost 0 20.193 * * [simplify]: Extracting # 4 : cost 0 20.195 * * [simplify]: iteration 2 : 2640 enodes (cost 6678 ) 21.064 * * [simplify]: Extracting # 0 : cost 0 21.072 * * [simplify]: Extracting # 1 : cost 0 21.076 * * [simplify]: Extracting # 2 : cost 0 21.080 * * [simplify]: Extracting # 3 : cost 0 21.084 * * [simplify]: Extracting # 4 : cost 0 21.093 * * [simplify]: Extracting # 5 : cost 0 21.098 * * [simplify]: iteration done: 5000 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(- a) (acos a)) (/ (- a) (acos a)) (/ (- a) (acos a)) (/ 1 (acos a)) (/ 1 (acos a)) (/ 1 (acos a)) 21.106 * * * [progress]: adding candidates to table 21.594 * [progress]: [Phase 3 of 3] Extracting. 21.594 * * [regime]: Finding splitpoints for: (# # # # # #) 21.596 * * * [regime-changes]: Trying 2 branch expressions: ((/ a (- (acos a))) a) 21.596 * * * * [regimes]: Trying to branch on (/ a (- (acos a))) from (# # # # # #) 21.629 * * * * [regimes]: Trying to branch on a from (# # # # # #) 21.659 * * * [regime]: Found split indices: #