8.956 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.011 * * * [progress]: [2/2] Setting up program. 0.012 * [progress]: [Phase 2 of 3] Improving. 0.013 * [simplify]: Simplifying using # : (sqrt (+ (* x x) (* y y))) 0.015 * * [simplify]: iteration 0 : 7 enodes (cost 4 ) 0.016 * * [simplify]: iteration 1 : 7 enodes (cost 4 ) 0.016 * [simplify]: Simplified to: (sqrt (+ (* x x) (* y y))) 0.017 * * [progress]: iteration 1 / 4 0.017 * * * [progress]: picking best candidate 0.018 * * * * [pick]: Picked # 0.018 * * * [progress]: localizing error 0.024 * * * [progress]: generating rewritten candidates 0.024 * * * * [progress]: [ 1 / 2 ] rewriting at (2) 0.028 * * * * [progress]: [ 2 / 2 ] rewriting at (2 1) 0.031 * * * [progress]: generating series expansions 0.031 * * * * [progress]: [ 1 / 2 ] generating series at (2) 0.031 * [approximate]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in (x y) around 0 0.031 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in y 0.032 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in y 0.032 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.032 * [taylor]: Taking taylor expansion of x in y 0.032 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.032 * [taylor]: Taking taylor expansion of y in y 0.032 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in x 0.032 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.032 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.032 * [taylor]: Taking taylor expansion of x in x 0.032 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.032 * [taylor]: Taking taylor expansion of y in x 0.033 * [taylor]: Taking taylor expansion of (sqrt (+ (pow x 2) (pow y 2))) in x 0.033 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.033 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.033 * [taylor]: Taking taylor expansion of x in x 0.033 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.033 * [taylor]: Taking taylor expansion of y in x 0.033 * [taylor]: Taking taylor expansion of y in y 0.034 * [taylor]: Taking taylor expansion of 0 in y 0.035 * [taylor]: Taking taylor expansion of (/ 1/2 y) in y 0.035 * [taylor]: Taking taylor expansion of 1/2 in y 0.035 * [taylor]: Taking taylor expansion of y in y 0.037 * [taylor]: Taking taylor expansion of 0 in y 0.037 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in (x y) around 0 0.037 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in y 0.037 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.037 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.037 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.037 * [taylor]: Taking taylor expansion of x in y 0.038 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.038 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.038 * [taylor]: Taking taylor expansion of y in y 0.040 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.040 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.040 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.040 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.040 * [taylor]: Taking taylor expansion of x in x 0.040 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.040 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.040 * [taylor]: Taking taylor expansion of y in x 0.042 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.042 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.042 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.042 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.043 * [taylor]: Taking taylor expansion of x in x 0.043 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.043 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.043 * [taylor]: Taking taylor expansion of y in x 0.045 * [taylor]: Taking taylor expansion of 1 in y 0.045 * [taylor]: Taking taylor expansion of 0 in y 0.047 * [taylor]: Taking taylor expansion of (/ 1/2 (pow y 2)) in y 0.047 * [taylor]: Taking taylor expansion of 1/2 in y 0.047 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.047 * [taylor]: Taking taylor expansion of y in y 0.050 * [taylor]: Taking taylor expansion of 0 in y 0.051 * [approximate]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in (x y) around 0 0.051 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in y 0.051 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.051 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.051 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.051 * [taylor]: Taking taylor expansion of x in y 0.051 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.051 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.051 * [taylor]: Taking taylor expansion of y in y 0.053 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.054 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.054 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.054 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.054 * [taylor]: Taking taylor expansion of x in x 0.054 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.054 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.054 * [taylor]: Taking taylor expansion of y in x 0.056 * [taylor]: Taking taylor expansion of (sqrt (+ (/ 1 (pow x 2)) (/ 1 (pow y 2)))) in x 0.056 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.056 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.056 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.056 * [taylor]: Taking taylor expansion of x in x 0.056 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.056 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.057 * [taylor]: Taking taylor expansion of y in x 0.058 * [taylor]: Taking taylor expansion of 1 in y 0.058 * [taylor]: Taking taylor expansion of 0 in y 0.060 * [taylor]: Taking taylor expansion of (/ 1/2 (pow y 2)) in y 0.060 * [taylor]: Taking taylor expansion of 1/2 in y 0.060 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.060 * [taylor]: Taking taylor expansion of y in y 0.063 * [taylor]: Taking taylor expansion of 0 in y 0.064 * * * * [progress]: [ 2 / 2 ] generating series at (2 1) 0.065 * [approximate]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in (x y) around 0 0.065 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in y 0.065 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.065 * [taylor]: Taking taylor expansion of x in y 0.065 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.065 * [taylor]: Taking taylor expansion of y in y 0.065 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.065 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.065 * [taylor]: Taking taylor expansion of x in x 0.065 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.065 * [taylor]: Taking taylor expansion of y in x 0.065 * [taylor]: Taking taylor expansion of (+ (pow x 2) (pow y 2)) in x 0.065 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.065 * [taylor]: Taking taylor expansion of x in x 0.065 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.065 * [taylor]: Taking taylor expansion of y in x 0.065 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.065 * [taylor]: Taking taylor expansion of y in y 0.065 * [taylor]: Taking taylor expansion of 0 in y 0.066 * [taylor]: Taking taylor expansion of 1 in y 0.067 * [taylor]: Taking taylor expansion of 0 in y 0.070 * [taylor]: Taking taylor expansion of 0 in y 0.070 * [approximate]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in (x y) around 0 0.070 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.070 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.070 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.070 * [taylor]: Taking taylor expansion of x in y 0.070 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.070 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.070 * [taylor]: Taking taylor expansion of y in y 0.071 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.071 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.071 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.071 * [taylor]: Taking taylor expansion of x in x 0.071 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.071 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.071 * [taylor]: Taking taylor expansion of y in x 0.071 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.071 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.071 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.071 * [taylor]: Taking taylor expansion of x in x 0.072 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.072 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.072 * [taylor]: Taking taylor expansion of y in x 0.072 * [taylor]: Taking taylor expansion of 1 in y 0.073 * [taylor]: Taking taylor expansion of 0 in y 0.074 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.074 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.074 * [taylor]: Taking taylor expansion of y in y 0.076 * [taylor]: Taking taylor expansion of 0 in y 0.079 * [taylor]: Taking taylor expansion of 0 in y 0.080 * [approximate]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in (x y) around 0 0.080 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in y 0.080 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in y 0.080 * [taylor]: Taking taylor expansion of (pow x 2) in y 0.080 * [taylor]: Taking taylor expansion of x in y 0.080 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.080 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.080 * [taylor]: Taking taylor expansion of y in y 0.081 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.081 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.081 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.081 * [taylor]: Taking taylor expansion of x in x 0.081 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.081 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.081 * [taylor]: Taking taylor expansion of y in x 0.081 * [taylor]: Taking taylor expansion of (+ (/ 1 (pow x 2)) (/ 1 (pow y 2))) in x 0.081 * [taylor]: Taking taylor expansion of (/ 1 (pow x 2)) in x 0.081 * [taylor]: Taking taylor expansion of (pow x 2) in x 0.082 * [taylor]: Taking taylor expansion of x in x 0.082 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in x 0.082 * [taylor]: Taking taylor expansion of (pow y 2) in x 0.082 * [taylor]: Taking taylor expansion of y in x 0.082 * [taylor]: Taking taylor expansion of 1 in y 0.086 * [taylor]: Taking taylor expansion of 0 in y 0.087 * [taylor]: Taking taylor expansion of (/ 1 (pow y 2)) in y 0.087 * [taylor]: Taking taylor expansion of (pow y 2) in y 0.087 * [taylor]: Taking taylor expansion of y in y 0.089 * [taylor]: Taking taylor expansion of 0 in y 0.092 * [taylor]: Taking taylor expansion of 0 in y 0.093 * * * [progress]: simplifying candidates 0.094 * [simplify]: Simplifying using # : (log (sqrt (+ (* x x) (* y y)))) (exp (sqrt (+ (* x x) (* y y)))) (* (cbrt (sqrt (+ (* x x) (* y y)))) (cbrt (sqrt (+ (* x x) (* y y))))) (cbrt (sqrt (+ (* x x) (* y y)))) (* (* (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y)))) (sqrt (+ (* x x) (* y y)))) (sqrt (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y))))) (sqrt (cbrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt 1) (sqrt (+ (* x x) (* y y))) (sqrt (+ (pow (* x x) 3) (pow (* y y) 3))) (sqrt (+ (* (* x x) (* x x)) (- (* (* y y) (* y y)) (* (* x x) (* y y))))) (sqrt (- (* (* x x) (* x x)) (* (* y y) (* y y)))) (sqrt (- (* x x) (* y y))) (/ 1 2) (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) (* (exp (* x x)) (exp (* y y))) (log (+ (* x x) (* y y))) (exp (+ (* x x) (* y y))) (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y))) (* (* (+ (* x x) (* y y)) (+ (* x x) (* y y))) (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))) (+ (pow (* x x) 3) (pow (* y y) 3)) (+ (* (* x x) (* x x)) (- (* (* y y) (* y y)) (* (* x x) (* y y)))) (- (* (* x x) (* x x)) (* (* y y) (* y y))) (- (* x x) (* y y)) y x (* -1 x) (+ (pow x 2) (pow y 2)) (+ (pow x 2) (pow y 2)) (+ (pow x 2) (pow y 2)) 0.097 * * [simplify]: iteration 0 : 125 enodes (cost 177 ) 0.100 * * [simplify]: iteration 1 : 530 enodes (cost 163 ) 0.108 * * [simplify]: iteration 2 : 1540 enodes (cost 163 ) 0.142 * * [simplify]: iteration 3 : 5001 enodes (cost 162 ) 0.143 * [simplify]: Simplified to: (log (sqrt (+ (* x x) (* y y)))) (exp (sqrt (+ (* x x) (* y y)))) (* (cbrt (sqrt (+ (* x x) (* y y)))) (cbrt (sqrt (+ (* x x) (* y y))))) (cbrt (sqrt (+ (* x x) (* y y)))) (pow (sqrt (+ (* x x) (* y y))) 3) (fabs (cbrt (+ (* x x) (* y y)))) (sqrt (cbrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) 1 (sqrt (+ (* x x) (* y y))) (sqrt (+ (pow (* x x) 3) (pow (* y y) 3))) (sqrt (+ (* (* x x) (* x x)) (- (* (* y y) (* y y)) (* (* x x) (* y y))))) (sqrt (- (* (* x x) (* x x)) (* (* y y) (* y y)))) (sqrt (- (* x x) (* y y))) 1/2 (sqrt (sqrt (+ (* x x) (* y y)))) (sqrt (sqrt (+ (* x x) (* y y)))) (exp (+ (* x x) (* y y))) (log (+ (* x x) (* y y))) (exp (+ (* x x) (* y y))) (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y))) (pow (+ (* x x) (* y y)) 3) (sqrt (+ (* x x) (* y y))) (sqrt (+ (* x x) (* y y))) (+ (pow (* x x) 3) (pow (* y y) 3)) (- (pow y 4) (- (* (* x x) (* y y)) (pow x 4))) (+ (* (- (pow y 3)) y) (pow x 4)) (- (* x x) (* y y)) y x (* -1 x) (+ (* x x) (* y y)) (+ (* x x) (* y y)) (+ (* x x) (* y y)) 0.143 * * * [progress]: adding candidates to table 0.212 * * [progress]: iteration 2 / 4 0.212 * * * [progress]: picking best candidate 0.215 * * * * [pick]: Picked # 0.215 * * * [progress]: localizing error 0.216 * * * [progress]: generating rewritten candidates 0.216 * * * [progress]: generating series expansions 0.216 * * * [progress]: simplifying candidates 0.216 * [simplify]: Simplifying using # : 0.218 * * [simplify]: iteration 0 : 0 enodes (cost 0 ) 0.218 * [simplify]: Simplified to: 0.218 * * * [progress]: adding candidates to table 0.219 * * [progress]: iteration 3 / 4 0.219 * * * [progress]: picking best candidate 0.220 * * * * [pick]: Picked # 0.220 * * * [progress]: localizing error 0.222 * * * [progress]: generating rewritten candidates 0.222 * * * [progress]: generating series expansions 0.222 * * * [progress]: simplifying candidates 0.223 * [simplify]: Simplifying using # : 0.225 * * [simplify]: iteration 0 : 0 enodes (cost 0 ) 0.226 * [simplify]: Simplified to: 0.226 * * * [progress]: adding candidates to table 0.226 * * [progress]: iteration 4 / 4 0.226 * * * [progress]: picking best candidate 0.227 * * * * [pick]: Picked # 0.227 * * * [progress]: localizing error 0.228 * * * [progress]: generating rewritten candidates 0.228 * * * [progress]: generating series expansions 0.228 * * * [progress]: simplifying candidates 0.228 * [simplify]: Simplifying using # : 0.231 * * [simplify]: iteration 0 : 0 enodes (cost 0 ) 0.231 * [simplify]: Simplified to: 0.231 * * * [progress]: adding candidates to table 0.231 * [progress]: [Phase 3 of 3] Extracting. 0.231 * * [regime]: Finding splitpoints for: (# # # #) 0.231 * * * [regime-changes]: Trying 6 branch expressions: ((* y y) (* x x) (+ (* x x) (* y y)) (sqrt (+ (* x x) (* y y))) y x) 0.231 * * * * [regimes]: Trying to branch on (* y y) from (# # # #) 0.258 * * * * [regimes]: Trying to branch on (* y y) from (# # #) 0.284 * * * * [regimes]: Trying to branch on (* x x) from (# # # #) 0.302 * * * * [regimes]: Trying to branch on (* x x) from (# #) 0.315 * * * * [regimes]: Trying to branch on (+ (* x x) (* y y)) from (# # # #) 0.337 * * * * [regimes]: Trying to branch on (sqrt (+ (* x x) (* y y))) from (# # # #) 0.365 * * * * [regimes]: Trying to branch on y from (# # # #) 0.413 * * * * [regimes]: Trying to branch on x from (# # # #) 0.451 * * * [regime]: Found split indices: #