Details

analyze448.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

sample39.0ms

Algorithm

intervals

Results

9.0ms	172×	body	80	valid
6.0ms	22×	body	2560	valid
6.0ms	26×	body	1280	valid
3.0ms	17×	body	640	valid
2.0ms	7×	body	5120	valid
1.0ms	22×	body	80	nan
1.0ms	7×	body	320	valid
1.0ms	11×	body	80	invalid
0.0ms	5×	body	160	valid

simplify196.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (181.0ms)

Iter	Nodes	Cost
0	5071	24

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 32.6b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `insert-posit16` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 74

Calls

4 calls:

15.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
6.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series1.2s

Counts

4 → 12

Calls

4 calls:

417.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
281.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
234.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
261.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	728	764
1	728	764
0	728	764
1	728	764
0	22	11
1	22	11
0	676	357
1	676	357
0	676	357
1	676	357
0	1	3
1	1	3
0	786	92
1	786	92
0	786	92
1	786	92
0	22	11
1	22	11
0	1108	90
1	1108	90
0	1108	90
1	1108	90
0	1	3
1	1	3

simplify117.0ms

Counts

86 → 86

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5066	1913

prune130.0ms

Filtered

64 candidates to 86 candidates (-34.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	69	17	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	17	87

Merged error: 26.6b

Counts

87 → 17

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
1.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
10×	`pow1_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
6×	`add-cube-cbrt_binary64`
4×	`insert-posit16` `sqrt-prod_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`

Counts

4 → 62

Calls

4 calls:

7.0ms	(.f64 (.f64 3 a) c)
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
6.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series924.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(.f64 (.f64 3 a) c)
288.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
232.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
263.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	728	764
1	728	764
0	728	764
1	728	764
0	22	11
1	22	11
0	676	357
1	676	357
0	676	357
1	676	357
0	1	3
1	1	3
0	786	92
1	786	92
0	786	92
1	786	92
0	22	11
1	22	11
0	324	227
1	324	227
0	324	227
1	324	227
0	1	3
1	1	3

simplify89.0ms

Counts

74 → 74

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4878	1150
1	4878	1150

prune80.0ms

Filtered

54 candidates to 74 candidates (-37.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	69	5	74
Fresh	7	9	16
Picked	1	0	1
Done	0	0	0
Total	77	14	91

Merged error: 19.9b

Counts

91 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

2.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
3.4b	(/.f64 (/.f64 (/.f64 (.f64 (.f64 a c) -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) 3) a)
9.2b	(/.f64 (.f64 (.f64 a c) -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

274×	`times-frac_binary64`
140×	`*-un-lft-identity_binary64`
111×	`add-sqr-sqrt_binary64`
110×	`add-cube-cbrt_binary64`
35×	`associate-/l*_binary64`
33×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
26×	`associate-/r/_binary64`
18×	`div-inv_binary64`
15×	`distribute-lft-out_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
14×	`flip3-+_binary64` `flip-+_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
5×	`pow1_binary64`
4×	`insert-posit16`
3×	`sqrt-prod_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 218

Calls

4 calls:

8.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
26.0ms	(/.f64 (/.f64 (/.f64 (.f64 (.f64 a c) -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) 3) a)
16.0ms	(/.f64 (.f64 (.f64 a c) -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series2.2s

Counts

4 → 12

Calls

4 calls:

283.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
1.1s	(/.f64 (/.f64 (/.f64 (.f64 (.f64 a c) -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))) 3) a)
571.0ms	(/.f64 (.f64 (.f64 a c) -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
262.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	728	764
1	728	764
0	728	764
1	728	764
0	22	11
1	22	11
0	2454	323
1	2454	323
0	2454	323
1	2454	323
0	64	3
1	64	3
0	4044	30
1	4044	30
0	4044	30
1	4044	30
0	1	3
1	1	3
0	792	92
1	792	92
0	792	92
1	792	92
0	22	11
1	22	11

simplify173.0ms

Counts

230 → 230

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5029	10122

prune377.0ms

Filtered

186 candidates to 230 candidates (-23.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	223	7	230
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	228	16	244

Merged error: 18.8b

Counts

244 → 16

localize13.0ms

Local error

Found 4 expressions with local error:

2.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
3.4b	(/.f64 (/.f64 (/.f64 (.f64 (.f64 3 a) c) (neg.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))) 3) a)
9.2b	(/.f64 (.f64 (.f64 3 a) c) (neg.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

546×	`times-frac_binary64`
252×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
194×	`add-cube-cbrt_binary64`
59×	`associate-/l*_binary64`
56×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
33×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
29×	`distribute-lft-out_binary64`
26×	`distribute-neg-frac_binary64` `associate-/r/_binary64`
18×	`div-inv_binary64`
15×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
14×	`flip3-+_binary64` `neg-mul-1_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
5×	`pow1_binary64`
4×	`insert-posit16`
3×	`sqrt-prod_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 330

Calls

4 calls:

8.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
33.0ms	(/.f64 (/.f64 (/.f64 (.f64 (.f64 3 a) c) (neg.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))) 3) a)
20.0ms	(/.f64 (.f64 (.f64 3 a) c) (neg.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series2.0s

Counts

4 → 12

Calls

4 calls:

279.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
931.0ms	(/.f64 (/.f64 (/.f64 (.f64 (.f64 3 a) c) (neg.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))) 3) a)
502.0ms	(/.f64 (.f64 (.f64 3 a) c) (neg.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))))
262.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	728	764
1	728	764
0	728	764
1	728	764
0	22	11
1	22	11
0	2120	1312
1	2120	1312
0	2120	1312
1	2120	1312
0	1	3
1	1	3
0	3277	30
1	3277	30
0	3277	30
1	3277	30
0	1	3
1	1	3
0	792	92
1	792	92
0	792	92
1	792	92
0	22	11
1	22	11

simplify232.0ms

Counts

342 → 342

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	5299	16150

prune572.0ms

Filtered

255 candidates to 342 candidates (-34.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	335	7	342
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	339	19	358

Merged error: 17.3b

Counts

358 → 19

regimes296.0ms

Accuracy

84.1% (2.4b remaining)

Error of 20.5b against oracle of 18.1b and baseline of 33.1b

bsearch56.0ms

Steps

Iters	Range		Point
7	1.5520443031153497e-123	4.1821284620795483e-122	8.442885290902578e-123
9	-6.817450176320684e+154	-3.728509989128717e+148	-1.360963170256676e+154

simplify8.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	102	90
1	102	90

end0.0ms

sample1.2s

Algorithm

intervals

Results

301.0ms	1039×	body	2560	valid
264.0ms	5152×	body	80	valid
209.0ms	882×	body	1280	valid
85.0ms	459×	body	640	valid
45.0ms	125×	body	5120	valid
32.0ms	654×	body	80	nan
31.0ms	222×	body	320	valid
20.0ms	387×	body	80	invalid
11.0ms	121×	body	160	valid

Iter	Nodes	Cost
0	728	764
1	728	764
0	728	764
1	728	764
0	22	11
1	22	11
0	676	357
1	676	357
0	676	357
1	676	357
0	1	3
1	1	3
0	786	92
1	786	92
0	786	92
1	786	92
0	22	11
1	22	11
0	324	227
1	324	227
0	324	227
1	324	227
0	1	3
1	1	3

Iter	Nodes	Cost
0	728	764
1	728	764
0	728	764
1	728	764
0	22	11
1	22	11
0	676	357
1	676	357
0	676	357
1	676	357
0	1	3
1	1	3
0	786	92
1	786	92
0	786	92
1	786	92
0	22	11
1	22	11
0	324	227
1	324	227
0	324	227
1	324	227
0	1	3
1	1	3

Details

analyze448.0ms

sample39.0ms

simplify196.0ms

prune6.0ms

localize9.0ms

rewrite39.0ms

series1.2s

simplify117.0ms

prune130.0ms

localize10.0ms

rewrite30.0ms

series924.0ms

simplify89.0ms

prune80.0ms

localize15.0ms

rewrite76.0ms

series2.2s

simplify173.0ms

prune377.0ms

localize13.0ms

rewrite95.0ms

series2.0s

simplify232.0ms

prune572.0ms

regimes296.0ms

bsearch56.0ms

simplify8.0ms

end0.0ms

sample1.2s

Profiling

Iter	Nodes	Cost
0	728	764
1	728	764
0	728	764
1	728	764
0	22	11
1	22	11
0	676	357
1	676	357
0	676	357
1	676	357
0	1	3
1	1	3
0	786	92
1	786	92
0	786	92
1	786	92
0	22	11
1	22	11
0	324	227
1	324	227
0	324	227
1	324	227
0	1	3
1	1	3