Details

analyze327.0ms

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

9.0ms	198×	body	80	valid
5.0ms	19×	body	2560	valid
3.0ms	10×	body	5120	valid
3.0ms	256×	pre	80	true
2.0ms	11×	body	1280	valid
2.0ms	11×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	271	15
1	271	15

prune4.0ms

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: 38.0b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* re re) (* im im))
0.2b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.8b	(- (sqrt (+ (* re re) (* im im))) re)
29.2b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
5×	`add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`sqrt-pow1`
2×	`flip3--` `flip3-+` `pow1/2` `associate-*r/` `flip--` `flip-+` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `diff-log` `pow-prod-down` `sum-log` `distribute-lft-out--`

Counts

4 → 53

Calls

4 calls:

4.0ms	(+ (* re re) (* im im))
8.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
4.0ms	(sqrt (+ (* re re) (* im im)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* re re) (* im im))
26.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
7.0ms	(sqrt (+ (* re re) (* im im)))

simplify60.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4905	734
1	4905	734

prune131.0ms

Filtered

52 candidates to 65 candidates (-25.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	59	6	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	6	66

Merged error: 8.7b

Counts

66 → 6

localize6.0ms

Local error

Found 1 expressions with local error:

0.2b	(sqrt (* 2.0 (- im re)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1`
2×	`sqrt-pow1` `sqrt-div` `associate-*r/`
1×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `flip3--` `*-un-lft-identity` `pow1/2` `pow-prod-down` `sqrt-prod` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

1 → 13

Calls

1 calls:

4.0ms

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

series16.0ms

Counts

1 → 3

Calls

1 calls:

16.0ms

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

simplify44.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4914	162
1	4914	162

prune45.0ms

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	0	5	5
Picked	0	1	1
Done	0	0	0
Total	15	7	22

Merged error: 8.5b

Counts

22 → 7

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (- im re))
0.4b	(* (sqrt 2.0) (sqrt (- im re)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
17×	`sqrt-prod`
11×	`*-un-lft-identity`
8×	`associate-r`
7×	`pow1` `add-cube-cbrt`
6×	`associate-l`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `unswap-sqr`
3×	`sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

2 → 51

Calls

2 calls:

3.0ms	(sqrt (- im re))
10.0ms	(* (sqrt 2.0) (sqrt (- im re)))

series22.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(sqrt (- im re))
14.0ms	(* (sqrt 2.0) (sqrt (- im re)))

simplify50.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4936	522
1	4936	522

prune90.0ms

Filtered

37 candidates to 57 candidates (-54.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	55	9	64

Merged error: 8.5b

Counts

64 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (sqrt (- im re))) (cbrt (sqrt (- im re))))
0.4b	(cbrt (sqrt (- im re)))
0.4b	(cbrt (sqrt (- im re)))
0.4b	(cbrt (sqrt (- im re)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

76×	`cbrt-prod`
58×	`add-sqr-sqrt`
47×	`sqrt-prod`
42×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`cbrt-div` `sqrt-div`
15×	`swap-sqr`
11×	`pow1` `associate-r` `associate-l`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `unswap-sqr`
7×	`difference-of-squares`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 126

Calls

4 calls:

14.0ms	(* (cbrt (sqrt (- im re))) (cbrt (sqrt (- im re))))
4.0ms	(cbrt (sqrt (- im re)))
4.0ms	(cbrt (sqrt (- im re)))
4.0ms	(cbrt (sqrt (- im re)))

series105.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (cbrt (sqrt (- im re))) (cbrt (sqrt (- im re))))
25.0ms	(cbrt (sqrt (- im re)))
28.0ms	(cbrt (sqrt (- im re)))
27.0ms	(cbrt (sqrt (- im re)))

simplify58.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4855	1497
1	4855	1497

prune143.0ms

Filtered

84 candidates to 138 candidates (-64.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	138	9	147

Merged error: 8.5b

Counts

147 → 9

regimes277.0ms

Accuracy

40.6% (11.4b remaining)

Error of 20.9b against oracle of 9.5b and baseline of 28.7b

bsearch44.0ms

Steps

Iters	Range		Point
9	1.8194042955542765e-86	5.962847531226846e-80	2.9410417356698102e-86
9	-4.739904829321799e+72	-5.128198797833013e+67	-5.258042462680681e+67

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	117	44
1	117	44

end0.0ms

sample1.0s

Algorithm

intervals

Results

299.0ms	6059×	body	80	valid
185.0ms	664×	body	2560	valid
106.0ms	466×	body	1280	valid
100.0ms	8000×	pre	80	true
98.0ms	291×	body	5120	valid
52.0ms	292×	body	640	valid
21.0ms	140×	body	320	valid
8.0ms	88×	body	160	valid

Details

analyze327.0ms

sample38.0ms

simplify18.0ms

prune4.0ms

localize10.0ms

rewrite24.0ms

series45.0ms

simplify60.0ms

prune131.0ms

localize6.0ms

rewrite5.0ms

series16.0ms

simplify44.0ms

prune45.0ms

localize7.0ms

rewrite15.0ms

series22.0ms

simplify50.0ms

prune90.0ms

localize13.0ms

rewrite31.0ms

series105.0ms

simplify58.0ms

prune143.0ms

regimes277.0ms

bsearch44.0ms

simplify2.0ms

end0.0ms

sample1.0s

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