Details

analyze356.0ms

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

sample38.0ms

Algorithm

intervals

Results

12.0ms	199×	body	80	valid
6.0ms	22×	body	2560	valid
4.0ms	17×	body	1280	valid
3.0ms	9×	body	5120	valid
3.0ms	256×	pre	80	true
1.0ms	4×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	248	15
1	248	15

prune2.0ms

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: 38.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.2b	(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))
9.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+.f64 (.f64 re re) (.f64 im im))
31.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5089	741

prune62.0ms

Filtered

52 candidates to 65 candidates (-25.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	60	5	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	5	66

Merged error: 8.8b

Counts

66 → 5

localize6.0ms

Local error

Found 1 expressions with local error:

0.2b	(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)))

series17.0ms

Counts

1 → 3

Calls

1 calls:

17.0ms

(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

prune24.0ms

Filtered

13 candidates to 16 candidates (-23.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	13	3	16
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	13	8	21

Merged error: 8.7b

Counts

21 → 8

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)))

series28.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(sqrt.f64 (-.f64 im re))
17.0ms	(*.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

prune37.0ms

Filtered

38 candidates to 57 candidates (-50.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	58	7	65

Merged error: 8.7b

Counts

65 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.0b	(log.f64 (sqrt.f64 (-.f64 im re)))
0.3b	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
3.6b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
28×	`log-prod_binary64` `sqrt-prod_binary64`
23×	`*-un-lft-identity_binary64`
20×	`exp-sum_binary64`
15×	`add-cube-cbrt_binary64`
11×	`pow1_binary64` `associate-r_binary64`
8×	`sqrt-div_binary64`
6×	`log-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64` `unswap-sqr_binary64` `log-div_binary64` `exp-prod_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `exp-diff_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64`
2×	`associate-*r/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 im re))
4.0ms	(log.f64 (sqrt.f64 (-.f64 im re)))
15.0ms	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
6.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))

series51.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt.f64 (-.f64 im re))
13.0ms	(log.f64 (sqrt.f64 (-.f64 im re)))
17.0ms	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
11.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))

simplify48.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4988	997
1	4988	997

prune46.0ms

Filtered

74 candidates to 110 candidates (-48.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	109	8	117

Merged error: 8.7b

Counts

117 → 8

regimes223.0ms

Accuracy

42% (11.0b remaining)

Error of 20.7b against oracle of 9.7b and baseline of 28.6b

bsearch69.0ms

Steps

Iters	Range		Point
8	4.857766540650864e-86	4.914180506642986e-82	4.9416823499771336e-86
8	-6.891067251738444e-153	-1.489254594080065e-156	-1.5169450701399806e-156
8	-7.796189668603222e+69	-1.152788478412939e+66	-7.62416769797486e+69
9	-2.107020587490051e+128	-4.234831751072293e+121	-4.324366802345398e+121

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	86
1	64	86

end0.0ms

sample1.0s

Algorithm

intervals

Results

297.0ms	6076×	body	80	valid
196.0ms	687×	body	2560	valid
117.0ms	484×	body	1280	valid
103.0ms	8000×	pre	80	true
99.0ms	280×	body	5120	valid
49.0ms	254×	body	640	valid
19.0ms	141×	body	320	valid
7.0ms	78×	body	160	valid

Details

analyze356.0ms

sample38.0ms

simplify20.0ms

prune2.0ms

localize10.0ms

rewrite27.0ms

series52.0ms

simplify49.0ms

prune62.0ms

localize6.0ms

rewrite5.0ms

series17.0ms

simplify34.0ms

prune24.0ms

localize7.0ms

rewrite14.0ms

series28.0ms

simplify43.0ms

prune37.0ms

localize10.0ms

rewrite32.0ms

series51.0ms

simplify48.0ms

prune46.0ms

regimes223.0ms

bsearch69.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling