Details

analyze755.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

sample46.0ms

Algorithm

intervals

Results

28.0ms	256×	body	80	valid
2.0ms	22×	body	80	nan
1.0ms	13×	body	80	invalid

simplify615.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (216.0ms)

Iter	Nodes	Cost
0	3270	37
1	3270	37

prune22.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 17.9b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* c (* 4.0 a)))
1.2b	(- (* b b) (* c (* 4.0 a)))
19.0b	(sqrt (- (* b b) (* c (* 4.0 a))))
19.0b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 52

Calls

4 calls:

4.0ms	(- (* b b) (* c (* 4.0 a)))
4.0ms	(- (* b b) (* c (* 4.0 a)))
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
6.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series58.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (* b b) (* c (* 4.0 a)))
9.0ms	(- (* b b) (* c (* 4.0 a)))
14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
22.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify38.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5179	824

prune165.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	57	7	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	7	65

Merged error: 5.4b

Counts

65 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

8.3b	(- (* (sqrt (sqrt (- (* b b) (* c (* 4.0 a))))) (sqrt (sqrt (- (* b b) (* c (* 4.0 a)))))) b)
19.0b	(sqrt (- (* b b) (* c (* 4.0 a))))
19.0b	(sqrt (- (* b b) (* c (* 4.0 a))))
19.0b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `diff-log` `difference-of-squares`

Counts

4 → 57

Calls

4 calls:

15.0ms	(- (* (sqrt (sqrt (- (* b b) (* c (* 4.0 a))))) (sqrt (sqrt (- (* b b) (* c (* 4.0 a)))))) b)
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (sqrt (sqrt (- (* b b) (* c (* 4.0 a))))) (sqrt (sqrt (- (* b b) (* c (* 4.0 a)))))) b)
14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
16.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify41.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4950	935
1	4950	935

prune202.0ms

Filtered

59 candidates to 69 candidates (-16.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	71	5	76

Merged error: 5.4b

Counts

76 → 5

localize35.0ms

Local error

Found 4 expressions with local error:

19.0b	(sqrt (- (* b b) (* c (* 4.0 a))))
19.0b	(sqrt (- (* b b) (* c (* 4.0 a))))
19.0b	(sqrt (- (* b b) (* c (* 4.0 a))))
19.0b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
15.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify44.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4979	932
1	4979	932

prune312.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	71	6	77

Merged error: 5.4b

Counts

77 → 6

localize42.0ms

Local error

Found 4 expressions with local error:

19.0b	(sqrt (- (* b b) (* c (* 4.0 a))))
19.0b	(sqrt (- (* b b) (* c (* 4.0 a))))
19.8b	(cbrt (- (* b b) (* c (* 4.0 a))))
19.8b	(cbrt (- (* b b) (* c (* 4.0 a))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
4.0ms	(cbrt (- (* b b) (* c (* 4.0 a))))
4.0ms	(cbrt (- (* b b) (* c (* 4.0 a))))

series80.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
24.0ms	(cbrt (- (* b b) (* c (* 4.0 a))))
29.0ms	(cbrt (- (* b b) (* c (* 4.0 a))))

simplify40.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5386	936

prune325.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	68	6	74

Merged error: 5.4b

Counts

74 → 6

regimes248.0ms

Accuracy

90.9% (1.3b remaining)

Error of 7.0b against oracle of 5.7b and baseline of 19.9b

bsearch62.0ms

Steps

Iters	Range		Point
7	1.4651889279160543e+52	5.6142198538305575e+53	5.5357752852941396e+53
8	-1.7057252453383498e+134	-3.320779543352626e+131	-4.993472345130425e+132

simplify13.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	600	167
1	600	167

end0.0ms

sample1.1s

Algorithm

intervals

Results

765.0ms	8000×	body	80	valid
58.0ms	645×	body	80	nan
34.0ms	371×	body	80	invalid

Details

analyze755.0ms

sample46.0ms

simplify615.0ms

prune22.0ms

localize24.0ms

rewrite20.0ms

series58.0ms

simplify38.0ms

prune165.0ms

localize25.0ms

rewrite28.0ms

series60.0ms

simplify41.0ms

prune202.0ms

localize35.0ms

rewrite18.0ms

series59.0ms

simplify44.0ms

prune312.0ms

localize42.0ms

rewrite18.0ms

series80.0ms

simplify40.0ms

prune325.0ms

regimes248.0ms

bsearch62.0ms

simplify13.0ms

end0.0ms

sample1.1s

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