9.696 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.076 * * * [progress]: [2/2] Setting up program. 0.086 * [progress]: [Phase 2 of 3] Improving. 0.086 * [simplify]: Simplifying using # : (* r (/ (sin b) (cos (+ a b)))) 0.089 * * [simplify]: iteration 0 : 12 enodes (cost 5 ) 0.090 * * [simplify]: iteration 1 : 16 enodes (cost 5 ) 0.091 * * [simplify]: iteration 2 : 20 enodes (cost 5 ) 0.091 * * [simplify]: iteration 3 : 21 enodes (cost 5 ) 0.092 * * [simplify]: iteration 4 : 21 enodes (cost 5 ) 0.093 * [simplify]: Simplified to: (* r (/ (sin b) (cos (+ a b)))) 0.093 * * [progress]: iteration 1 / 4 0.093 * * * [progress]: picking best candidate 0.097 * * * * [pick]: Picked # 0.097 * * * [progress]: localizing error 0.107 * * * [progress]: generating rewritten candidates 0.107 * * * * [progress]: [ 1 / 3 ] rewriting at (2 2 2) 0.110 * * * * [progress]: [ 2 / 3 ] rewriting at (2 2) 0.114 * * * * [progress]: [ 3 / 3 ] rewriting at (2) 0.123 * * * [progress]: generating series expansions 0.123 * * * * [progress]: [ 1 / 3 ] generating series at (2 2 2) 0.123 * [approximate]: Approximating (cos (+ a b)) in (a b) around 0 0.125 * [taylor]: Taking taylor expansion of (cos (+ a b)) in b 0.128 * [taylor]: Taking taylor expansion of (cos (+ a b)) in b 0.131 * [taylor]: Taking taylor expansion of (cos (+ a b)) in b 0.134 * [approximate]: Approximating (cos (+ (/ 1 b) (/ 1 a))) in (a b) around 0 0.136 * [taylor]: Taking taylor expansion of (cos (+ (/ 1 b) (/ 1 a))) in b 0.137 * [taylor]: Taking taylor expansion of (cos (+ (/ 1 b) (/ 1 a))) in b 0.137 * [taylor]: Taking taylor expansion of (cos (+ (/ 1 b) (/ 1 a))) in b 0.137 * [taylor]: Taking taylor expansion of (cos (+ (/ 1 b) (/ 1 a))) in b 0.137 * [approximate]: Approximating (cos (neg (+ (/ 1 b) (/ 1 a)))) in (a b) around 0 0.141 * [taylor]: Taking taylor expansion of (cos (neg (+ (/ 1 b) (/ 1 a)))) in b 0.142 * [taylor]: Taking taylor expansion of (cos (neg (+ (/ 1 b) (/ 1 a)))) in b 0.142 * [taylor]: Taking taylor expansion of (cos (neg (+ (/ 1 b) (/ 1 a)))) in b 0.142 * [taylor]: Taking taylor expansion of (cos (neg (+ (/ 1 b) (/ 1 a)))) in b 0.142 * * * * [progress]: [ 2 / 3 ] generating series at (2 2) 0.142 * [approximate]: Approximating (/ (sin b) (cos (+ a b))) in (b a) around 0 0.145 * [taylor]: Taking taylor expansion of (/ (sin b) (cos (+ a b))) in a 0.148 * [taylor]: Taking taylor expansion of (/ (sin b) (cos (+ a b))) in a 0.154 * [taylor]: Taking taylor expansion of (/ (sin b) (cos (+ a b))) in a 0.158 * [approximate]: Approximating (/ (sin (/ 1 b)) (cos (+ (/ 1 b) (/ 1 a)))) in (b a) around 0 0.162 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (cos (+ (/ 1 b) (/ 1 a)))) in a 0.163 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (cos (+ (/ 1 b) (/ 1 a)))) in a 0.166 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (cos (+ (/ 1 b) (/ 1 a)))) in a 0.170 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (cos (+ (/ 1 b) (/ 1 a)))) in a 0.170 * [approximate]: Approximating (/ (sin (/ -1 b)) (cos (neg (+ (/ 1 b) (/ 1 a))))) in (b a) around 0 0.180 * [taylor]: Taking taylor expansion of (/ (sin (/ -1 b)) (cos (neg (+ (/ 1 b) (/ 1 a))))) in a 0.182 * [taylor]: Taking taylor expansion of (/ (sin (/ -1 b)) (cos (neg (+ (/ 1 b) (/ 1 a))))) in a 0.184 * [taylor]: Taking taylor expansion of (/ (sin (/ -1 b)) (cos (neg (+ (/ 1 b) (/ 1 a))))) in a 0.188 * [taylor]: Taking taylor expansion of (/ (sin (/ -1 b)) (cos (neg (+ (/ 1 b) (/ 1 a))))) in a 0.188 * * * * [progress]: [ 3 / 3 ] generating series at (2) 0.188 * [approximate]: Approximating (/ (* r (sin b)) (cos (+ a b))) in (r b a) around 0 0.196 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (cos (+ a b))) in b 0.198 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (cos (+ a b))) in a 0.204 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (cos (+ a b))) in b 0.204 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (cos (+ a b))) in a 0.207 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (cos (+ a b))) in a 0.216 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (cos (+ a b))) in b 0.216 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (cos (+ a b))) in a 0.216 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (cos (+ a b))) in a 0.221 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (cos (+ a b))) in a 0.224 * [approximate]: Approximating (/ (sin (/ 1 b)) (* (cos (+ (/ 1 b) (/ 1 a))) r)) in (r b a) around 0 0.235 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* (cos (+ (/ 1 b) (/ 1 a))) r)) in b 0.236 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* (cos (+ (/ 1 b) (/ 1 a))) r)) in a 0.244 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* (cos (+ (/ 1 b) (/ 1 a))) r)) in b 0.244 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* (cos (+ (/ 1 b) (/ 1 a))) r)) in a 0.244 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* (cos (+ (/ 1 b) (/ 1 a))) r)) in a 0.254 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* (cos (+ (/ 1 b) (/ 1 a))) r)) in b 0.254 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* (cos (+ (/ 1 b) (/ 1 a))) r)) in a 0.254 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* (cos (+ (/ 1 b) (/ 1 a))) r)) in a 0.254 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* (cos (+ (/ 1 b) (/ 1 a))) r)) in a 0.255 * [approximate]: Approximating (* -1 (/ (sin (/ -1 b)) (* (cos (neg (+ (/ 1 b) (/ 1 a)))) r))) in (r b a) around 0 0.273 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (cos (neg (+ (/ 1 b) (/ 1 a)))) r))) in b 0.274 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (cos (neg (+ (/ 1 b) (/ 1 a)))) r))) in a 0.283 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (cos (neg (+ (/ 1 b) (/ 1 a)))) r))) in b 0.283 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (cos (neg (+ (/ 1 b) (/ 1 a)))) r))) in a 0.284 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (cos (neg (+ (/ 1 b) (/ 1 a)))) r))) in a 0.297 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (cos (neg (+ (/ 1 b) (/ 1 a)))) r))) in b 0.297 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (cos (neg (+ (/ 1 b) (/ 1 a)))) r))) in a 0.297 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (cos (neg (+ (/ 1 b) (/ 1 a)))) r))) in a 0.298 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (cos (neg (+ (/ 1 b) (/ 1 a)))) r))) in a 0.298 * * * [progress]: simplifying candidates 0.299 * [simplify]: Simplifying using # : (* (cos a) (cos b)) (* (sin a) (sin b)) (log (cos (+ a b))) (exp (cos (+ a b))) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))) (cbrt (cos (+ a b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))) (sqrt (cos (+ a b))) (sqrt (cos (+ a b))) (- (log (sin b)) (log (cos (+ a b)))) (log (/ (sin b) (cos (+ a b)))) (exp (/ (sin b) (cos (+ a b)))) (/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b)))) (* (cbrt (/ (sin b) (cos (+ a b)))) (cbrt (/ (sin b) (cos (+ a b))))) (cbrt (/ (sin b) (cos (+ a b)))) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b)))) (sqrt (/ (sin b) (cos (+ a b)))) (sqrt (/ (sin b) (cos (+ a b)))) (neg (sin b)) (neg (cos (+ a b))) (/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b))))) (/ (cbrt (sin b)) (cbrt (cos (+ a b)))) (/ (* (cbrt (sin b)) (cbrt (sin b))) (sqrt (cos (+ a b)))) (/ (cbrt (sin b)) (sqrt (cos (+ a b)))) (/ (* (cbrt (sin b)) (cbrt (sin b))) 1) (/ (cbrt (sin b)) (cos (+ a b))) (/ (sqrt (sin b)) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b))))) (/ (sqrt (sin b)) (cbrt (cos (+ a b)))) (/ (sqrt (sin b)) (sqrt (cos (+ a b)))) (/ (sqrt (sin b)) (sqrt (cos (+ a b)))) (/ (sqrt (sin b)) 1) (/ (sqrt (sin b)) (cos (+ a b))) (/ 1 (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b))))) (/ (sin b) (cbrt (cos (+ a b)))) (/ 1 (sqrt (cos (+ a b)))) (/ (sin b) (sqrt (cos (+ a b)))) (/ 1 1) (/ (sin b) (cos (+ a b))) (/ 1 (cos (+ a b))) (/ (cos (+ a b)) (sin b)) (/ (sin b) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b))))) (/ (sin b) (sqrt (cos (+ a b)))) (/ (sin b) 1) (/ (cos (+ a b)) (cbrt (sin b))) (/ (cos (+ a b)) (sqrt (sin b))) (/ (cos (+ a b)) (sin b)) (* r (/ (sin b) (cos (+ a b)))) (+ (log r) (- (log (sin b)) (log (cos (+ a b))))) (+ (log r) (log (/ (sin b) (cos (+ a b))))) (log (* r (/ (sin b) (cos (+ a b))))) (exp (* r (/ (sin b) (cos (+ a b))))) (* (* (* r r) r) (/ (* (* (sin b) (sin b)) (sin b)) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))) (* (* (* r r) r) (* (* (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b)))) (/ (sin b) (cos (+ a b))))) (* (cbrt (* r (/ (sin b) (cos (+ a b))))) (cbrt (* r (/ (sin b) (cos (+ a b)))))) (cbrt (* r (/ (sin b) (cos (+ a b))))) (* (* (* r (/ (sin b) (cos (+ a b)))) (* r (/ (sin b) (cos (+ a b))))) (* r (/ (sin b) (cos (+ a b))))) (sqrt (* r (/ (sin b) (cos (+ a b))))) (sqrt (* r (/ (sin b) (cos (+ a b))))) (* (sqrt r) (sqrt (/ (sin b) (cos (+ a b))))) (* (sqrt r) (sqrt (/ (sin b) (cos (+ a b))))) (* (sqrt r) (/ (sqrt (sin b)) (sqrt (cos (+ a b))))) (* (sqrt r) (/ (sqrt (sin b)) (sqrt (cos (+ a b))))) (* r (* (cbrt (/ (sin b) (cos (+ a b)))) (cbrt (/ (sin b) (cos (+ a b)))))) (* r (sqrt (/ (sin b) (cos (+ a b))))) (* r (/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))))) (* r (/ (* (cbrt (sin b)) (cbrt (sin b))) (sqrt (cos (+ a b))))) (* r (/ (* (cbrt (sin b)) (cbrt (sin b))) 1)) (* r (/ (sqrt (sin b)) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))))) (* r (/ (sqrt (sin b)) (sqrt (cos (+ a b))))) (* r (/ (sqrt (sin b)) 1)) (* r (/ 1 (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))))) (* r (/ 1 (sqrt (cos (+ a b))))) (* r (/ 1 1)) (* r 1) (* r (sin b)) (* (cbrt r) (/ (sin b) (cos (+ a b)))) (* (sqrt r) (/ (sin b) (cos (+ a b)))) (* r (/ (sin b) (cos (+ a b)))) (* r (sin b)) (- 1 (+ (* 1/2 (pow a 2)) (* a b))) (cos (+ a b)) (cos (+ a b)) (+ (* a (pow b 2)) (+ (* 1/3 (pow b 3)) b)) (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b))) (+ (* a (* r (pow b 2))) (+ (* r b) (* 1/3 (* r (pow b 3))))) (/ (* r (sin b)) (cos (+ a b))) (/ (* r (sin b)) (cos (+ a b))) 0.303 * * [simplify]: iteration 0 : 252 enodes (cost 536 ) 0.308 * * [simplify]: iteration 1 : 1064 enodes (cost 480 ) 0.331 * * [simplify]: iteration 2 : 5001 enodes (cost 477 ) 0.334 * [simplify]: Simplified to: (* (cos a) (cos b)) (* (sin a) (sin b)) (log (cos (+ a b))) (exp (cos (+ a b))) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))) (cbrt (cos (+ a b))) (pow (cos (+ a b)) 3) (sqrt (cos (+ a b))) (sqrt (cos (+ a b))) (log (/ (sin b) (cos (+ a b)))) (log (/ (sin b) (cos (+ a b)))) (exp (/ (sin b) (cos (+ a b)))) (pow (/ (sin b) (cos (+ a b))) 3) (* (cbrt (/ (sin b) (cos (+ a b)))) (cbrt (/ (sin b) (cos (+ a b))))) (cbrt (/ (sin b) (cos (+ a b)))) (pow (/ (sin b) (cos (+ a b))) 3) (sqrt (/ (sin b) (cos (+ a b)))) (sqrt (/ (sin b) (cos (+ a b)))) (neg (sin b)) (neg (cos (+ a b))) (/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b))))) (/ (cbrt (sin b)) (cbrt (cos (+ a b)))) (/ (* (cbrt (sin b)) (cbrt (sin b))) (sqrt (cos (+ a b)))) (/ (cbrt (sin b)) (sqrt (cos (+ a b)))) (* (cbrt (sin b)) (cbrt (sin b))) (/ (cbrt (sin b)) (cos (+ a b))) (/ (sqrt (sin b)) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b))))) (/ (sqrt (sin b)) (cbrt (cos (+ a b)))) (/ (sqrt (sin b)) (sqrt (cos (+ a b)))) (/ (sqrt (sin b)) (sqrt (cos (+ a b)))) (sqrt (sin b)) (/ (sqrt (sin b)) (cos (+ a b))) (/ 1 (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b))))) (/ (sin b) (cbrt (cos (+ a b)))) (/ 1 (sqrt (cos (+ a b)))) (/ (sin b) (sqrt (cos (+ a b)))) 1 (/ (sin b) (cos (+ a b))) (/ 1 (cos (+ a b))) (/ (cos (+ a b)) (sin b)) (/ (sin b) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b))))) (/ (sin b) (sqrt (cos (+ a b)))) (sin b) (/ (cos (+ a b)) (cbrt (sin b))) (/ (cos (+ a b)) (sqrt (sin b))) (/ (cos (+ a b)) (sin b)) (* r (/ (sin b) (cos (+ a b)))) (log (* r (/ (sin b) (cos (+ a b))))) (log (* r (/ (sin b) (cos (+ a b))))) (log (* r (/ (sin b) (cos (+ a b))))) (exp (* r (/ (sin b) (cos (+ a b))))) (pow (* r (/ (sin b) (cos (+ a b)))) 3) (pow (* r (/ (sin b) (cos (+ a b)))) 3) (* (cbrt (* r (/ (sin b) (cos (+ a b))))) (cbrt (* r (/ (sin b) (cos (+ a b)))))) (cbrt (* r (/ (sin b) (cos (+ a b))))) (pow (* r (/ (sin b) (cos (+ a b)))) 3) (sqrt (* r (/ (sin b) (cos (+ a b))))) (sqrt (* r (/ (sin b) (cos (+ a b))))) (* (sqrt r) (sqrt (/ (sin b) (cos (+ a b))))) (* (sqrt r) (sqrt (/ (sin b) (cos (+ a b))))) (* (sqrt r) (/ (sqrt (sin b)) (sqrt (cos (+ a b))))) (* (sqrt r) (/ (sqrt (sin b)) (sqrt (cos (+ a b))))) (* r (* (cbrt (/ (sin b) (cos (+ a b)))) (cbrt (/ (sin b) (cos (+ a b)))))) (* r (sqrt (/ (sin b) (cos (+ a b))))) (* r (/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))))) (* r (/ (* (cbrt (sin b)) (cbrt (sin b))) (sqrt (cos (+ a b))))) (* (* (cbrt (sin b)) (cbrt (sin b))) r) (* r (/ (sqrt (sin b)) (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b)))))) (* r (/ (sqrt (sin b)) (sqrt (cos (+ a b))))) (* (sqrt (sin b)) r) (/ r (* (cbrt (cos (+ a b))) (cbrt (cos (+ a b))))) (/ r (sqrt (cos (+ a b)))) r r (* r (sin b)) (* (cbrt r) (/ (sin b) (cos (+ a b)))) (* (sqrt r) (/ (sin b) (cos (+ a b)))) (* r (/ (sin b) (cos (+ a b)))) (* r (sin b)) (- 1 (+ (* 1/2 (pow a 2)) (* a b))) (cos (+ a b)) (cos (+ a b)) (+ (* (pow b 2) (+ (* b 1/3) a)) b) (/ (sin b) (cos (+ a b))) (/ (sin b) (cos (+ a b))) (+ (* r b) (* r (* (pow b 2) (+ (* b 1/3) a)))) (* r (/ (sin b) (cos (+ a b)))) (* r (/ (sin b) (cos (+ a b)))) 0.335 * * * [progress]: adding candidates to table 0.557 * * [progress]: iteration 2 / 4 0.557 * * * [progress]: picking best candidate 0.600 * * * * [pick]: Picked # 0.600 * * * [progress]: localizing error 0.615 * * * [progress]: generating rewritten candidates 0.616 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 2) 0.620 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2) 0.631 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 0.642 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2) 0.650 * * * [progress]: generating series expansions 0.650 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 2) 0.650 * [approximate]: Approximating (* (sin b) (sin a)) in (a b) around 0 0.650 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 0.653 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 0.657 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 0.662 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 0.669 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 0.669 * [approximate]: Approximating (* (sin (/ 1 a)) (sin (/ 1 b))) in (a b) around 0 0.671 * [taylor]: Taking taylor expansion of (* (sin (/ 1 a)) (sin (/ 1 b))) in b 0.673 * [taylor]: Taking taylor expansion of (* (sin (/ 1 a)) (sin (/ 1 b))) in b 0.678 * [taylor]: Taking taylor expansion of (* (sin (/ 1 a)) (sin (/ 1 b))) in b 0.685 * [taylor]: Taking taylor expansion of (* (sin (/ 1 a)) (sin (/ 1 b))) in b 0.686 * [approximate]: Approximating (* (sin (/ -1 a)) (sin (/ -1 b))) in (a b) around 0 0.687 * [taylor]: Taking taylor expansion of (* (sin (/ -1 a)) (sin (/ -1 b))) in b 0.690 * [taylor]: Taking taylor expansion of (* (sin (/ -1 a)) (sin (/ -1 b))) in b 0.695 * [taylor]: Taking taylor expansion of (* (sin (/ -1 a)) (sin (/ -1 b))) in b 0.702 * [taylor]: Taking taylor expansion of (* (sin (/ -1 a)) (sin (/ -1 b))) in b 0.702 * * * * [progress]: [ 2 / 4 ] generating series at (2 2) 0.703 * [approximate]: Approximating (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in (b a) around 0 0.707 * [taylor]: Taking taylor expansion of (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 0.714 * [taylor]: Taking taylor expansion of (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 0.731 * [taylor]: Taking taylor expansion of (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 0.735 * [approximate]: Approximating (/ (sin (/ 1 b)) (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b))))) in (b a) around 0 0.742 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b))))) in a 0.749 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b))))) in a 0.765 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b))))) in a 0.784 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b))))) in a 0.785 * [approximate]: Approximating (/ (sin (/ -1 b)) (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b))))) in (b a) around 0 0.792 * [taylor]: Taking taylor expansion of (/ (sin (/ -1 b)) (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b))))) in a 0.800 * [taylor]: Taking taylor expansion of (/ (sin (/ -1 b)) (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b))))) in a 0.820 * [taylor]: Taking taylor expansion of (/ (sin (/ -1 b)) (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b))))) in a 0.840 * [taylor]: Taking taylor expansion of (/ (sin (/ -1 b)) (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b))))) in a 0.840 * * * * [progress]: [ 3 / 4 ] generating series at (2) 0.840 * [approximate]: Approximating (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in (r b a) around 0 0.851 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in b 0.852 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 0.865 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in b 0.865 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 0.872 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 0.895 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in b 0.895 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 0.895 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 0.905 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 0.908 * [approximate]: Approximating (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in (r b a) around 0 0.937 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in b 0.939 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 0.957 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in b 0.957 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 0.963 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 0.995 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in b 0.995 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 0.995 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 1.003 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 1.003 * [approximate]: Approximating (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in (r b a) around 0 1.032 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in b 1.035 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 1.054 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in b 1.054 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 1.065 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 1.094 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in b 1.094 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 1.094 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 1.102 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 1.103 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2) 1.103 * [approximate]: Approximating (- (* (cos b) (cos a)) (* (sin a) (sin b))) in (a b) around 0 1.104 * [taylor]: Taking taylor expansion of (- (* (cos b) (cos a)) (* (sin a) (sin b))) in b 1.110 * [taylor]: Taking taylor expansion of (- (* (cos b) (cos a)) (* (sin a) (sin b))) in b 1.119 * [taylor]: Taking taylor expansion of (- (* (cos b) (cos a)) (* (sin a) (sin b))) in b 1.121 * [approximate]: Approximating (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))) in (a b) around 0 1.124 * [taylor]: Taking taylor expansion of (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))) in b 1.131 * [taylor]: Taking taylor expansion of (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))) in b 1.144 * [taylor]: Taking taylor expansion of (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))) in b 1.165 * [taylor]: Taking taylor expansion of (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))) in b 1.166 * [approximate]: Approximating (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) in (a b) around 0 1.170 * [taylor]: Taking taylor expansion of (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) in b 1.177 * [taylor]: Taking taylor expansion of (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) in b 1.189 * [taylor]: Taking taylor expansion of (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) in b 1.205 * [taylor]: Taking taylor expansion of (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) in b 1.205 * * * [progress]: simplifying candidates 1.207 * [simplify]: Simplifying using # : (- (cos (- a b)) (cos (+ a b))) (* (sin a) (sin b)) (+ (log (sin a)) (log (sin b))) (log (* (sin a) (sin b))) (exp (* (sin a) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (cbrt (* (sin a) (sin b))) (cbrt (* (sin a) (sin b)))) (cbrt (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (sqrt (* (sin a) (sin b))) (sqrt (* (sin a) (sin b))) (* (sqrt (sin a)) (sqrt (sin b))) (* (sqrt (sin a)) (sqrt (sin b))) (* (sin a) (* (cbrt (sin b)) (cbrt (sin b)))) (* (sin a) (sqrt (sin b))) (* (sin a) 1) (* (cbrt (sin a)) (sin b)) (* (sqrt (sin a)) (sin b)) (* (sin a) (sin b)) (- (log (sin b)) (log (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (log (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (exp (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (* (cbrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (cbrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (cbrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (* (* (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (sqrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (sqrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (neg (sin b)) (neg (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (/ (cbrt (sin b)) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (* (cbrt (sin b)) (cbrt (sin b))) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (cbrt (sin b)) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (* (cbrt (sin b)) (cbrt (sin b))) 1) (/ (cbrt (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (sqrt (sin b)) (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (/ (sqrt (sin b)) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (sqrt (sin b)) 1) (/ (sqrt (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ 1 (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (/ (sin b) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ 1 (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (sin b) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ 1 1) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)) (/ (sin b) (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (/ (sin b) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (sin b) 1) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (cbrt (sin b))) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sqrt (sin b))) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)) (/ (sin b) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))) (/ (sin b) (- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))) (/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3))) (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (+ (log r) (- (log (sin b)) (log (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (+ (log r) (log (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (log (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (exp (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* (* (* r r) r) (/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* (* (* r r) r) (* (* (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* (cbrt (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (cbrt (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))))) (cbrt (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* (* (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (sqrt (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (sqrt (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* (sqrt r) (sqrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* (sqrt r) (sqrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* (sqrt r) (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* (sqrt r) (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* r (* (cbrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (cbrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))))) (* r (sqrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* r (/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))))) (* r (/ (* (cbrt (sin b)) (cbrt (sin b))) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* r (/ (* (cbrt (sin b)) (cbrt (sin b))) 1)) (* r (/ (sqrt (sin b)) (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))))) (* r (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* r (/ (sqrt (sin b)) 1)) (* r (/ 1 (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))))) (* r (/ 1 (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* r (/ 1 1)) (* r 1) (* r (sin b)) (* r (/ (sin b) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b)))))) (* r (/ (sin b) (- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b))))))) (* r (/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)))) (* r (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))) (* (cbrt r) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (* (sqrt r) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (* r (sin b)) (/ (exp (* (cos a) (cos b))) (exp (* (sin a) (sin b)))) (log (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (exp (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b)))) (- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b))))) (* 2 2) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b))))) (neg (* (sin a) (sin b))) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (neg (* (sin a) (sin b))) (* a b) (* (sin b) (sin a)) (* (sin b) (sin a)) (+ (* a (pow b 2)) (+ (* 1/3 (pow b 3)) b)) (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (+ (* a (* r (pow b 2))) (+ (* r b) (* 1/3 (* r (pow b 3))))) (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (- 1 (+ (* 1/2 (pow a 2)) (* a b))) (- (* (cos b) (cos a)) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b))) 1.213 * * [simplify]: iteration 0 : 405 enodes (cost 1307 ) 1.220 * * [simplify]: iteration 1 : 1761 enodes (cost 1182 ) 1.252 * * [simplify]: iteration 2 : 5001 enodes (cost 1173 ) 1.257 * [simplify]: Simplified to: (- (cos (- a b)) (cos (+ a b))) (* (sin a) (sin b)) (log (* (sin a) (sin b))) (log (* (sin a) (sin b))) (exp (* (sin a) (sin b))) (pow (* (sin a) (sin b)) 3) (* (cbrt (* (sin a) (sin b))) (cbrt (* (sin a) (sin b)))) (cbrt (* (sin a) (sin b))) (pow (* (sin a) (sin b)) 3) (sqrt (* (sin a) (sin b))) (sqrt (* (sin a) (sin b))) (* (sqrt (sin a)) (sqrt (sin b))) (* (sqrt (sin a)) (sqrt (sin b))) (* (sin a) (* (cbrt (sin b)) (cbrt (sin b)))) (* (sin a) (sqrt (sin b))) (sin a) (* (cbrt (sin a)) (sin b)) (* (sqrt (sin a)) (sin b)) (* (sin a) (sin b)) (log (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (log (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (exp (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))) (pow (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) 3) (* (cbrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (cbrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (cbrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (pow (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) 3) (sqrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (sqrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (neg (sin b)) (neg (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (/ (cbrt (sin b)) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (* (cbrt (sin b)) (cbrt (sin b))) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (cbrt (sin b)) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (* (cbrt (sin b)) (cbrt (sin b))) (/ (cbrt (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (sqrt (sin b)) (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (/ (sqrt (sin b)) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (sqrt (sin b)) (/ (sqrt (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ 1 (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (/ (sin b) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ 1 (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (sin b) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) 1 (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)) (/ (sin b) (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (/ (sin b) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (sin b) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (cbrt (sin b))) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sqrt (sin b))) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)) (/ (sin b) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))) (/ (sin b) (* 2 (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b)))))) (/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3))) (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (log (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (log (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (log (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (exp (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (pow (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) 3) (pow (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) 3) (* (cbrt (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (cbrt (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))))) (cbrt (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (pow (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) 3) (sqrt (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (sqrt (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* (sqrt r) (sqrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* (sqrt r) (sqrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* (sqrt r) (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* (sqrt r) (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* r (* (cbrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (cbrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))))) (* r (sqrt (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* r (/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))))) (* r (/ (* (cbrt (sin b)) (cbrt (sin b))) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* (* (cbrt (sin b)) (cbrt (sin b))) r) (* r (/ (sqrt (sin b)) (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))))) (* r (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (* (sqrt (sin b)) r) (/ r (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (/ r (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) r r (* r (sin b)) (* r (/ (sin b) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b)))))) (/ (* r (sin b)) (* 2 (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b)))))) (* r (/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)))) (* r (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))) (* (cbrt r) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (* (sqrt r) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (* r (sin b)) (exp (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (log (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (exp (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (pow (- (* (cos b) (cos a)) (* (sin a) (sin b))) 3) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (+ (+ (cos (+ a b)) (cos (+ a b))) 0) (* 2 (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))) 4 (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (sin a) (sin b)) (+ (* (sin a) (sin b)) (* (cos a) (cos b)))) (* (* (cos a) (cos b)) (* (cos a) (cos b)))) (neg (* (sin a) (sin b))) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (neg (* (sin a) (sin b))) (* a b) (* (sin a) (sin b)) (* (sin a) (sin b)) (+ (* (pow b 2) (+ (* b 1/3) a)) b) (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (+ (* r b) (* r (* (pow b 2) (+ (* b 1/3) a)))) (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (- 1 (+ (* 1/2 (pow a 2)) (* a b))) (- (* (cos b) (cos a)) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b))) 1.258 * * * [progress]: adding candidates to table 1.905 * * [progress]: iteration 3 / 4 1.905 * * * [progress]: picking best candidate 1.977 * * * * [pick]: Picked # 1.977 * * * [progress]: localizing error 1.992 * * * [progress]: generating rewritten candidates 1.992 * * * * [progress]: [ 1 / 4 ] rewriting at (2) 2.001 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2) 2.005 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 2.009 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2) 2.015 * * * [progress]: generating series expansions 2.015 * * * * [progress]: [ 1 / 4 ] generating series at (2) 2.016 * [approximate]: Approximating (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in (r b a) around 0 2.026 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in b 2.028 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 2.043 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in b 2.043 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 2.050 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 2.068 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in b 2.068 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 2.068 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 2.077 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 2.081 * [approximate]: Approximating (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in (r b a) around 0 2.109 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in b 2.112 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 2.132 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in b 2.132 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 2.138 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 2.165 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in b 2.165 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 2.165 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 2.172 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 2.173 * [approximate]: Approximating (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in (r b a) around 0 2.205 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in b 2.207 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 2.226 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in b 2.226 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 2.232 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 2.260 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in b 2.261 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 2.261 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 2.269 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 2.270 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2) 2.270 * [approximate]: Approximating (* (sin b) (sin a)) in (a b) around 0 2.270 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 2.275 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 2.279 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 2.284 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 2.291 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 2.291 * [approximate]: Approximating (* (sin (/ 1 a)) (sin (/ 1 b))) in (a b) around 0 2.293 * [taylor]: Taking taylor expansion of (* (sin (/ 1 a)) (sin (/ 1 b))) in b 2.296 * [taylor]: Taking taylor expansion of (* (sin (/ 1 a)) (sin (/ 1 b))) in b 2.301 * [taylor]: Taking taylor expansion of (* (sin (/ 1 a)) (sin (/ 1 b))) in b 2.307 * [taylor]: Taking taylor expansion of (* (sin (/ 1 a)) (sin (/ 1 b))) in b 2.308 * [approximate]: Approximating (* (sin (/ -1 a)) (sin (/ -1 b))) in (a b) around 0 2.309 * [taylor]: Taking taylor expansion of (* (sin (/ -1 a)) (sin (/ -1 b))) in b 2.312 * [taylor]: Taking taylor expansion of (* (sin (/ -1 a)) (sin (/ -1 b))) in b 2.317 * [taylor]: Taking taylor expansion of (* (sin (/ -1 a)) (sin (/ -1 b))) in b 2.324 * [taylor]: Taking taylor expansion of (* (sin (/ -1 a)) (sin (/ -1 b))) in b 2.324 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 2.324 * [approximate]: Approximating (* r (sin b)) in (r b) around 0 2.325 * [taylor]: Taking taylor expansion of (* r (sin b)) in b 2.327 * [taylor]: Taking taylor expansion of (* r (sin b)) in b 2.330 * [taylor]: Taking taylor expansion of (* r (sin b)) in b 2.335 * [taylor]: Taking taylor expansion of (* r (sin b)) in b 2.340 * [taylor]: Taking taylor expansion of (* r (sin b)) in b 2.340 * [approximate]: Approximating (/ (sin (/ 1 b)) r) in (r b) around 0 2.341 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) r) in b 2.344 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) r) in b 2.348 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) r) in b 2.356 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) r) in b 2.356 * [approximate]: Approximating (* -1 (/ (sin (/ -1 b)) r)) in (r b) around 0 2.357 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) r)) in b 2.361 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) r)) in b 2.366 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) r)) in b 2.372 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) r)) in b 2.372 * * * * [progress]: [ 4 / 4 ] generating series at (2 2) 2.373 * [approximate]: Approximating (- (* (cos b) (cos a)) (* (sin a) (sin b))) in (a b) around 0 2.374 * [taylor]: Taking taylor expansion of (- (* (cos b) (cos a)) (* (sin a) (sin b))) in b 2.379 * [taylor]: Taking taylor expansion of (- (* (cos b) (cos a)) (* (sin a) (sin b))) in b 2.388 * [taylor]: Taking taylor expansion of (- (* (cos b) (cos a)) (* (sin a) (sin b))) in b 2.390 * [approximate]: Approximating (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))) in (a b) around 0 2.393 * [taylor]: Taking taylor expansion of (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))) in b 2.400 * [taylor]: Taking taylor expansion of (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))) in b 2.412 * [taylor]: Taking taylor expansion of (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))) in b 2.427 * [taylor]: Taking taylor expansion of (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))) in b 2.428 * [approximate]: Approximating (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) in (a b) around 0 2.434 * [taylor]: Taking taylor expansion of (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) in b 2.441 * [taylor]: Taking taylor expansion of (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) in b 2.453 * [taylor]: Taking taylor expansion of (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) in b 2.469 * [taylor]: Taking taylor expansion of (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) in b 2.470 * * * [progress]: simplifying candidates 2.471 * [simplify]: Simplifying using # : (- (+ (log r) (log (sin b))) (log (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (- (log (* r (sin b))) (log (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (log (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (exp (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (* (cbrt (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (cbrt (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (cbrt (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (* (* (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (sqrt (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (sqrt (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (neg (* r (sin b))) (neg (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ r (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (/ (sin b) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ r (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (sin b) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ r 1) (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (* r (sin b))) (/ (* r (sin b)) (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (/ (* r (sin b)) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (* r (sin b)) 1) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)) (/ (* r (sin b)) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))) (/ (* r (sin b)) (- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))) (/ (* r (sin b)) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3))) (/ (* r (sin b)) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (- (cos (- a b)) (cos (+ a b))) (* (sin a) (sin b)) (+ (log (sin a)) (log (sin b))) (log (* (sin a) (sin b))) (exp (* (sin a) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (cbrt (* (sin a) (sin b))) (cbrt (* (sin a) (sin b)))) (cbrt (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (sqrt (* (sin a) (sin b))) (sqrt (* (sin a) (sin b))) (* (sqrt (sin a)) (sqrt (sin b))) (* (sqrt (sin a)) (sqrt (sin b))) (* (sin a) (* (cbrt (sin b)) (cbrt (sin b)))) (* (sin a) (sqrt (sin b))) (* (sin a) 1) (* (cbrt (sin a)) (sin b)) (* (sqrt (sin a)) (sin b)) (* (sin a) (sin b)) (* r (sin b)) (+ (log r) (log (sin b))) (log (* r (sin b))) (exp (* r (sin b))) (* (* (* r r) r) (* (* (sin b) (sin b)) (sin b))) (* (cbrt (* r (sin b))) (cbrt (* r (sin b)))) (cbrt (* r (sin b))) (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (sqrt (* r (sin b))) (sqrt (* r (sin b))) (* (sqrt r) (sqrt (sin b))) (* (sqrt r) (sqrt (sin b))) (* r (* (cbrt (sin b)) (cbrt (sin b)))) (* r (sqrt (sin b))) (* r 1) (* (cbrt r) (sin b)) (* (sqrt r) (sin b)) (* r (sin b)) (/ (exp (* (cos a) (cos b))) (exp (* (sin a) (sin b)))) (log (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (exp (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b)))) (- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b))))) (* 2 2) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b))))) (neg (* (sin a) (sin b))) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (neg (* (sin a) (sin b))) (+ (* a (* r (pow b 2))) (+ (* r b) (* 1/3 (* r (pow b 3))))) (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (* a b) (* (sin b) (sin a)) (* (sin b) (sin a)) (* r b) (* r (sin b)) (* r (sin b)) (- 1 (+ (* 1/2 (pow a 2)) (* a b))) (- (* (cos b) (cos a)) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b))) 2.475 * * [simplify]: iteration 0 : 344 enodes (cost 770 ) 2.482 * * [simplify]: iteration 1 : 1513 enodes (cost 673 ) 2.511 * * [simplify]: iteration 2 : 5002 enodes (cost 663 ) 2.514 * [simplify]: Simplified to: (log (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (log (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (log (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (exp (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (pow (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) 3) (pow (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) 3) (* (cbrt (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (cbrt (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (cbrt (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (pow (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) 3) (sqrt (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (sqrt (/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (neg (* r (sin b))) (neg (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ r (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (/ (sin b) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ r (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (/ (sin b) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (* r (sin b))) (/ (* r (sin b)) (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))))) (/ (* r (sin b)) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (* r (sin b)) (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)) (/ (* r (sin b)) (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))) (/ (sin b) (/ (* 2 (- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))) r)) (/ (* r (sin b)) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3))) (/ (* r (sin b)) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (- (cos (- a b)) (cos (+ a b))) (* (sin a) (sin b)) (log (* (sin a) (sin b))) (log (* (sin a) (sin b))) (exp (* (sin a) (sin b))) (pow (* (sin a) (sin b)) 3) (* (cbrt (* (sin a) (sin b))) (cbrt (* (sin a) (sin b)))) (cbrt (* (sin a) (sin b))) (pow (* (sin a) (sin b)) 3) (sqrt (* (sin a) (sin b))) (sqrt (* (sin a) (sin b))) (* (sqrt (sin a)) (sqrt (sin b))) (* (sqrt (sin a)) (sqrt (sin b))) (* (sin a) (* (cbrt (sin b)) (cbrt (sin b)))) (* (sin a) (sqrt (sin b))) (sin a) (* (cbrt (sin a)) (sin b)) (* (sqrt (sin a)) (sin b)) (* (sin a) (sin b)) (* r (sin b)) (log (* r (sin b))) (log (* r (sin b))) (exp (* r (sin b))) (pow (* r (sin b)) 3) (* (cbrt (* r (sin b))) (cbrt (* r (sin b)))) (cbrt (* r (sin b))) (pow (* r (sin b)) 3) (sqrt (* r (sin b))) (sqrt (* r (sin b))) (* (sqrt r) (sqrt (sin b))) (* (sqrt r) (sqrt (sin b))) (* r (* (cbrt (sin b)) (cbrt (sin b)))) (* r (sqrt (sin b))) r (* (cbrt r) (sin b)) (* (sqrt r) (sin b)) (* r (sin b)) (exp (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (log (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (exp (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (* (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b))))) (cbrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (pow (- (* (cos b) (cos a)) (* (sin a) (sin b))) 3) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sqrt (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (+ (+ (cos (+ a b)) (cos (+ a b))) 0) (* 2 (* 1 (+ (+ (cos (+ a b)) (cos (+ a b))) 0))) 4 (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)) (+ (* (* (sin a) (sin b)) (+ (* (sin a) (sin b)) (* (cos a) (cos b)))) (* (* (cos a) (cos b)) (* (cos a) (cos b)))) (neg (* (sin a) (sin b))) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))) (+ (* (cos a) (cos b)) (* (sin a) (sin b))) (neg (* (sin a) (sin b))) (+ (* r (+ (* (pow b 3) 1/3) (* (pow b 2) a))) (* r b)) (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (* a b) (* (sin a) (sin b)) (* (sin a) (sin b)) (* r b) (* r (sin b)) (* r (sin b)) (- 1 (+ (* 1/2 (pow a 2)) (* a b))) (- (* (cos b) (cos a)) (* (sin a) (sin b))) (- (* (cos b) (cos a)) (* (sin a) (sin b))) 2.514 * * * [progress]: adding candidates to table 2.783 * * [progress]: iteration 4 / 4 2.783 * * * [progress]: picking best candidate 2.849 * * * * [pick]: Picked # 2.849 * * * [progress]: localizing error 2.867 * * * [progress]: generating rewritten candidates 2.867 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 2) 2.869 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 2 1 1) 2.874 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 2.882 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 2.895 * * * [progress]: generating series expansions 2.895 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 2) 2.895 * [approximate]: Approximating (* (sin b) (sin a)) in (a b) around 0 2.895 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 2.901 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 2.905 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 2.910 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 2.917 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 2.917 * [approximate]: Approximating (* (sin (/ 1 a)) (sin (/ 1 b))) in (a b) around 0 2.919 * [taylor]: Taking taylor expansion of (* (sin (/ 1 a)) (sin (/ 1 b))) in b 2.921 * [taylor]: Taking taylor expansion of (* (sin (/ 1 a)) (sin (/ 1 b))) in b 2.926 * [taylor]: Taking taylor expansion of (* (sin (/ 1 a)) (sin (/ 1 b))) in b 2.934 * [taylor]: Taking taylor expansion of (* (sin (/ 1 a)) (sin (/ 1 b))) in b 2.934 * [approximate]: Approximating (* (sin (/ -1 a)) (sin (/ -1 b))) in (a b) around 0 2.936 * [taylor]: Taking taylor expansion of (* (sin (/ -1 a)) (sin (/ -1 b))) in b 2.938 * [taylor]: Taking taylor expansion of (* (sin (/ -1 a)) (sin (/ -1 b))) in b 2.944 * [taylor]: Taking taylor expansion of (* (sin (/ -1 a)) (sin (/ -1 b))) in b 2.950 * [taylor]: Taking taylor expansion of (* (sin (/ -1 a)) (sin (/ -1 b))) in b 2.951 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 2 1 1) 2.951 * [approximate]: Approximating (* (sin b) (sin a)) in (a b) around 0 2.951 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 2.954 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 2.958 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 2.963 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 2.970 * [taylor]: Taking taylor expansion of (* (sin b) (sin a)) in b 2.970 * [approximate]: Approximating (* (sin (/ 1 a)) (sin (/ 1 b))) in (a b) around 0 2.971 * [taylor]: Taking taylor expansion of (* (sin (/ 1 a)) (sin (/ 1 b))) in b 2.974 * [taylor]: Taking taylor expansion of (* (sin (/ 1 a)) (sin (/ 1 b))) in b 2.982 * [taylor]: Taking taylor expansion of (* (sin (/ 1 a)) (sin (/ 1 b))) in b 2.989 * [taylor]: Taking taylor expansion of (* (sin (/ 1 a)) (sin (/ 1 b))) in b 2.989 * [approximate]: Approximating (* (sin (/ -1 a)) (sin (/ -1 b))) in (a b) around 0 2.991 * [taylor]: Taking taylor expansion of (* (sin (/ -1 a)) (sin (/ -1 b))) in b 2.994 * [taylor]: Taking taylor expansion of (* (sin (/ -1 a)) (sin (/ -1 b))) in b 2.999 * [taylor]: Taking taylor expansion of (* (sin (/ -1 a)) (sin (/ -1 b))) in b 3.006 * [taylor]: Taking taylor expansion of (* (sin (/ -1 a)) (sin (/ -1 b))) in b 3.006 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 3.007 * [approximate]: Approximating (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in (b a) around 0 3.011 * [taylor]: Taking taylor expansion of (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 3.018 * [taylor]: Taking taylor expansion of (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 3.029 * [taylor]: Taking taylor expansion of (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 3.033 * [approximate]: Approximating (/ (sin (/ 1 b)) (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b))))) in (b a) around 0 3.039 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b))))) in a 3.047 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b))))) in a 3.066 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b))))) in a 3.086 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b))))) in a 3.087 * [approximate]: Approximating (/ (sin (/ -1 b)) (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b))))) in (b a) around 0 3.094 * [taylor]: Taking taylor expansion of (/ (sin (/ -1 b)) (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b))))) in a 3.102 * [taylor]: Taking taylor expansion of (/ (sin (/ -1 b)) (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b))))) in a 3.118 * [taylor]: Taking taylor expansion of (/ (sin (/ -1 b)) (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b))))) in a 3.141 * [taylor]: Taking taylor expansion of (/ (sin (/ -1 b)) (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b))))) in a 3.141 * * * * [progress]: [ 4 / 4 ] generating series at (2) 3.141 * [approximate]: Approximating (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in (r b a) around 0 3.152 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in b 3.154 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 3.167 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in b 3.167 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 3.173 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 3.192 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in b 3.192 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 3.192 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 3.201 * [taylor]: Taking taylor expansion of (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) in a 3.205 * [approximate]: Approximating (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in (r b a) around 0 3.237 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in b 3.239 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 3.257 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in b 3.258 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 3.263 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 3.290 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in b 3.290 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 3.290 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 3.300 * [taylor]: Taking taylor expansion of (/ (sin (/ 1 b)) (* r (- (* (cos (/ 1 a)) (cos (/ 1 b))) (* (sin (/ 1 a)) (sin (/ 1 b)))))) in a 3.301 * [approximate]: Approximating (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in (r b a) around 0 3.330 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in b 3.333 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 3.351 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in b 3.352 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 3.358 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 3.390 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in b 3.390 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 3.390 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 3.399 * [taylor]: Taking taylor expansion of (* -1 (/ (sin (/ -1 b)) (* (- (* (cos (/ -1 a)) (cos (/ -1 b))) (* (sin (/ -1 a)) (sin (/ -1 b)))) r))) in a 3.399 * * * [progress]: simplifying candidates 3.400 * [simplify]: Simplifying using # : (log (* (cbrt (exp (* (sin a) (sin b)))) (cbrt (exp (* (sin a) (sin b)))))) (log (cbrt (exp (* (sin a) (sin b))))) (log (sqrt (exp (* (sin a) (sin b))))) (log (sqrt (exp (* (sin a) (sin b))))) (log 1) (log (exp (* (sin a) (sin b)))) (log (exp (sin a))) (log (exp (* (sin a) (sin b)))) (log (exp (sin a))) (log (log (exp (* (sin a) (sin b))))) (exp (log (exp (* (sin a) (sin b))))) (* (cbrt (log (exp (* (sin a) (sin b))))) (cbrt (log (exp (* (sin a) (sin b)))))) (cbrt (log (exp (* (sin a) (sin b))))) (* (* (log (exp (* (sin a) (sin b)))) (log (exp (* (sin a) (sin b))))) (log (exp (* (sin a) (sin b))))) (sqrt (log (exp (* (sin a) (sin b))))) (sqrt (log (exp (* (sin a) (sin b))))) (- (cos (- a b)) (cos (+ a b))) (* (sin a) (sin b)) (+ (log (sin a)) (log (sin b))) (log (* (sin a) (sin b))) (exp (* (sin a) (sin b))) (* (* (* (sin a) (sin a)) (sin a)) (* (* (sin b) (sin b)) (sin b))) (* (cbrt (* (sin a) (sin b))) (cbrt (* (sin a) (sin b)))) (cbrt (* (sin a) (sin b))) (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))) (sqrt (* (sin a) (sin b))) (sqrt (* (sin a) (sin b))) (* (sqrt (sin a)) (sqrt (sin b))) (* (sqrt (sin a)) (sqrt (sin b))) (* (sin a) (* (cbrt (sin b)) (cbrt (sin b)))) (* (sin a) (sqrt (sin b))) (* (sin a) 1) (* (cbrt (sin a)) (sin b)) (* (sqrt (sin a)) (sin b)) (* (sin a) (sin b)) (- (log (sin b)) (log (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (log (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (exp (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (* (cbrt (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (cbrt (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (cbrt (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (* (* (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (sqrt (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (sqrt (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (neg (sin b)) (neg (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (/ (cbrt (sin b)) (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (/ (* (cbrt (sin b)) (cbrt (sin b))) (sqrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (/ (cbrt (sin b)) (sqrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (/ (* (cbrt (sin b)) (cbrt (sin b))) 1) (/ (cbrt (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (/ (sqrt (sin b)) (* (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (/ (sqrt (sin b)) (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (/ (sqrt (sin b)) 1) (/ (sqrt (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (/ 1 (* (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (/ (sin b) (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (/ 1 (sqrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (/ (sin b) (sqrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (/ 1 1) (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (/ 1 (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (/ (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))) (sin b)) (/ (sin b) (* (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (/ (sin b) (sqrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (/ (sin b) 1) (/ (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))) (cbrt (sin b))) (/ (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))) (sqrt (sin b))) (/ (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))) (sin b)) (/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (log (exp (* (sin a) (sin b)))) 3))) (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (log (exp (* (sin a) (sin b)))) (log (exp (* (sin a) (sin b))))))) (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (+ (log r) (- (log (sin b)) (log (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (+ (log r) (log (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (log (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (exp (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* (* (* r r) r) (/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* (* (* r r) r) (* (* (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* (cbrt (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (cbrt (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))))) (cbrt (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* (* (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (sqrt (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (sqrt (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* (sqrt r) (sqrt (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* (sqrt r) (sqrt (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* (sqrt r) (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* (sqrt r) (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* r (* (cbrt (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (cbrt (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))))) (* r (sqrt (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* r (/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))))) (* r (/ (* (cbrt (sin b)) (cbrt (sin b))) (sqrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* r (/ (* (cbrt (sin b)) (cbrt (sin b))) 1)) (* r (/ (sqrt (sin b)) (* (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))))) (* r (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* r (/ (sqrt (sin b)) 1)) (* r (/ 1 (* (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))))) (* r (/ 1 (sqrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* r (/ 1 1)) (* r 1) (* r (sin b)) (* r (/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (log (exp (* (sin a) (sin b)))) 3)))) (* r (/ (sin b) (- (* (* (cos a) (cos b)) (* (cos a) (cos b))) (* (log (exp (* (sin a) (sin b)))) (log (exp (* (sin a) (sin b)))))))) (* (cbrt r) (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (* (sqrt r) (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (* r (sin b)) (* a b) (* (sin b) (sin a)) (* (sin b) (sin a)) (* a b) (* (sin b) (sin a)) (* (sin b) (sin a)) (+ (* a (pow b 2)) (+ (* 1/3 (pow b 3)) b)) (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (+ (* a (* r (pow b 2))) (+ (* r b) (* 1/3 (* r (pow b 3))))) (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) 3.406 * * [simplify]: iteration 0 : 360 enodes (cost 1301 ) 3.413 * * [simplify]: iteration 1 : 1546 enodes (cost 1128 ) 3.442 * * [simplify]: iteration 2 : 5001 enodes (cost 1121 ) 3.447 * [simplify]: Simplified to: (* 2 (log 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a) (sin b)))))) (+ (log r) (log (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))) (+ (log r) (log (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))) (pow (exp r) (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))) (pow (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) 3) (pow (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) 3) (* (cbrt (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (cbrt (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))))) (cbrt (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (pow (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) 3) (sqrt (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (sqrt (* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* (sqrt r) (sqrt (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* (sqrt r) (sqrt (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* (sqrt r) (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* (sqrt r) (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* r (* (cbrt (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) (cbrt (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))))) (* r (sqrt (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* r (/ (* (cbrt (sin b)) (cbrt (sin b))) (* (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))))) (* r (/ (* (cbrt (sin b)) (cbrt (sin b))) (sqrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* (* (cbrt (sin b)) (cbrt (sin b))) r) (* r (/ (sqrt (sin b)) (* (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))))) (* r (/ (sqrt (sin b)) (sqrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (* (sqrt (sin b)) r) (/ r (* (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (cbrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))) (/ r (sqrt (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))) r r (* r (sin b)) (* r (/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (log (exp (* (sin a) (sin b)))) 3)))) (* (/ (sin b) (+ (* (cos a) (cos b)) (* (sin a) (sin b)))) (/ r (- (* (cos b) (cos a)) (* (sin a) (sin b))))) (/ (* (cbrt r) (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (/ (* (sqrt r) (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (* r (sin b)) (* a b) (* (sin a) (sin b)) (* (sin a) (sin b)) (* a b) (* (sin a) (sin b)) (* (sin a) (sin b)) (+ (* (pow b 2) (+ (* b 1/3) a)) b) (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (+ (* r b) (* r (* (pow b 2) (+ (* b 1/3) a)))) (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) (/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b)))) 3.448 * * * [progress]: adding candidates to table 3.964 * [progress]: [Phase 3 of 3] Extracting. 3.964 * * [regime]: Finding splitpoints for: (# # # # # # # # # # # # #) 3.970 * * * [regime-changes]: Trying 3 branch expressions: (b a r) 3.970 * * * * [regimes]: Trying to branch on b from (# # # # # # # # # # # # #) 4.078 * * * * [regimes]: Trying to branch on a from (# # # # # # # # # # # # #) 4.187 * * * * [regimes]: Trying to branch on r from (# # # # # # # # # # # # #) 4.294 * * * [regime]: Found split indices: #