Details

analyze345.0ms

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

sample34.0ms

Algorithm

intervals

Results

9.0ms	203×	body	80	valid
6.0ms	21×	body	2560	valid
3.0ms	256×	pre	80	true
3.0ms	14×	body	1280	valid
3.0ms	9×	body	5120	valid
1.0ms	4×	body	640	valid
1.0ms	5×	body	320	valid

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	250	23
1	250	23

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: 38.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.2b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.3b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite30.0ms

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:

8.0ms	(+.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)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+.f64 (.f64 re re) (.f64 im im))
106.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
28.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
25.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify106.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4963	1134
1	4963	1134

prune73.0ms

Filtered

52 candidates to 65 candidates (-25.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	58	7	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	7	66

Merged error: 8.5b

Counts

66 → 7

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)))

series55.0ms

Counts

1 → 3

Calls

1 calls:

55.0ms

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

simplify112.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4947	255
1	4947	255

prune18.0ms

Filtered

13 candidates to 16 candidates (-23.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	16	7	23

Merged error: 8.2b

Counts

23 → 7

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.4b	(*.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)))

series90.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(sqrt.f64 (-.f64 im re))
58.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))

simplify69.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5001	838

prune41.0ms

Filtered

37 candidates to 57 candidates (-54.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	56	8	64

Merged error: 8.2b

Counts

64 → 8

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.2b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (sqrt.f64 (-.f64 im re)) (cbrt.f64 (sqrt.f64 2))))
0.3b	(*.f64 (sqrt.f64 (-.f64 im re)) (cbrt.f64 (sqrt.f64 2)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 77

Calls

3 calls:

3.0ms	(sqrt.f64 (-.f64 im re))
15.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (sqrt.f64 (-.f64 im re)) (cbrt.f64 (sqrt.f64 2))))
10.0ms	(*.f64 (sqrt.f64 (-.f64 im re)) (cbrt.f64 (sqrt.f64 2)))

series215.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(sqrt.f64 (-.f64 im re))
66.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (sqrt.f64 (-.f64 im re)) (cbrt.f64 (sqrt.f64 2))))
111.0ms	(*.f64 (sqrt.f64 (-.f64 im re)) (cbrt.f64 (sqrt.f64 2)))

simplify66.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5046	1426

prune73.0ms

Filtered

55 candidates to 86 candidates (-56.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	86	8	94

Merged error: 8.2b

Counts

94 → 8

regimes113.0ms

Accuracy

50.4% (9.9b remaining)

Error of 19.1b against oracle of 9.2b and baseline of 29.2b

bsearch75.0ms

Steps

Iters	Range	Point
9	6.07957724680453e+32	1.178861782811963e+39	2.3022147910728526e+34
5	-1.8753115706695628e-136	-4.967375807539172e-137	-5.097372440926994e-137
9	-2.374504773962348e+117	-3.876979159476512e+109	-1.2016967219475596e+114

Iters

Range

Point

6.07957724680453e+32

1.178861782811963e+39

2.3022147910728526e+34

-1.8753115706695628e-136

-4.967375807539172e-137

-5.097372440926994e-137

-2.374504773962348e+117

-3.876979159476512e+109

-1.2016967219475596e+114

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	132
1	68	132

end0.0ms

sample1.0s

Algorithm

intervals

Results

282.0ms	6103×	body	80	valid
182.0ms	668×	body	2560	valid
102.0ms	448×	body	1280	valid
99.0ms	8000×	pre	80	true
94.0ms	287×	body	5120	valid
55.0ms	282×	body	640	valid
21.0ms	149×	body	320	valid
5.0ms	63×	body	160	valid

Details

analyze345.0ms

sample34.0ms

simplify34.0ms

prune2.0ms

localize10.0ms

rewrite30.0ms

series181.0ms

simplify106.0ms

prune73.0ms

localize6.0ms

rewrite5.0ms

series55.0ms

simplify112.0ms

prune18.0ms

localize7.0ms

rewrite14.0ms

series90.0ms

simplify69.0ms

prune41.0ms

localize10.0ms

rewrite31.0ms

series215.0ms

simplify66.0ms

prune73.0ms

regimes113.0ms

bsearch75.0ms

simplify4.0ms

end0.0ms

sample1.0s

Profiling