Details

analyze353.0ms

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

sample40.0ms

Algorithm

intervals

Results

9.0ms	24×	body	2560	valid
9.0ms	182×	body	80	valid
4.0ms	13×	body	5120	valid
4.0ms	19×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	9×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	2×	body	160	valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	265	15
1	265	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: 39.6b

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 2.0 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.0b	(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 2.0 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+.f64 (.f64 re re) (.f64 im im))
31.0ms	(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	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4962	739
1	4962	739

prune98.0ms

Filtered

52 candidates to 65 candidates (-25.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	58	7	65
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	8	66

Merged error: 11.6b

Counts

66 → 8

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

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 2.0 (-.f64 im re)))

series17.0ms

Counts

1 → 3

Calls

1 calls:

17.0ms

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

simplify47.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5758	162

prune40.0ms

Filtered

13 candidates to 16 candidates (-23.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	13	3	16
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	13	11	24

Merged error: 11.6b

Counts

24 → 11

localize7.0ms

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)))

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

series28.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(sqrt.f64 (-.f64 im re))
17.0ms	(*.f64 (sqrt.f64 2.0) (sqrt.f64 (-.f64 im re)))

simplify56.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4936	522
1	4936	522

prune67.0ms

Filtered

38 candidates to 57 candidates (-50.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	57	11	68

Merged error: 11.6b

Counts

68 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (sqrt.f64 (-.f64 im re)))
0.0b	(sqrt.f64 (-.f64 im re))
0.3b	(*.f64 (sqrt.f64 2.0) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
3.3b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))

rewrite33.0ms

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:

5.0ms	(log.f64 (sqrt.f64 (-.f64 im re)))
4.0ms	(sqrt.f64 (-.f64 im re))
13.0ms	(*.f64 (sqrt.f64 2.0) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
8.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(log.f64 (sqrt.f64 (-.f64 im re)))
11.0ms	(sqrt.f64 (-.f64 im re))
17.0ms	(*.f64 (sqrt.f64 2.0) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
11.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))

simplify77.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4955	997
1	4955	997

prune84.0ms

Filtered

74 candidates to 110 candidates (-48.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	2	6	8
Picked	1	0	1
Done	0	2	2
Total	110	11	121

Merged error: 11.6b

Counts

121 → 11

regimes705.0ms

Accuracy

49.5% (10.1b remaining)

Error of 20.0b against oracle of 9.9b and baseline of 29.8b

bsearch47.0ms

Steps

Iters	Range		Point
7	1.0250922956797423e-98	3.9960023839108e-97	1.040253303888319e-98
9	-4.18142418170851e-60	-2.756128105475179e-68	-2.8053796276591436e-68
7	-4.285299441618348e+123	-2.2129268921572134e+122	-3.0912337318531483e+123

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	63
1	59	63

end0.0ms

sample1.0s

Algorithm

intervals

Results

282.0ms	5958×	body	80	valid
201.0ms	687×	body	2560	valid
116.0ms	499×	body	1280	valid
112.0ms	305×	body	5120	valid
95.0ms	8000×	pre	80	true
53.0ms	291×	body	640	valid
23.0ms	174×	body	320	valid
8.0ms	86×	body	160	valid

Details

analyze353.0ms

sample40.0ms

simplify21.0ms

prune3.0ms

localize10.0ms

rewrite27.0ms

series51.0ms

simplify61.0ms

prune98.0ms

localize6.0ms

rewrite6.0ms

series17.0ms

simplify47.0ms

prune40.0ms

localize7.0ms

rewrite14.0ms

series28.0ms

simplify56.0ms

prune67.0ms

localize10.0ms

rewrite33.0ms

series54.0ms

simplify77.0ms

prune84.0ms

regimes705.0ms

bsearch47.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling