Details

analyze763.0ms

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

sample43.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
1.0ms	15×	body	80	nan
1.0ms	10×	body	80	invalid

simplify638.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (217.0ms)

Iter	Nodes	Cost
0	3270	37
1	3270	37

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 18.0b

Counts

2 → 1

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.7b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 62

Calls

4 calls:

8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4900	1063
1	4900	1063

prune186.0ms

Filtered

63 candidates to 74 candidates (-17.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	6	75

Merged error: 6.0b

Counts

75 → 6

localize29.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 62

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify51.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5034	1039

prune222.0ms

Filtered

62 candidates to 74 candidates (-19.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	72	8	80

Merged error: 5.9b

Counts

80 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

6.6b	(- (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b	(cbrt (- (* b b) (* 4.0 (* a c))))
22.4b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 54

Calls

4 calls:

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

series101.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
28.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
26.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify69.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4903	1193
1	4903	1193

prune216.0ms

Filtered

55 candidates to 66 candidates (-20.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	65	9	74

Merged error: 5.9b

Counts

74 → 9

localize42.0ms

Local error

Found 4 expressions with local error:

21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

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

series58.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify48.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4955	932
1	4955	932

prune288.0ms

Filtered

61 candidates to 72 candidates (-18.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	72	9	81

Merged error: 5.9b

Counts

81 → 9

regimes329.0ms

Accuracy

92.2% (1.1b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 19.9b

bsearch61.0ms

Steps

Iters	Range		Point
7	9.996722395672268e+99	2.1038526948328307e+102	7.827501062721053e+101
9	-5.681220368940046e+91	-1.1290992070726796e+83	-4.118384396451869e+91

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	144	131
1	144	131

end0.0ms

sample1.0s

Algorithm

intervals

Results

733.0ms	8000×	body	80	valid
57.0ms	651×	body	80	nan
39.0ms	395×	body	80	invalid

Details

analyze763.0ms

sample43.0ms

simplify638.0ms

prune13.0ms

localize33.0ms

rewrite29.0ms

series71.0ms

simplify57.0ms

prune186.0ms

localize29.0ms

rewrite22.0ms

series59.0ms

simplify51.0ms

prune222.0ms

localize33.0ms

rewrite18.0ms

series101.0ms

simplify69.0ms

prune216.0ms

localize42.0ms

rewrite18.0ms

series58.0ms

simplify48.0ms

prune288.0ms

regimes329.0ms

bsearch61.0ms

simplify3.0ms

end0.0ms

sample1.0s

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