Details

analyze43.0ms

Algorithm

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

sample39.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify109.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5377	79

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 54.3b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
0.1b	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
37.5b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
46.3b	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

86×	`times-frac_binary64`
66×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`
61×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
46×	`add-sqr-sqrt_binary64`
44×	`*-un-lft-identity_binary64` `frac-times_binary64`
34×	`associate-*r/_binary64`
30×	`add-cube-cbrt_binary64`
28×	`difference-of-squares_binary64`
22×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-*l/_binary64`
19×	`cbrt-undiv_binary64` `div-exp_binary64`
16×	`pow1_binary64`
14×	`difference-of-sqr-1_binary64` `associate-/l*_binary64`
9×	`associate-/l/_binary64` `div-inv_binary64`
7×	`associate-/r*_binary64`
6×	`associate-r_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-l_binary64` `insert-posit16`
3×	`swap-sqr_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `pow-sqr_binary64` `flip--_binary64` `pow2_binary64`

Counts

4 → 232

Calls

4 calls:

17.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
17.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
54.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
34.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

series2.7s

Counts

4 → 12

Calls

4 calls:

357.0ms	(.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))
553.0ms	(.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i))))
912.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
844.0ms	(/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	4347	1379
1	4347	1379
0	4347	1379
1	4347	1379
0	1	3
1	1	3
0	4352	1774
1	4352	1774
0	4352	1774
1	4352	1774
0	1	3
1	1	3
0	3507	465
1	3507	465
0	3507	465
1	3507	465
0	1	3
1	1	3
0	1086	121
1	1086	121
0	1086	121
1	1086	121
0	1	3
1	1	3

simplify223.0ms

Counts

244 → 244

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5152	19565

prune453.0ms

Filtered

150 candidates to 244 candidates (-62.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	236	8	244
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	237	8	245

Merged error: 34.5b

Counts

245 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
0.3b	(/.f64 (/.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
35.3b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
36.3b	(/.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac_binary64`
174×	`*-un-lft-identity_binary64`
170×	`add-sqr-sqrt_binary64`
106×	`add-cube-cbrt_binary64`
34×	`associate-/r/_binary64`
32×	`difference-of-squares_binary64`
28×	`associate-/l*_binary64`
25×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`flip3-+_binary64` `flip-+_binary64`
17×	`associate-/r*_binary64` `div-inv_binary64`
16×	`difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
11×	`cbrt-undiv_binary64` `div-exp_binary64`
10×	`distribute-lft-out_binary64`
6×	`associate-/l/_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `insert-posit16`
2×	`cbrt-unprod_binary64` `associate-*r/_binary64` `prod-exp_binary64`
1×	`flip3--_binary64` `flip--_binary64`

Counts

4 → 272

Calls

4 calls:

27.0ms	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
33.0ms	(/.f64 (/.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
20.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
20.0ms	(/.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series2.1s

Counts

4 → 12

Calls

4 calls:

293.0ms	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
285.0ms	(/.f64 (/.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1))
762.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
796.0ms	(/.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	4356	163
1	4356	163
0	4356	163
1	4356	163
0	1	3
1	1	3
0	4335	117
1	4335	117
0	4335	117
1	4335	117
0	1	3
1	1	3
0	5186	2724
0	5186	2724
0	1	3
1	1	3
0	5123	1867
0	5123	1867
0	1	3
1	1	3

simplify194.0ms

Counts

284 → 284

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5623	17022

prune519.0ms

Filtered

187 candidates to 284 candidates (-51.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	281	3	284
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	284	8	292

Merged error: 34.5b

Counts

292 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
0.3b	(/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1) (/.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))))
35.3b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
36.3b	(/.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac_binary64`
174×	`*-un-lft-identity_binary64`
170×	`add-sqr-sqrt_binary64`
106×	`add-cube-cbrt_binary64`
33×	`associate-/r/_binary64`
32×	`difference-of-squares_binary64`
25×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`associate-/l*_binary64`
18×	`flip3-+_binary64` `flip-+_binary64`
17×	`div-inv_binary64`
16×	`difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
11×	`cbrt-undiv_binary64` `div-exp_binary64`
10×	`distribute-lft-out_binary64`
7×	`associate-/l/_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `insert-posit16`
2×	`cbrt-unprod_binary64` `associate-*r/_binary64` `prod-exp_binary64`
1×	`flip3--_binary64` `div-sub_binary64` `flip--_binary64`

Counts

4 → 273

Calls

4 calls:

27.0ms	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
30.0ms	(/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1) (/.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))))
19.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
20.0ms	(/.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

series2.2s

Counts

4 → 12

Calls

4 calls:

290.0ms	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 i 2)) 1))
343.0ms	(/.f64 (-.f64 (+.f64 (+.f64 alpha beta) (.f64 i 2)) 1) (/.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (.f64 i 2))))
757.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
786.0ms	(/.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)) (+.f64 (+.f64 alpha beta) (*.f64 i 2)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	4356	163
1	4356	163
0	4356	163
1	4356	163
0	1	3
1	1	3
0	4335	117
1	4335	117
0	4335	117
1	4335	117
0	1	3
1	1	3
0	4596	809
1	4596	809
0	4596	809
1	4596	809
0	1	3
1	1	3
0	5123	1867
0	5123	1867
0	1	3
1	1	3

simplify204.0ms

Counts

285 → 285

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4996	17111
1	4996	17111

prune543.0ms

Filtered

188 candidates to 285 candidates (-51.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	285	8	293

Merged error: 34.5b

Counts

293 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

35.3b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
37.0b	(cbrt.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)))
37.0b	(cbrt.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)))
37.0b	(cbrt.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `cbrt-prod_binary64`
6×	`cbrt-div_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `insert-posit16`
3×	`associate-/r*_binary64` `pow1/3_binary64` `times-frac_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `div-exp_binary64`
1×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 68

Calls

4 calls:

17.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
11.0ms	(cbrt.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)))
10.0ms	(cbrt.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)))
11.0ms	(cbrt.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)))

series1.2s

Counts

4 → 12

Calls

4 calls:

760.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (+.f64 alpha beta) (.f64 i 2)))
159.0ms	(cbrt.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)))
159.0ms	(cbrt.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)))
162.0ms	(cbrt.f64 (+.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 alpha beta)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	431	1799
1	431	1799
0	431	1799
1	431	1799
0	22	11
1	22	11
0	431	1799
1	431	1799
0	431	1799
1	431	1799
0	22	11
1	22	11
0	431	1799
1	431	1799
0	431	1799
1	431	1799
0	22	11
1	22	11
0	4335	117
1	4335	117
0	4335	117
1	4335	117
0	1	3
1	1	3

simplify97.0ms

Counts

80 → 80

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5149	1988

prune206.0ms

Filtered

70 candidates to 80 candidates (-14.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	80	8	88

Merged error: 34.5b

Counts

88 → 8

regimes112.0ms

Accuracy

30.7% (2.6b remaining)

Error of 36.4b against oracle of 33.9b and baseline of 37.5b

bsearch36.0ms

Steps

Iters	Range		Point
9	1.328684977000544e+191	3.7787918522221063e+198	7.276070824574049e+194

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	45	92
1	45	92

end0.0ms

sample1.0s

Algorithm

intervals

Results

643.0ms	8000×	body	80	valid
177.0ms	8000×	pre	80	true

Details

analyze43.0ms

sample39.0ms

simplify109.0ms

prune4.0ms

localize16.0ms

rewrite139.0ms

series2.7s

simplify223.0ms

prune453.0ms

localize19.0ms

rewrite117.0ms

series2.1s

simplify194.0ms

prune519.0ms

localize19.0ms

rewrite113.0ms

series2.2s

simplify204.0ms

prune543.0ms

localize29.0ms

rewrite50.0ms

series1.2s

simplify97.0ms

prune206.0ms

regimes112.0ms

bsearch36.0ms

simplify7.0ms

end0.0ms

sample1.0s

Profiling