Details

analyze738.0ms

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

sample45.0ms

Algorithm

intervals

Results

27.0ms	256×	body	80	valid
2.0ms	27×	body	80	nan
2.0ms	18×	body	80	invalid

simplify423.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	57	38
1	57	38

prune10.0ms

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: 19.1b

Counts

2 → 1

localize33.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

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))))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify39.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5034	1074

prune211.0ms

Filtered

63 candidates to 74 candidates (-17.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	65	9	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	9	75

Merged error: 6.7b

Counts

75 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

7.8b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

6.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (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))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5080	983

prune202.0ms

Filtered

58 candidates to 71 candidates (-22.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	71	9	80

Merged error: 6.7b

Counts

80 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

7.5b	(- (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(cbrt (- (* b b) (* 4.0 (* a c))))
21.8b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite15.0ms

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)))))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series98.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
25.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify58.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4978	1215
1	4978	1215

prune220.0ms

Filtered

60 candidates to 66 candidates (-10.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	66	9	75

Merged error: 6.7b

Counts

75 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

6.8b	(+ (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(cbrt (- (* b b) (* 4.0 (* a c))))
21.8b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite17.0ms

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` `add-cbrt-cube`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`pow1/3` `sqrt-div` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

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)))))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
5.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series91.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
23.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify59.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4981	1186
1	4981	1186

prune190.0ms

Filtered

60 candidates to 66 candidates (-10.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	66	9	75

Merged error: 6.7b

Counts

75 → 9

regimes317.0ms

Accuracy

93.1% (1.0b remaining)

Error of 6.9b against oracle of 5.9b and baseline of 19.9b

bsearch684.0ms

Steps

Iters	Range		Point
10	6.967524857617703e+70	4.6816618922476424e+80	4.6437836518398973e+80
10	-1.531036332870136e+158	-7.446961072820802e+145	-2.9425467623133534e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	131
1	52	131

end0.0ms

analyze522.0ms

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

sample1.0s

Algorithm

intervals

Results

722.0ms	8000×	body	80	valid
57.0ms	655×	body	80	nan
38.0ms	415×	body	80	invalid

Details

analyze738.0ms

sample45.0ms

simplify423.0ms

prune10.0ms

localize33.0ms

rewrite26.0ms

series70.0ms

simplify39.0ms

prune211.0ms

localize29.0ms

rewrite17.0ms

series56.0ms

simplify51.0ms

prune202.0ms

localize33.0ms

rewrite15.0ms

series98.0ms

simplify58.0ms

prune220.0ms

localize29.0ms

rewrite17.0ms

series91.0ms

simplify59.0ms

prune190.0ms

regimes317.0ms

bsearch684.0ms

simplify2.0ms

end0.0ms

analyze522.0ms

sample1.0s

Profiling