Details

analyze460.0ms

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample46.0ms

Algorithm

intervals

Results

9.0ms	167×	body	80	valid
8.0ms	29×	body	2560	valid
7.0ms	31×	body	1280	valid
5.0ms	13×	body	640	valid
2.0ms	36×	body	80	nan
1.0ms	6×	body	320	valid
1.0ms	8×	body	160	valid
1.0ms	2×	body	5120	valid
1.0ms	11×	body	80	invalid

simplify473.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	713	12
1	713	12

prune10.0ms

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: 31.6b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

10.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
15.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
24.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5743	1403

prune81.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	85	9	94
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	85	10	95

Merged error: 4.8b

Counts

95 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
11×	`times-frac_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
4×	`prod-exp_binary64` `difference-of-squares_binary64`
3×	`unswap-sqr_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

17.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
15.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
14.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify40.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4984	1258
1	4984	1258

prune58.0ms

Filtered

66 candidates to 95 candidates (-43.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	94	11	105

Merged error: 4.8b

Counts

105 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac_binary64`
123×	`add-sqr-sqrt_binary64`
96×	`*-un-lft-identity_binary64`
70×	`add-cube-cbrt_binary64`
26×	`difference-of-squares_binary64`
24×	`associate-/r*_binary64`
16×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-lft-out--_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64`
7×	`flip3--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 160

Calls

4 calls:

15.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
15.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4972	3316
1	4972	3316

prune79.0ms

Filtered

100 candidates to 172 candidates (-72.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	0	8	8
Picked	0	1	1
Done	1	1	2
Total	171	12	183

Merged error: 4.8b

Counts

183 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

1.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
21.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
21.0b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
10×	`sqrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`difference-of-squares_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `distribute-lft-out--_binary64`

Counts

4 → 59

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
14.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
14.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
14.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify56.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5078	823

prune38.0ms

Filtered

58 candidates to 71 candidates (-22.4%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	71	12	83

Merged error: 4.8b

Counts

83 → 12

regimes290.0ms

Accuracy

83% (4.9b remaining)

Error of 10.5b against oracle of 5.6b and baseline of 34.2b

bsearch48.0ms

Steps

Iters	Range		Point
10	2.8094764760583883e-83	8.968703192404019e-72	4.2792376823364103e-75
4	-3.130046301571015e+63	-1.9202272889123593e+63	-3.0922394574254323e+63

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	87	36
1	87	36

end0.0ms

sample1.2s

Algorithm

intervals

Results

302.0ms	1077×	body	2560	valid
245.0ms	5118×	body	80	valid
203.0ms	895×	body	1280	valid
80.0ms	436×	body	640	valid
37.0ms	112×	body	5120	valid
35.0ms	779×	body	80	nan
32.0ms	240×	body	320	valid
14.0ms	242×	body	80	invalid
11.0ms	122×	body	160	valid

Details

analyze460.0ms

sample46.0ms

simplify473.0ms

prune10.0ms

localize20.0ms

rewrite33.0ms

series76.0ms

simplify55.0ms

prune81.0ms

localize10.0ms

rewrite37.0ms

series60.0ms

simplify40.0ms

prune58.0ms

localize12.0ms

rewrite39.0ms

series75.0ms

simplify73.0ms

prune79.0ms

localize19.0ms

rewrite23.0ms

series56.0ms

simplify56.0ms

prune38.0ms

regimes290.0ms

bsearch48.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling