Details

analyze343.0ms

Algorithm

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

sample35.0ms

Algorithm

intervals

Results

9.0ms	192×	body	80	valid
6.0ms	22×	body	2560	valid
4.0ms	19×	body	1280	valid
3.0ms	256×	pre	80	true
3.0ms	8×	body	5120	valid
2.0ms	10×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	248	15
1	248	15

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 38.8b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.2b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
0.2b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64` `pow1_binary64`
7×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`sqrt-pow1_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-*r/_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 53

Calls

4 calls:

5.0ms	(+.f64 (.f64 re re) (.f64 im im))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
9.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+.f64 (.f64 re re) (.f64 im im))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
32.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
11.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify48.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5089	741

prune104.0ms

Filtered

52 candidates to 65 candidates (-25.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	55	10	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	10	66

Merged error: 11.8b

Counts

66 → 10

localize6.0ms

Local error

Found 1 expressions with local error:

0.3b	(sqrt.f64 (*.f64 2 (-.f64 im re)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1_binary64`
2×	`associate-*r/_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1/2_binary64` `flip3--_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `flip--_binary64` `sqrt-prod_binary64`

Counts

1 → 13

Calls

1 calls:

5.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

simplify34.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4961	162
1	4961	162

prune44.0ms

Filtered

13 candidates to 16 candidates (-23.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	14	2	16
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	14	12	26

Merged error: 11.6b

Counts

26 → 12

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.3b	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
17×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
8×	`associate-r_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`associate-l_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `pow1/2_binary64` `sqrt-pow1_binary64`
2×	`add-log-exp_binary64` `flip3--_binary64` `associate-*r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
1×	`cbrt-unprod_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

2 → 51

Calls

2 calls:

3.0ms	(sqrt.f64 (-.f64 im re))
9.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))

series33.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(sqrt.f64 (-.f64 im re))
21.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))

simplify43.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4971	522
1	4971	522

prune71.0ms

Filtered

38 candidates to 57 candidates (-50.0%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	56	13	69

Merged error: 11.6b

Counts

69 → 13

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.2b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (-.f64 im re)) (sqrt.f64 (sqrt.f64 2))))
0.2b	(*.f64 (sqrt.f64 (-.f64 im re)) (sqrt.f64 (sqrt.f64 2)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

37×	`sqrt-prod_binary64`
29×	`add-sqr-sqrt_binary64`
17×	`associate-l_binary64`
16×	`*-un-lft-identity_binary64` `pow1_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow-prod-down_binary64` `associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1/2_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `sqrt-div_binary64`
4×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-*l/_binary64`
3×	`add-log-exp_binary64` `flip3--_binary64` `sqrt-unprod_binary64` `flip--_binary64`
2×	`associate-r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `-commutative_binary64`
1×	`rem-sqrt-square_binary64`

Counts

3 → 85

Calls

3 calls:

4.0ms	(sqrt.f64 (-.f64 im re))
14.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (-.f64 im re)) (sqrt.f64 (sqrt.f64 2))))
11.0ms	(*.f64 (sqrt.f64 (-.f64 im re)) (sqrt.f64 (sqrt.f64 2)))

series58.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(sqrt.f64 (-.f64 im re))
19.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (sqrt.f64 (-.f64 im re)) (sqrt.f64 (sqrt.f64 2))))
26.0ms	(*.f64 (sqrt.f64 (-.f64 im re)) (sqrt.f64 (sqrt.f64 2)))

simplify34.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5196	952

prune78.0ms

Filtered

63 candidates to 94 candidates (-49.2%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	94	13	107

Merged error: 11.6b

Counts

107 → 13

regimes413.0ms

Accuracy

48.9% (9.7b remaining)

Error of 19.3b against oracle of 9.7b and baseline of 28.6b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	122
1	72	122

end0.0ms

sample1.0s

Algorithm

intervals

Results

280.0ms	6044×	body	80	valid
175.0ms	644×	body	2560	valid
112.0ms	500×	body	1280	valid
104.0ms	295×	body	5120	valid
102.0ms	8000×	pre	80	true
53.0ms	285×	body	640	valid
20.0ms	154×	body	320	valid
7.0ms	78×	body	160	valid

Details

analyze343.0ms

sample35.0ms

simplify19.0ms

prune3.0ms

localize10.0ms

rewrite27.0ms

series60.0ms

simplify48.0ms

prune104.0ms

localize6.0ms

rewrite5.0ms

series19.0ms

simplify34.0ms

prune44.0ms

localize7.0ms

rewrite14.0ms

series33.0ms

simplify43.0ms

prune71.0ms

localize9.0ms

rewrite33.0ms

series58.0ms

simplify34.0ms

prune78.0ms

regimes413.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling