Details

analyze329.0ms

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

sample33.0ms

Algorithm

intervals

Results

9.0ms	206×	body	80	valid
4.0ms	15×	body	2560	valid
3.0ms	14×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	7×	body	5120	valid
2.0ms	9×	body	640	valid
0.0ms	4×	body	160	valid
0.0ms	1×	body	320	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	15
1	15	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: 36.6b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.8b	(- (sqrt (+ (* re re) (* im im))) re)
28.9b	(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

11.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
6.0ms	(- (sqrt (+ (* re re) (* im im))) re)
6.0ms	(sqrt (+ (* re re) (* im im)))

series44.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms	(- (sqrt (+ (* re re) (* im im))) re)
14.0ms	(sqrt (+ (* re re) (* im im)))

simplify32.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5393	599

prune105.0ms

Filtered

42 candidates to 51 candidates (-21.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	7	52

Merged error: 7.5b

Counts

52 → 7

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(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:

5.0ms

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

series14.0ms

Counts

1 → 3

Calls

1 calls:

14.0ms

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

simplify33.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5318	162

prune47.0ms

Filtered

13 candidates to 16 candidates (-23.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	14	2	16
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	14	9	23

Merged error: 7.5b

Counts

23 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod`
23×	`add-sqr-sqrt`
20×	`associate-*r/`
18×	`cbrt-div` `sqrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3--` `pow1/3` `flip--`
7×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-*l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

8.0ms	(* (cbrt (sqrt (* 2.0 (- im re)))) (cbrt (sqrt (* 2.0 (- im re)))))
5.0ms	(cbrt (sqrt (* 2.0 (- im re))))
5.0ms	(cbrt (sqrt (* 2.0 (- im re))))
5.0ms	(cbrt (sqrt (* 2.0 (- im re))))

series190.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cbrt (sqrt (* 2.0 (- im re)))) (cbrt (sqrt (* 2.0 (- im re)))))
48.0ms	(cbrt (sqrt (* 2.0 (- im re))))
47.0ms	(cbrt (sqrt (* 2.0 (- im re))))
52.0ms	(cbrt (sqrt (* 2.0 (- im re))))

simplify77.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5134	1363

prune267.0ms

Filtered

82 candidates to 105 candidates (-28.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	105	9	114

Merged error: 7.5b

Counts

114 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (sqrt (* 2.0 (- im re))))
0.5b	(cbrt (pow (cbrt (sqrt (* 2.0 (- im re)))) 2))
0.5b	(cbrt (pow (cbrt (sqrt (* 2.0 (- im re)))) 2))
0.5b	(cbrt (pow (cbrt (sqrt (* 2.0 (- im re)))) 2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

52×	`cbrt-prod`
21×	`unpow-prod-down`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
3×	`unpow2` `sqr-pow`
2×	`cbrt-div` `sqrt-div` `associate-*r/`
1×	`flip3--` `flip--`

Counts

4 → 74

Calls

4 calls:

5.0ms	(cbrt (sqrt (* 2.0 (- im re))))
6.0ms	(cbrt (pow (cbrt (sqrt (* 2.0 (- im re)))) 2))
4.0ms	(cbrt (pow (cbrt (sqrt (* 2.0 (- im re)))) 2))
4.0ms	(cbrt (pow (cbrt (sqrt (* 2.0 (- im re)))) 2))

series179.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(cbrt (sqrt (* 2.0 (- im re))))
43.0ms	(cbrt (pow (cbrt (sqrt (* 2.0 (- im re)))) 2))
44.0ms	(cbrt (pow (cbrt (sqrt (* 2.0 (- im re)))) 2))
42.0ms	(cbrt (pow (cbrt (sqrt (* 2.0 (- im re)))) 2))

simplify59.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4939	1208
1	4939	1208

prune364.0ms

Filtered

69 candidates to 86 candidates (-24.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	85	10	95

Merged error: 7.5b

Counts

95 → 10

regimes327.0ms

Accuracy

45.2% (10.6b remaining)

Error of 19.9b against oracle of 9.4b and baseline of 28.6b

bsearch148.0ms

Steps

Iters	Range		Point
6	9.455217976743407e+164	6.054425216238732e+165	5.828409004054647e+165
9	1.5309169041329428e-75	2.2285262272569004e-69	1.9400859152886943e-72
9	-1.0488877131575525e-120	-2.993879734672821e-126	-3.046798939941476e-126
8	-2.417395872741667e+89	-2.3322219335648337e+86	-2.2927799014051263e+89

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	89
1	57	89

end0.0ms

analyze320.0ms

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

sample996.0ms

Algorithm

intervals

Results

288.0ms	6087×	body	80	valid
183.0ms	682×	body	2560	valid
111.0ms	493×	body	1280	valid
101.0ms	8000×	pre	80	true
90.0ms	270×	body	5120	valid
47.0ms	256×	body	640	valid
17.0ms	130×	body	320	valid
7.0ms	82×	body	160	valid

Details

analyze329.0ms

sample33.0ms

simplify3.0ms

prune3.0ms

localize10.0ms

rewrite24.0ms

series44.0ms

simplify32.0ms

prune105.0ms

localize6.0ms

rewrite5.0ms

series14.0ms

simplify33.0ms

prune47.0ms

localize10.0ms

rewrite25.0ms

series190.0ms

simplify77.0ms

prune267.0ms

localize15.0ms

rewrite21.0ms

series179.0ms

simplify59.0ms

prune364.0ms

regimes327.0ms

bsearch148.0ms

simplify2.0ms

end0.0ms

analyze320.0ms

sample996.0ms

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