Details

analyze789.0ms (17.5%)

Algorithm

1×

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 (1%)

Algorithm

1×

intervals

Results

28.0ms	256×	body	80	valid
1.0ms	17×	body	80	nan
1.0ms	13×	body	80	invalid

simplify674.0ms (14.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (261.0ms)

Iter	Nodes	Cost
0	3270	37
1	3270	37

prune13.0ms (0.3%)

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: 19.0b

Counts

2 → 1

localize33.0ms (0.7%)

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* c (* 4.0 a)))
1.5b	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
22.3b	(sqrt (- (* b b) (* c (* 4.0 a))))
22.3b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

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

series65.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
20.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
8.0ms	(- (* b b) (* c (* 4.0 a)))

simplify46.0ms (1%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4994	921
1	4994	921

prune201.0ms (4.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	61	6	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	6	68

Merged error: 7.0b

Counts

68 → 6

localize25.0ms (0.6%)

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
22.3b	(sqrt (- (* b b) (* c (* 4.0 a))))
22.3b	(sqrt (- (* b b) (* c (* 4.0 a))))
22.3b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

7.0ms	(- (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))))

series59.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

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

simplify41.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4974	975
1	4974	975

prune253.0ms (5.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	71	6	77

Merged error: 7.0b

Counts

77 → 6

localize26.0ms (0.6%)

Local error

Found 4 expressions with local error:

22.3b	(sqrt (- (* b b) (* c (* 4.0 a))))
22.3b	(sqrt (- (* b b) (* c (* 4.0 a))))
22.3b	(sqrt (- (* b b) (* c (* 4.0 a))))
22.3b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite18.0ms (0.4%)

Algorithm

1×	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))))

series56.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
13.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
13.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify46.0ms (1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4979	932
1	4979	932

prune294.0ms (6.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	72	6	78

Merged error: 7.0b

Counts

78 → 6

localize26.0ms (0.6%)

Local error

Found 4 expressions with local error:

22.3b	(sqrt (- (* b b) (* c (* 4.0 a))))
22.3b	(sqrt (- (* b b) (* c (* 4.0 a))))
22.3b	(sqrt (- (* b b) (* c (* 4.0 a))))
22.3b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite17.0ms (0.4%)

Algorithm

1×	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))))

series56.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

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

simplify46.0ms (1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4979	932
1	4979	932

prune283.0ms (6.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	72	6	78

Merged error: 7.0b

Counts

78 → 6

regimes263.0ms (5.8%)

Accuracy

Total 1.2b remaining (13.8%)

Threshold costs 0b (0%)

bsearch60.0ms (1.3%)

Steps

Iters	Range		Point
9	4.978070574921307e+116	5.588961238148798e+121	6.490997278865284e+120
8	-1.0112877333575733e+66	-2.4780880203930075e+62	-9.12593955228803e+65

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	559	131
1	559	131

end0.0ms (0%)

sample1.0s (22.6%)

Algorithm

1×

intervals

Results

727.0ms	8000×	body	80	valid
57.0ms	680×	body	80	nan
34.0ms	394×	body	80	invalid

Details

analyze789.0ms (17.5%)

sample45.0ms (1%)

simplify674.0ms (14.9%)

prune13.0ms (0.3%)

localize33.0ms (0.7%)

rewrite24.0ms (0.5%)

series65.0ms (1.4%)

simplify46.0ms (1%)

prune201.0ms (4.5%)

localize25.0ms (0.6%)

rewrite21.0ms (0.5%)

series59.0ms (1.3%)

simplify41.0ms (0.9%)

prune253.0ms (5.6%)

localize26.0ms (0.6%)

rewrite18.0ms (0.4%)

series56.0ms (1.3%)

simplify46.0ms (1%)

prune294.0ms (6.5%)

localize26.0ms (0.6%)

rewrite17.0ms (0.4%)

series56.0ms (1.2%)

simplify46.0ms (1%)

prune283.0ms (6.3%)

regimes263.0ms (5.8%)

bsearch60.0ms (1.3%)

simplify12.0ms (0.3%)

end0.0ms (0%)

sample1.0s (22.6%)

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