Details

analyze334.0ms (12.8%)

Algorithm

1×

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

sample34.0ms (1.3%)

Algorithm

1×

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

simplify21.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	265	15
1	265	15

prune5.0ms (0.2%)

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 (0.4%)

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 2.0 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
29.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite31.0ms (1.2%)

Algorithm

1×	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:

9.0ms	(sqrt.f64 (.f64 2.0 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
8.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series55.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt.f64 (.f64 2.0 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
9.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
7.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify61.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4962	739
1	4962	739

prune112.0ms (4.3%)

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

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.3b	(sqrt.f64 (*.f64 2.0 (-.f64 im re)))

rewrite6.0ms (0.2%)

Algorithm

1×	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 2.0 (-.f64 im re)))

series21.0ms (0.8%)

Counts

1 → 3

Calls

1 calls:

21.0ms

(sqrt.f64 (*.f64 2.0 (-.f64 im re)))

simplify47.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5758	162

prune44.0ms (1.7%)

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

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.3b	(*.f64 (sqrt.f64 2.0) (sqrt.f64 (-.f64 im re)))

rewrite15.0ms (0.6%)

Algorithm

1×	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:

9.0ms	(*.f64 (sqrt.f64 2.0) (sqrt.f64 (-.f64 im re)))
4.0ms	(sqrt.f64 (-.f64 im re))

series31.0ms (1.2%)

Counts

2 → 6

Calls

2 calls:

19.0ms	(*.f64 (sqrt.f64 2.0) (sqrt.f64 (-.f64 im re)))
12.0ms	(sqrt.f64 (-.f64 im re))

simplify56.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4936	522
1	4936	522

prune88.0ms (3.4%)

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

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.2b	(.f64 (sqrt.f64 (sqrt.f64 2.0)) (.f64 (sqrt.f64 (-.f64 im re)) (sqrt.f64 (sqrt.f64 2.0))))
0.2b	(*.f64 (sqrt.f64 (-.f64 im re)) (sqrt.f64 (sqrt.f64 2.0)))

rewrite32.0ms (1.2%)

Algorithm

1×	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:

15.0ms	(.f64 (sqrt.f64 (sqrt.f64 2.0)) (.f64 (sqrt.f64 (-.f64 im re)) (sqrt.f64 (sqrt.f64 2.0))))
11.0ms	(*.f64 (sqrt.f64 (-.f64 im re)) (sqrt.f64 (sqrt.f64 2.0)))
4.0ms	(sqrt.f64 (-.f64 im re))

series59.0ms (2.2%)

Counts

3 → 9

Calls

3 calls:

25.0ms	(*.f64 (sqrt.f64 (-.f64 im re)) (sqrt.f64 (sqrt.f64 2.0)))
21.0ms	(.f64 (sqrt.f64 (sqrt.f64 2.0)) (.f64 (sqrt.f64 (-.f64 im re)) (sqrt.f64 (sqrt.f64 2.0))))
12.0ms	(sqrt.f64 (-.f64 im re))

simplify32.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5241	956

prune109.0ms (4.2%)

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

regimes402.0ms (15.4%)

Accuracy

Total 9.7b remaining (50.1%)

Threshold costs 0b (0%)

bsearch2.0ms (0.1%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	122
1	72	122

end0.0ms (0%)

sample980.0ms (37.5%)

Algorithm

1×

intervals

Results

277.0ms	6044×	body	80	valid
176.0ms	644×	body	2560	valid
109.0ms	500×	body	1280	valid
98.0ms	295×	body	5120	valid
91.0ms	8000×	pre	80	true
50.0ms	285×	body	640	valid
20.0ms	154×	body	320	valid
7.0ms	78×	body	160	valid

Details

analyze334.0ms (12.8%)

sample34.0ms (1.3%)

simplify21.0ms (0.8%)

prune5.0ms (0.2%)

localize10.0ms (0.4%)

rewrite31.0ms (1.2%)

series55.0ms (2.1%)

simplify61.0ms (2.3%)

prune112.0ms (4.3%)

localize5.0ms (0.2%)

rewrite6.0ms (0.2%)

series21.0ms (0.8%)

simplify47.0ms (1.8%)

prune44.0ms (1.7%)

localize9.0ms (0.3%)

rewrite15.0ms (0.6%)

series31.0ms (1.2%)

simplify56.0ms (2.2%)

prune88.0ms (3.4%)

localize8.0ms (0.3%)

rewrite32.0ms (1.2%)

series59.0ms (2.2%)

simplify32.0ms (1.2%)

prune109.0ms (4.2%)

regimes402.0ms (15.4%)

bsearch2.0ms (0.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample980.0ms (37.5%)

Profiling