0.009 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.438 * * * [progress]: [2/2] Setting up program. 0.442 * [progress]: [Phase 2 of 3] Improving. 0.442 * [simplify]: Simplifying using # : (fabs (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) 0.444 * * [simplify]: iteration 0 : 8 enodes (cost 7 ) 0.444 * [simplify]: Simplified to: (fabs (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) 0.445 * * [progress]: iteration 1 / 4 0.445 * * * [progress]: picking best candidate 0.448 * * * * [pick]: Picked # 0.448 * * * [progress]: localizing error 0.460 * * * [progress]: generating rewritten candidates 0.460 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1) 0.460 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1 1) 0.462 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 1) 0.463 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 0.464 * * * [progress]: generating series expansions 0.464 * * * * [progress]: [ 1 / 4 ] generating series at (2 1) 0.464 * [approximate]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) in (a) around 0 0.464 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) in a 0.464 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) in a 0.465 * [approximate]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) (/ 1 a)) in (a) around 0 0.465 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) (/ 1 a)) in a 0.465 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) (/ 1 a)) in a 0.465 * [approximate]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) (/ -1 a)) in (a) around 0 0.466 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) (/ -1 a)) in a 0.466 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) (/ -1 a)) in a 0.466 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1 1) 0.466 * [approximate]: Taking taylor expansion of (sin (expm1 a)) in (a) around 0 0.466 * [taylor]: Taking taylor expansion of (sin (expm1 a)) in a 0.466 * [taylor]: Taking taylor expansion of (expm1 a) in a 0.466 * [taylor]: Rewrote expression to (- (exp a) 1) 0.466 * [taylor]: Taking taylor expansion of (exp a) in a 0.466 * [taylor]: Taking taylor expansion of a in a 0.466 * [taylor]: Taking taylor expansion of 1 in a 0.468 * [taylor]: Taking taylor expansion of (sin (expm1 a)) in a 0.468 * [taylor]: Taking taylor expansion of (expm1 a) in a 0.468 * [taylor]: Rewrote expression to (- (exp a) 1) 0.468 * [taylor]: Taking taylor expansion of (exp a) in a 0.468 * [taylor]: Taking taylor expansion of a in a 0.468 * [taylor]: Taking taylor expansion of 1 in a 0.479 * [approximate]: Taking taylor expansion of (sin (expm1 (/ 1 a))) in (a) around 0 0.479 * [taylor]: Taking taylor expansion of (sin (expm1 (/ 1 a))) in a 0.479 * [taylor]: Taking taylor expansion of (expm1 (/ 1 a)) in a 0.479 * [taylor]: Rewrote expression to (- (exp (/ 1 a)) 1) 0.479 * [taylor]: Taking taylor expansion of (exp (/ 1 a)) in a 0.479 * [taylor]: Taking taylor expansion of (/ 1 a) in a 0.479 * [taylor]: Taking taylor expansion of a in a 0.479 * [taylor]: Taking taylor expansion of 1 in a 0.480 * [taylor]: Taking taylor expansion of (sin (expm1 (/ 1 a))) in a 0.480 * [taylor]: Taking taylor expansion of (expm1 (/ 1 a)) in a 0.480 * [taylor]: Rewrote expression to (- (exp (/ 1 a)) 1) 0.480 * [taylor]: Taking taylor expansion of (exp (/ 1 a)) in a 0.480 * [taylor]: Taking taylor expansion of (/ 1 a) in a 0.480 * [taylor]: Taking taylor expansion of a in a 0.480 * [taylor]: Taking taylor expansion of 1 in a 0.507 * [approximate]: Taking taylor expansion of (sin (expm1 (/ -1 a))) in (a) around 0 0.507 * [taylor]: Taking taylor expansion of (sin (expm1 (/ -1 a))) in a 0.507 * [taylor]: Taking taylor expansion of (expm1 (/ -1 a)) in a 0.507 * [taylor]: Rewrote expression to (- (exp (/ -1 a)) 1) 0.507 * [taylor]: Taking taylor expansion of (exp (/ -1 a)) in a 0.508 * [taylor]: Taking taylor expansion of (/ -1 a) in a 0.508 * [taylor]: Taking taylor expansion of -1 in a 0.508 * [taylor]: Taking taylor expansion of a in a 0.508 * [taylor]: Taking taylor expansion of 1 in a 0.508 * [taylor]: Taking taylor expansion of (sin (expm1 (/ -1 a))) in a 0.508 * [taylor]: Taking taylor expansion of (expm1 (/ -1 a)) in a 0.508 * [taylor]: Rewrote expression to (- (exp (/ -1 a)) 1) 0.508 * [taylor]: Taking taylor expansion of (exp (/ -1 a)) in a 0.508 * [taylor]: Taking taylor expansion of (/ -1 a) in a 0.508 * [taylor]: Taking taylor expansion of -1 in a 0.508 * [taylor]: Taking taylor expansion of a in a 0.509 * [taylor]: Taking taylor expansion of 1 in a 0.530 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 1) 0.530 * [approximate]: Taking taylor expansion of (expm1 (sin (expm1 a))) in (a) around 0 0.530 * [taylor]: Taking taylor expansion of (expm1 (sin (expm1 a))) in a 0.530 * [taylor]: Rewrote expression to (- (exp (sin (expm1 a))) 1) 0.530 * [taylor]: Taking taylor expansion of (exp (sin (expm1 a))) in a 0.530 * [taylor]: Taking taylor expansion of (sin (expm1 a)) in a 0.530 * [taylor]: Taking taylor expansion of (expm1 a) in a 0.531 * [taylor]: Rewrote expression to (- (exp a) 1) 0.531 * [taylor]: Taking taylor expansion of (exp a) in a 0.531 * [taylor]: Taking taylor expansion of a in a 0.531 * [taylor]: Taking taylor expansion of 1 in a 0.533 * [taylor]: Taking taylor expansion of 1 in a 0.533 * [taylor]: Taking taylor expansion of (expm1 (sin (expm1 a))) in a 0.533 * [taylor]: Rewrote expression to (- (exp (sin (expm1 a))) 1) 0.533 * [taylor]: Taking taylor expansion of (exp (sin (expm1 a))) in a 0.533 * [taylor]: Taking taylor expansion of (sin (expm1 a)) in a 0.533 * [taylor]: Taking taylor expansion of (expm1 a) in a 0.533 * [taylor]: Rewrote expression to (- (exp a) 1) 0.533 * [taylor]: Taking taylor expansion of (exp a) in a 0.533 * [taylor]: Taking taylor expansion of a in a 0.533 * [taylor]: Taking taylor expansion of 1 in a 0.535 * [taylor]: Taking taylor expansion of 1 in a 0.544 * [approximate]: Taking taylor expansion of (expm1 (sin (expm1 (/ 1 a)))) in (a) around 0 0.545 * [taylor]: Taking taylor expansion of (expm1 (sin (expm1 (/ 1 a)))) in a 0.545 * [taylor]: Rewrote expression to (- (exp (sin (expm1 (/ 1 a)))) 1) 0.545 * [taylor]: Taking taylor expansion of (exp (sin (expm1 (/ 1 a)))) in a 0.545 * [taylor]: Taking taylor expansion of (sin (expm1 (/ 1 a))) in a 0.545 * [taylor]: Taking taylor expansion of (expm1 (/ 1 a)) in a 0.545 * [taylor]: Rewrote expression to (- (exp (/ 1 a)) 1) 0.545 * [taylor]: Taking taylor expansion of (exp (/ 1 a)) in a 0.545 * [taylor]: Taking taylor expansion of (/ 1 a) in a 0.545 * [taylor]: Taking taylor expansion of a in a 0.545 * [taylor]: Taking taylor expansion of 1 in a 0.546 * [taylor]: Taking taylor expansion of 1 in a 0.546 * [taylor]: Taking taylor expansion of (expm1 (sin (expm1 (/ 1 a)))) in a 0.546 * [taylor]: Rewrote expression to (- (exp (sin (expm1 (/ 1 a)))) 1) 0.546 * [taylor]: Taking taylor expansion of (exp (sin (expm1 (/ 1 a)))) in a 0.546 * [taylor]: Taking taylor expansion of (sin (expm1 (/ 1 a))) in a 0.546 * [taylor]: Taking taylor expansion of (expm1 (/ 1 a)) in a 0.546 * [taylor]: Rewrote expression to (- (exp (/ 1 a)) 1) 0.546 * [taylor]: Taking taylor expansion of (exp (/ 1 a)) in a 0.546 * [taylor]: Taking taylor expansion of (/ 1 a) in a 0.546 * [taylor]: Taking taylor expansion of a in a 0.546 * [taylor]: Taking taylor expansion of 1 in a 0.547 * [taylor]: Taking taylor expansion of 1 in a 0.585 * [approximate]: Taking taylor expansion of (expm1 (sin (expm1 (/ -1 a)))) in (a) around 0 0.585 * [taylor]: Taking taylor expansion of (expm1 (sin (expm1 (/ -1 a)))) in a 0.585 * [taylor]: Rewrote expression to (- (exp (sin (expm1 (/ -1 a)))) 1) 0.585 * [taylor]: Taking taylor expansion of (exp (sin (expm1 (/ -1 a)))) in a 0.585 * [taylor]: Taking taylor expansion of (sin (expm1 (/ -1 a))) in a 0.585 * [taylor]: Taking taylor expansion of (expm1 (/ -1 a)) in a 0.586 * [taylor]: Rewrote expression to (- (exp (/ -1 a)) 1) 0.586 * [taylor]: Taking taylor expansion of (exp (/ -1 a)) in a 0.586 * [taylor]: Taking taylor expansion of (/ -1 a) in a 0.586 * [taylor]: Taking taylor expansion of -1 in a 0.586 * [taylor]: Taking taylor expansion of a in a 0.586 * [taylor]: Taking taylor expansion of 1 in a 0.587 * [taylor]: Taking taylor expansion of 1 in a 0.587 * [taylor]: Taking taylor expansion of (expm1 (sin (expm1 (/ -1 a)))) in a 0.587 * [taylor]: Rewrote expression to (- (exp (sin (expm1 (/ -1 a)))) 1) 0.587 * [taylor]: Taking taylor expansion of (exp (sin (expm1 (/ -1 a)))) in a 0.587 * [taylor]: Taking taylor expansion of (sin (expm1 (/ -1 a))) in a 0.587 * [taylor]: Taking taylor expansion of (expm1 (/ -1 a)) in a 0.587 * [taylor]: Rewrote expression to (- (exp (/ -1 a)) 1) 0.587 * [taylor]: Taking taylor expansion of (exp (/ -1 a)) in a 0.587 * [taylor]: Taking taylor expansion of (/ -1 a) in a 0.587 * [taylor]: Taking taylor expansion of -1 in a 0.587 * [taylor]: Taking taylor expansion of a in a 0.587 * [taylor]: Taking taylor expansion of 1 in a 0.588 * [taylor]: Taking taylor expansion of 1 in a 0.620 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 0.620 * [approximate]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 a))) (atan a)) in (a) around 0 0.620 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 a))) (atan a)) in a 0.620 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 a))) (atan a)) in a 0.621 * [approximate]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) in (a) around 0 0.621 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) in a 0.621 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) in a 0.621 * [approximate]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) in (a) around 0 0.621 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) in a 0.622 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) in a 0.622 * * * [progress]: simplifying candidates 0.623 * [simplify]: Simplifying using # : (expm1 (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (log1p (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (log (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (exp (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (* (* (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (sqrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (sqrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (expm1 (sin (expm1 a))) (log1p (sin (expm1 a))) (* (sin (exp a)) (cos 1)) (* (cos (exp a)) (sin 1)) (log (sin (expm1 a))) (exp (sin (expm1 a))) (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))) (* (* (sin (expm1 a)) (sin (expm1 a))) (sin (expm1 a))) (sqrt (sin (expm1 a))) (sqrt (sin (expm1 a))) (exp (sin (expm1 a))) (expm1 (expm1 (sin (expm1 a)))) (log1p (expm1 (sin (expm1 a)))) (log (expm1 (sin (expm1 a)))) (exp (expm1 (sin (expm1 a)))) (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a)))) (* (* (expm1 (sin (expm1 a))) (expm1 (sin (expm1 a)))) (expm1 (sin (expm1 a)))) (sqrt (expm1 (sin (expm1 a)))) (sqrt (expm1 (sin (expm1 a)))) (expm1 (atan2 (expm1 (sin (expm1 a))) (atan a))) (log1p (atan2 (expm1 (sin (expm1 a))) (atan a))) (log (atan2 (expm1 (sin (expm1 a))) (atan a))) (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (* (* (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a))) (sqrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (sqrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (- (+ (* 1/2 (pow a 2)) a) (* 5/24 (pow a 4))) (sin (- (exp a) 1)) (sin (- (exp a) 1)) (+ (* 2/3 (pow a 3)) (+ (pow a 2) a)) (- (exp (sin (- (exp a) 1))) 1) (- (exp (sin (- (exp a) 1))) 1) (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)) 0.626 * * [simplify]: iteration 0 : 108 enodes (cost 302 ) 0.628 * * [simplify]: iteration 1 : 242 enodes (cost 264 ) 0.633 * * [simplify]: iteration 2 : 720 enodes (cost 264 ) 0.648 * * [simplify]: iteration 3 : 2933 enodes (cost 264 ) 0.740 * * [simplify]: iteration 4 : 5001 enodes (cost 264 ) 0.742 * [simplify]: Simplified to: (expm1 (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (log1p (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (log (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (exp (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (* (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))) (cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (pow (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) 3) (sqrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (sqrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)) (expm1 (sin (expm1 a))) (log1p (sin (expm1 a))) (* (sin (exp a)) (cos 1)) (* (cos (exp a)) (sin 1)) (log (sin (expm1 a))) (exp (sin (expm1 a))) (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))) (pow (sin (expm1 a)) 3) (sqrt (sin (expm1 a))) (sqrt (sin (expm1 a))) (exp (sin (expm1 a))) (expm1 (expm1 (sin (expm1 a)))) (sin (expm1 a)) (log (expm1 (sin (expm1 a)))) (exp (expm1 (sin (expm1 a)))) (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a)))) (pow (expm1 (sin (expm1 a))) 3) (sqrt (expm1 (sin (expm1 a)))) (sqrt (expm1 (sin (expm1 a)))) (expm1 (atan2 (expm1 (sin (expm1 a))) (atan a))) (log1p (atan2 (expm1 (sin (expm1 a))) (atan a))) (log (atan2 (expm1 (sin (expm1 a))) (atan a))) (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) (sqrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (sqrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fma (pow a 2) 1/2 (- a (* 5/24 (pow a 4)))) (sin (expm1 a)) (sin (expm1 a)) (fma (pow a 3) 2/3 (fma a a a)) (expm1 (sin (expm1 a))) (expm1 (sin (expm1 a))) (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)) 0.742 * * * [progress]: adding candidates to table 0.903 * * [progress]: iteration 2 / 4 0.903 * * * [progress]: picking best candidate 0.951 * * * * [pick]: Picked # 0.951 * * * [progress]: localizing error 0.970 * * * [progress]: generating rewritten candidates 0.971 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1) 0.971 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1 1 1 1) 0.973 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 1) 0.975 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 0.978 * * * [progress]: generating series expansions 0.978 * * * * [progress]: [ 1 / 4 ] generating series at (2 1) 0.978 * [approximate]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) in (a) around 0 0.978 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) in a 0.978 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) in a 0.978 * [approximate]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) (/ 1 a)) in (a) around 0 0.978 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) (/ 1 a)) in a 0.979 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) (/ 1 a)) in a 0.979 * [approximate]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) (/ -1 a)) in (a) around 0 0.979 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) (/ -1 a)) in a 0.979 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) (/ -1 a)) in a 0.980 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1 1 1 1) 0.980 * [approximate]: Taking taylor expansion of (sin (expm1 a)) in (a) around 0 0.980 * [taylor]: Taking taylor expansion of (sin (expm1 a)) in a 0.980 * [taylor]: Taking taylor expansion of (expm1 a) in a 0.980 * [taylor]: Rewrote expression to (- (exp a) 1) 0.980 * [taylor]: Taking taylor expansion of (exp a) in a 0.980 * [taylor]: Taking taylor expansion of a in a 0.980 * [taylor]: Taking taylor expansion of 1 in a 0.982 * [taylor]: Taking taylor expansion of (sin (expm1 a)) in a 0.982 * [taylor]: Taking taylor expansion of (expm1 a) in a 0.982 * [taylor]: Rewrote expression to (- (exp a) 1) 0.982 * [taylor]: Taking taylor expansion of (exp a) in a 0.982 * [taylor]: Taking taylor expansion of a in a 0.982 * [taylor]: Taking taylor expansion of 1 in a 0.993 * [approximate]: Taking taylor expansion of (sin (expm1 (/ 1 a))) in (a) around 0 0.993 * [taylor]: Taking taylor expansion of (sin (expm1 (/ 1 a))) in a 0.993 * [taylor]: Taking taylor expansion of (expm1 (/ 1 a)) in a 0.993 * [taylor]: Rewrote expression to (- (exp (/ 1 a)) 1) 0.993 * [taylor]: Taking taylor expansion of (exp (/ 1 a)) in a 0.993 * [taylor]: Taking taylor expansion of (/ 1 a) in a 0.993 * [taylor]: Taking taylor expansion of a in a 0.993 * [taylor]: Taking taylor expansion of 1 in a 0.993 * [taylor]: Taking taylor expansion of (sin (expm1 (/ 1 a))) in a 0.993 * [taylor]: Taking taylor expansion of (expm1 (/ 1 a)) in a 0.994 * [taylor]: Rewrote expression to (- (exp (/ 1 a)) 1) 0.994 * [taylor]: Taking taylor expansion of (exp (/ 1 a)) in a 0.994 * [taylor]: Taking taylor expansion of (/ 1 a) in a 0.994 * [taylor]: Taking taylor expansion of a in a 0.994 * [taylor]: Taking taylor expansion of 1 in a 1.016 * [approximate]: Taking taylor expansion of (sin (expm1 (/ -1 a))) in (a) around 0 1.016 * [taylor]: Taking taylor expansion of (sin (expm1 (/ -1 a))) in a 1.016 * [taylor]: Taking taylor expansion of (expm1 (/ -1 a)) in a 1.016 * [taylor]: Rewrote expression to (- (exp (/ -1 a)) 1) 1.016 * [taylor]: Taking taylor expansion of (exp (/ -1 a)) in a 1.016 * [taylor]: Taking taylor expansion of (/ -1 a) in a 1.016 * [taylor]: Taking taylor expansion of -1 in a 1.016 * [taylor]: Taking taylor expansion of a in a 1.016 * [taylor]: Taking taylor expansion of 1 in a 1.017 * [taylor]: Taking taylor expansion of (sin (expm1 (/ -1 a))) in a 1.017 * [taylor]: Taking taylor expansion of (expm1 (/ -1 a)) in a 1.017 * [taylor]: Rewrote expression to (- (exp (/ -1 a)) 1) 1.017 * [taylor]: Taking taylor expansion of (exp (/ -1 a)) in a 1.017 * [taylor]: Taking taylor expansion of (/ -1 a) in a 1.017 * [taylor]: Taking taylor expansion of -1 in a 1.017 * [taylor]: Taking taylor expansion of a in a 1.017 * [taylor]: Taking taylor expansion of 1 in a 1.038 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 1) 1.039 * [approximate]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) in (a) around 0 1.039 * [taylor]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) in a 1.039 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 a))) (atan a)) in a 1.039 * [taylor]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) in a 1.039 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 a))) (atan a)) in a 1.048 * [approximate]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a)))) in (a) around 0 1.048 * [taylor]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a)))) in a 1.053 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) in a 1.054 * [taylor]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a)))) in a 1.054 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) in a 1.063 * [approximate]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a)))) in (a) around 0 1.063 * [taylor]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a)))) in a 1.063 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) in a 1.063 * [taylor]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a)))) in a 1.063 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) in a 1.073 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 1.073 * [approximate]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 a))) (atan a)) in (a) around 0 1.073 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 a))) (atan a)) in a 1.073 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 a))) (atan a)) in a 1.073 * [approximate]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) in (a) around 0 1.073 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) in a 1.074 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) in a 1.074 * [approximate]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) in (a) around 0 1.074 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) in a 1.074 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) in a 1.075 * * * [progress]: simplifying candidates 1.075 * [simplify]: Simplifying using # : (expm1 (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (log1p (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (log (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (exp (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (* (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a))) (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (* (* (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a) (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (sqrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (sqrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (expm1 (sin (expm1 a))) (log1p (sin (expm1 a))) (* (sin (exp a)) (cos 1)) (* (cos (exp a)) (sin 1)) (log (sin (expm1 a))) (exp (sin (expm1 a))) (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))) (* (* (sin (expm1 a)) (sin (expm1 a))) (sin (expm1 a))) (sqrt (sin (expm1 a))) (sqrt (sin (expm1 a))) (expm1 (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (exp (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) (exp (sqrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (exp 1) (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (exp (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (* (cbrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (* (* (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (expm1 (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log1p (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (* (cbrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) (log (cbrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log 1) (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log (exp (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))))) (log (exp (sqrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (exp 1)) (log (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (exp (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (* (cbrt (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) (cbrt (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (* (* (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (sqrt (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (sqrt (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (- (+ (* 1/2 (pow a 2)) a) (* 5/24 (pow a 4))) (sin (- (exp a) 1)) (sin (- (exp a) 1)) (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)) 1.079 * * [simplify]: iteration 0 : 108 enodes (cost 467 ) 1.081 * * [simplify]: iteration 1 : 208 enodes (cost 407 ) 1.084 * * [simplify]: iteration 2 : 487 enodes (cost 407 ) 1.094 * * [simplify]: iteration 3 : 1838 enodes (cost 407 ) 1.151 * * [simplify]: iteration 4 : 5001 enodes (cost 407 ) 1.153 * [simplify]: Simplified to: (expm1 (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (log1p (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (log (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (exp (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (* (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a))) (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (pow (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) 3) (sqrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (sqrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (expm1 (sin (expm1 a))) (log1p (sin (expm1 a))) (* (sin (exp a)) (cos 1)) (* (cos (exp a)) (sin 1)) (log (sin (expm1 a))) (exp (sin (expm1 a))) (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))) (pow (sin (expm1 a)) 3) (sqrt (sin (expm1 a))) (sqrt (sin (expm1 a))) (expm1 (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (exp (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) (exp (sqrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) E (atan2 (expm1 (sin (expm1 a))) (atan a)) (exp (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (* (cbrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 3) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (expm1 (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log1p (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (* 2 (log (cbrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) (log (cbrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) 0 (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)) (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (atan2 (expm1 (sin (expm1 a))) (atan a))) 1 (log (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (pow (atan2 (expm1 (sin (expm1 a))) (atan a)) 3) (sqrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (sqrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fma (pow a 2) 1/2 (- a (* 5/24 (pow a 4)))) (sin (expm1 a)) (sin (expm1 a)) (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)) (atan2 (expm1 (sin (expm1 a))) (atan a)) 1.154 * * * [progress]: adding candidates to table 1.353 * * [progress]: iteration 3 / 4 1.353 * * * [progress]: picking best candidate 1.419 * * * * [pick]: Picked # 1.419 * * * [progress]: localizing error 1.438 * * * [progress]: generating rewritten candidates 1.438 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1) 1.438 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 2 1 1 1 1 1) 1.440 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 1 1 1 1 1 1) 1.442 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 2 1 1) 1.444 * * * [progress]: generating series expansions 1.445 * * * * [progress]: [ 1 / 4 ] generating series at (2 1) 1.445 * [approximate]: Taking taylor expansion of (fmod (* 2 (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a) in (a) around 0 1.445 * [taylor]: Taking taylor expansion of (fmod (* 2 (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a) in a 1.445 * [taylor]: Taking taylor expansion of (fmod (* 2 (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a) in a 1.446 * [approximate]: Taking taylor expansion of (fmod (* 2 (log (sqrt (exp (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))))))) (/ 1 a)) in (a) around 0 1.446 * [taylor]: Taking taylor expansion of (fmod (* 2 (log (sqrt (exp (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))))))) (/ 1 a)) in a 1.446 * [taylor]: Taking taylor expansion of (fmod (* 2 (log (sqrt (exp (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))))))) (/ 1 a)) in a 1.447 * [approximate]: Taking taylor expansion of (fmod (* 2 (log (sqrt (exp (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))))))) (/ -1 a)) in (a) around 0 1.447 * [taylor]: Taking taylor expansion of (fmod (* 2 (log (sqrt (exp (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))))))) (/ -1 a)) in a 1.447 * [taylor]: Taking taylor expansion of (fmod (* 2 (log (sqrt (exp (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))))))) (/ -1 a)) in a 1.448 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 2 1 1 1 1 1) 1.448 * [approximate]: Taking taylor expansion of (sin (expm1 a)) in (a) around 0 1.448 * [taylor]: Taking taylor expansion of (sin (expm1 a)) in a 1.448 * [taylor]: Taking taylor expansion of (expm1 a) in a 1.448 * [taylor]: Rewrote expression to (- (exp a) 1) 1.448 * [taylor]: Taking taylor expansion of (exp a) in a 1.448 * [taylor]: Taking taylor expansion of a in a 1.448 * [taylor]: Taking taylor expansion of 1 in a 1.450 * [taylor]: Taking taylor expansion of (sin (expm1 a)) in a 1.450 * [taylor]: Taking taylor expansion of (expm1 a) in a 1.450 * [taylor]: Rewrote expression to (- (exp a) 1) 1.450 * [taylor]: Taking taylor expansion of (exp a) in a 1.450 * [taylor]: Taking taylor expansion of a in a 1.450 * [taylor]: Taking taylor expansion of 1 in a 1.460 * [approximate]: Taking taylor expansion of (sin (expm1 (/ 1 a))) in (a) around 0 1.460 * [taylor]: Taking taylor expansion of (sin (expm1 (/ 1 a))) in a 1.461 * [taylor]: Taking taylor expansion of (expm1 (/ 1 a)) in a 1.461 * [taylor]: Rewrote expression to (- (exp (/ 1 a)) 1) 1.461 * [taylor]: Taking taylor expansion of (exp (/ 1 a)) in a 1.461 * [taylor]: Taking taylor expansion of (/ 1 a) in a 1.461 * [taylor]: Taking taylor expansion of a in a 1.461 * [taylor]: Taking taylor expansion of 1 in a 1.461 * [taylor]: Taking taylor expansion of (sin (expm1 (/ 1 a))) in a 1.461 * [taylor]: Taking taylor expansion of (expm1 (/ 1 a)) in a 1.461 * [taylor]: Rewrote expression to (- (exp (/ 1 a)) 1) 1.461 * [taylor]: Taking taylor expansion of (exp (/ 1 a)) in a 1.461 * [taylor]: Taking taylor expansion of (/ 1 a) in a 1.461 * [taylor]: Taking taylor expansion of a in a 1.462 * [taylor]: Taking taylor expansion of 1 in a 1.483 * [approximate]: Taking taylor expansion of (sin (expm1 (/ -1 a))) in (a) around 0 1.483 * [taylor]: Taking taylor expansion of (sin (expm1 (/ -1 a))) in a 1.483 * [taylor]: Taking taylor expansion of (expm1 (/ -1 a)) in a 1.483 * [taylor]: Rewrote expression to (- (exp (/ -1 a)) 1) 1.484 * [taylor]: Taking taylor expansion of (exp (/ -1 a)) in a 1.484 * [taylor]: Taking taylor expansion of (/ -1 a) in a 1.484 * [taylor]: Taking taylor expansion of -1 in a 1.484 * [taylor]: Taking taylor expansion of a in a 1.484 * [taylor]: Taking taylor expansion of 1 in a 1.488 * [taylor]: Taking taylor expansion of (sin (expm1 (/ -1 a))) in a 1.488 * [taylor]: Taking taylor expansion of (expm1 (/ -1 a)) in a 1.488 * [taylor]: Rewrote expression to (- (exp (/ -1 a)) 1) 1.488 * [taylor]: Taking taylor expansion of (exp (/ -1 a)) in a 1.488 * [taylor]: Taking taylor expansion of (/ -1 a) in a 1.488 * [taylor]: Taking taylor expansion of -1 in a 1.488 * [taylor]: Taking taylor expansion of a in a 1.489 * [taylor]: Taking taylor expansion of 1 in a 1.510 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 1 1 1 1 1 1) 1.510 * [approximate]: Taking taylor expansion of (sin (expm1 a)) in (a) around 0 1.510 * [taylor]: Taking taylor expansion of (sin (expm1 a)) in a 1.511 * [taylor]: Taking taylor expansion of (expm1 a) in a 1.511 * [taylor]: Rewrote expression to (- (exp a) 1) 1.511 * [taylor]: Taking taylor expansion of (exp a) in a 1.511 * [taylor]: Taking taylor expansion of a in a 1.511 * [taylor]: Taking taylor expansion of 1 in a 1.512 * [taylor]: Taking taylor expansion of (sin (expm1 a)) in a 1.512 * [taylor]: Taking taylor expansion of (expm1 a) in a 1.512 * [taylor]: Rewrote expression to (- (exp a) 1) 1.512 * [taylor]: Taking taylor expansion of (exp a) in a 1.512 * [taylor]: Taking taylor expansion of a in a 1.512 * [taylor]: Taking taylor expansion of 1 in a 1.523 * [approximate]: Taking taylor expansion of (sin (expm1 (/ 1 a))) in (a) around 0 1.523 * [taylor]: Taking taylor expansion of (sin (expm1 (/ 1 a))) in a 1.523 * [taylor]: Taking taylor expansion of (expm1 (/ 1 a)) in a 1.523 * [taylor]: Rewrote expression to (- (exp (/ 1 a)) 1) 1.523 * [taylor]: Taking taylor expansion of (exp (/ 1 a)) in a 1.523 * [taylor]: Taking taylor expansion of (/ 1 a) in a 1.523 * [taylor]: Taking taylor expansion of a in a 1.523 * [taylor]: Taking taylor expansion of 1 in a 1.524 * [taylor]: Taking taylor expansion of (sin (expm1 (/ 1 a))) in a 1.524 * [taylor]: Taking taylor expansion of (expm1 (/ 1 a)) in a 1.524 * [taylor]: Rewrote expression to (- (exp (/ 1 a)) 1) 1.524 * [taylor]: Taking taylor expansion of (exp (/ 1 a)) in a 1.524 * [taylor]: Taking taylor expansion of (/ 1 a) in a 1.524 * [taylor]: Taking taylor expansion of a in a 1.524 * [taylor]: Taking taylor expansion of 1 in a 1.546 * [approximate]: Taking taylor expansion of (sin (expm1 (/ -1 a))) in (a) around 0 1.546 * [taylor]: Taking taylor expansion of (sin (expm1 (/ -1 a))) in a 1.546 * [taylor]: Taking taylor expansion of (expm1 (/ -1 a)) in a 1.546 * [taylor]: Rewrote expression to (- (exp (/ -1 a)) 1) 1.546 * [taylor]: Taking taylor expansion of (exp (/ -1 a)) in a 1.546 * [taylor]: Taking taylor expansion of (/ -1 a) in a 1.546 * [taylor]: Taking taylor expansion of -1 in a 1.546 * [taylor]: Taking taylor expansion of a in a 1.546 * [taylor]: Taking taylor expansion of 1 in a 1.547 * [taylor]: Taking taylor expansion of (sin (expm1 (/ -1 a))) in a 1.547 * [taylor]: Taking taylor expansion of (expm1 (/ -1 a)) in a 1.547 * [taylor]: Rewrote expression to (- (exp (/ -1 a)) 1) 1.547 * [taylor]: Taking taylor expansion of (exp (/ -1 a)) in a 1.547 * [taylor]: Taking taylor expansion of (/ -1 a) in a 1.547 * [taylor]: Taking taylor expansion of -1 in a 1.547 * [taylor]: Taking taylor expansion of a in a 1.547 * [taylor]: Taking taylor expansion of 1 in a 1.574 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 2 1 1) 1.574 * [approximate]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) in (a) around 0 1.574 * [taylor]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) in a 1.574 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 a))) (atan a)) in a 1.574 * [taylor]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) in a 1.574 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 a))) (atan a)) in a 1.584 * [approximate]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a)))) in (a) around 0 1.584 * [taylor]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a)))) in a 1.584 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) in a 1.584 * [taylor]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a)))) in a 1.584 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) in a 1.594 * [approximate]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a)))) in (a) around 0 1.594 * [taylor]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a)))) in a 1.594 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) in a 1.594 * [taylor]: Taking taylor expansion of (exp (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a)))) in a 1.594 * [taylor]: Taking taylor expansion of (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) in a 1.604 * * * [progress]: simplifying candidates 1.604 * [simplify]: Simplifying using # : (expm1 (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (log1p (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (log (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (exp (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (* (cbrt (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (cbrt (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a))) (cbrt (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (* (* (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a) (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (sqrt (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (sqrt (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (expm1 (sin (expm1 a))) (log1p (sin (expm1 a))) (* (sin (exp a)) (cos 1)) (* (cos (exp a)) (sin 1)) (log (sin (expm1 a))) (exp (sin (expm1 a))) (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))) (* (* (sin (expm1 a)) (sin (expm1 a))) (sin (expm1 a))) (sqrt (sin (expm1 a))) (sqrt (sin (expm1 a))) (expm1 (sin (expm1 a))) (log1p (sin (expm1 a))) (* (sin (exp a)) (cos 1)) (* (cos (exp a)) (sin 1)) (log (sin (expm1 a))) (exp (sin (expm1 a))) (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))) (* (* (sin (expm1 a)) (sin (expm1 a))) (sin (expm1 a))) (sqrt (sin (expm1 a))) (sqrt (sin (expm1 a))) (expm1 (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (exp (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) (exp (sqrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) (exp 1) (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (exp (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (* (cbrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (* (* (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (fmod (* 2 (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a) (fmod (* 2 (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a) (fmod (* 2 (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a) (- (+ (* 1/2 (pow a 2)) a) (* 5/24 (pow a 4))) (sin (- (exp a) 1)) (sin (- (exp a) 1)) (- (+ (* 1/2 (pow a 2)) a) (* 5/24 (pow a 4))) (sin (- (exp a) 1)) (sin (- (exp a) 1)) (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1.608 * * [simplify]: iteration 0 : 94 enodes (cost 486 ) 1.610 * * [simplify]: iteration 1 : 191 enodes (cost 417 ) 1.613 * * [simplify]: iteration 2 : 475 enodes (cost 417 ) 1.623 * * [simplify]: iteration 3 : 1899 enodes (cost 417 ) 1.682 * * [simplify]: iteration 4 : 5002 enodes (cost 417 ) 1.684 * [simplify]: Simplified to: (expm1 (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (log1p (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (log (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (exp (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (* (cbrt (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (cbrt (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a))) (cbrt (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (pow (fmod (* 2 (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a) 3) (sqrt (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (sqrt (fmod (+ (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a)) (expm1 (sin (expm1 a))) (log1p (sin (expm1 a))) (* (sin (exp a)) (cos 1)) (* (cos (exp a)) (sin 1)) (log (sin (expm1 a))) (exp (sin (expm1 a))) (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))) (pow (sin (expm1 a)) 3) (sqrt (sin (expm1 a))) (sqrt (sin (expm1 a))) (expm1 (sin (expm1 a))) (log1p (sin (expm1 a))) (* (sin (exp a)) (cos 1)) (* (cos (exp a)) (sin 1)) (log (sin (expm1 a))) (exp (sin (expm1 a))) (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))) (pow (sin (expm1 a)) 3) (sqrt (sin (expm1 a))) (sqrt (sin (expm1 a))) (expm1 (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (log1p (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (exp (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) (exp (sqrt (atan2 (expm1 (sin (expm1 a))) (atan a)))) E (atan2 (expm1 (sin (expm1 a))) (atan a)) (exp (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (* (cbrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (cbrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (pow (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 3) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) (fmod (* 2 (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a) (fmod (* 2 (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a) (fmod (* 2 (log (sqrt (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))))) a) (fma (pow a 2) 1/2 (- a (* 5/24 (pow a 4)))) (sin (expm1 a)) (sin (expm1 a)) (fma (pow a 2) 1/2 (- a (* 5/24 (pow a 4)))) (sin (expm1 a)) (sin (expm1 a)) (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) (exp (atan2 (expm1 (sin (expm1 a))) (atan a))) 1.684 * * * [progress]: adding candidates to table 1.951 * * [progress]: iteration 4 / 4 1.951 * * * [progress]: picking best candidate 2.044 * * * * [pick]: Picked # 2.044 * * * [progress]: localizing error 2.069 * * * [progress]: generating rewritten candidates 2.069 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 2 1) 2.069 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 2 1) 2.070 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 1 1) 2.071 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 2 1 1 1 1 1 1) 2.073 * * * [progress]: generating series expansions 2.073 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 2 1) 2.073 * [approximate]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) in (a) around 0 2.073 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) in a 2.073 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) in a 2.074 * [approximate]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) (/ 1 a)) in (a) around 0 2.074 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) (/ 1 a)) in a 2.074 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) (/ 1 a)) in a 2.075 * [approximate]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) (/ -1 a)) in (a) around 0 2.075 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) (/ -1 a)) in a 2.075 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) (/ -1 a)) in a 2.075 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 2 1) 2.076 * [approximate]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) in (a) around 0 2.076 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) in a 2.076 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) in a 2.076 * [approximate]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) (/ 1 a)) in (a) around 0 2.076 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) (/ 1 a)) in a 2.076 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) (/ 1 a)) in a 2.077 * [approximate]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) (/ -1 a)) in (a) around 0 2.077 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) (/ -1 a)) in a 2.077 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) (/ -1 a)) in a 2.078 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 1 1) 2.078 * [approximate]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) in (a) around 0 2.078 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) in a 2.078 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) in a 2.078 * [approximate]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) (/ 1 a)) in (a) around 0 2.078 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) (/ 1 a)) in a 2.079 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ 1 a)))) (atan (/ 1 a))) (/ 1 a)) in a 2.079 * [approximate]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) (/ -1 a)) in (a) around 0 2.079 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) (/ -1 a)) in a 2.079 * [taylor]: Taking taylor expansion of (fmod (atan2 (expm1 (sin (expm1 (/ -1 a)))) (atan (/ -1 a))) (/ -1 a)) in a 2.080 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 2 1 1 1 1 1 1) 2.080 * [approximate]: Taking taylor expansion of (sin (expm1 a)) in (a) around 0 2.080 * [taylor]: Taking taylor expansion of (sin (expm1 a)) in a 2.080 * [taylor]: Taking taylor expansion of (expm1 a) in a 2.080 * [taylor]: Rewrote expression to (- (exp a) 1) 2.080 * [taylor]: Taking taylor expansion of (exp a) in a 2.080 * [taylor]: Taking taylor expansion of a in a 2.080 * [taylor]: Taking taylor expansion of 1 in a 2.083 * [taylor]: Taking taylor expansion of (sin (expm1 a)) in a 2.083 * [taylor]: Taking taylor expansion of (expm1 a) in a 2.083 * [taylor]: Rewrote expression to (- (exp a) 1) 2.083 * [taylor]: Taking taylor expansion of (exp a) in a 2.083 * [taylor]: Taking taylor expansion of a in a 2.083 * [taylor]: Taking taylor expansion of 1 in a 2.093 * [approximate]: Taking taylor expansion of (sin (expm1 (/ 1 a))) in (a) around 0 2.093 * [taylor]: Taking taylor expansion of (sin (expm1 (/ 1 a))) in a 2.093 * [taylor]: Taking taylor expansion of (expm1 (/ 1 a)) in a 2.093 * [taylor]: Rewrote expression to (- (exp (/ 1 a)) 1) 2.093 * [taylor]: Taking taylor expansion of (exp (/ 1 a)) in a 2.093 * [taylor]: Taking taylor expansion of (/ 1 a) in a 2.093 * [taylor]: Taking taylor expansion of a in a 2.094 * [taylor]: Taking taylor expansion of 1 in a 2.094 * [taylor]: Taking taylor expansion of (sin (expm1 (/ 1 a))) in a 2.094 * [taylor]: Taking taylor expansion of (expm1 (/ 1 a)) in a 2.094 * [taylor]: Rewrote expression to (- (exp (/ 1 a)) 1) 2.094 * [taylor]: Taking taylor expansion of (exp (/ 1 a)) in a 2.094 * [taylor]: Taking taylor expansion of (/ 1 a) in a 2.094 * [taylor]: Taking taylor expansion of a in a 2.095 * [taylor]: Taking taylor expansion of 1 in a 2.116 * [approximate]: Taking taylor expansion of (sin (expm1 (/ -1 a))) in (a) around 0 2.117 * [taylor]: Taking taylor expansion of (sin (expm1 (/ -1 a))) in a 2.117 * [taylor]: Taking taylor expansion of (expm1 (/ -1 a)) in a 2.117 * [taylor]: Rewrote expression to (- (exp (/ -1 a)) 1) 2.117 * [taylor]: Taking taylor expansion of (exp (/ -1 a)) in a 2.117 * [taylor]: Taking taylor expansion of (/ -1 a) in a 2.117 * [taylor]: Taking taylor expansion of -1 in a 2.117 * [taylor]: Taking taylor expansion of a in a 2.117 * [taylor]: Taking taylor expansion of 1 in a 2.117 * [taylor]: Taking taylor expansion of (sin (expm1 (/ -1 a))) in a 2.117 * [taylor]: Taking taylor expansion of (expm1 (/ -1 a)) in a 2.118 * [taylor]: Rewrote expression to (- (exp (/ -1 a)) 1) 2.118 * [taylor]: Taking taylor expansion of (exp (/ -1 a)) in a 2.118 * [taylor]: Taking taylor expansion of (/ -1 a) in a 2.118 * [taylor]: Taking taylor expansion of -1 in a 2.118 * [taylor]: Taking taylor expansion of a in a 2.118 * [taylor]: Taking taylor expansion of 1 in a 2.140 * * * [progress]: simplifying candidates 2.140 * [simplify]: Simplifying using # : (expm1 (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (log1p (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (log (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (exp (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (* (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a))) (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (* (* (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a) (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (sqrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (sqrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (expm1 (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (log1p (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (log (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (exp (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (* (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a))) (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (* (* (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a) (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (sqrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (sqrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (expm1 (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (log1p (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (log (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (exp (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (* (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a))) (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (* (* (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a) (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (sqrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (sqrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (expm1 (sin (expm1 a))) (log1p (sin (expm1 a))) (* (sin (exp a)) (cos 1)) (* (cos (exp a)) (sin 1)) (log (sin (expm1 a))) (exp (sin (expm1 a))) (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))) (* (* (sin (expm1 a)) (sin (expm1 a))) (sin (expm1 a))) (sqrt (sin (expm1 a))) (sqrt (sin (expm1 a))) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (- (+ (* 1/2 (pow a 2)) a) (* 5/24 (pow a 4))) (sin (- (exp a) 1)) (sin (- (exp a) 1)) 2.144 * * [simplify]: iteration 0 : 70 enodes (cost 432 ) 2.146 * * [simplify]: iteration 1 : 146 enodes (cost 369 ) 2.149 * * [simplify]: iteration 2 : 368 enodes (cost 369 ) 2.156 * * [simplify]: iteration 3 : 1398 enodes (cost 369 ) 2.203 * * [simplify]: iteration 4 : 5001 enodes (cost 369 ) 2.205 * [simplify]: Simplified to: (expm1 (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (log1p (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (log (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (exp (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (* (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a))) (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (pow (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) 3) (sqrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (sqrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (expm1 (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (log1p (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (log (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (exp (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (* (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a))) (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (pow (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) 3) (sqrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (sqrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (expm1 (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (log1p (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (log (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (exp (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (* (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a))) (cbrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (pow (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) 3) (sqrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (sqrt (fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)) (expm1 (sin (expm1 a))) (log1p (sin (expm1 a))) (* (sin (exp a)) (cos 1)) (* (cos (exp a)) (sin 1)) (log (sin (expm1 a))) (exp (sin (expm1 a))) (* (cbrt (sin (expm1 a))) (cbrt (sin (expm1 a)))) (cbrt (sin (expm1 a))) (pow (sin (expm1 a)) 3) (sqrt (sin (expm1 a))) (sqrt (sin (expm1 a))) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) (fma (pow a 2) 1/2 (- a (* 5/24 (pow a 4)))) (sin (expm1 a)) (sin (expm1 a)) 2.205 * * * [progress]: adding candidates to table 2.455 * [progress]: [Phase 3 of 3] Extracting. 2.455 * * [regime]: Finding splitpoints for: (# # # # # # # # # # # # # # # # # # # # # # # # # # #) 2.467 * * * [regime-changes]: Trying 2 branch expressions: ((fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) a) 2.467 * * * * [regimes]: Trying to branch on (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) from (# # # # # # # # # # # # # # # # # # # # # # # # # # #) 2.633 * * * * [regimes]: Trying to branch on (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a) from (# # # #) 2.677 * * * * [regimes]: Trying to branch on a from (# # # # # # # # # # # # # # # # # # # # # # # # # # #) 2.828 * * * [regime]: Found split indices: #