Details

analyze480.0ms

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample42.0ms

Algorithm

intervals

Results

9.0ms	173×	body	80	valid
8.0ms	27×	body	2560	valid
7.0ms	28×	body	1280	valid
4.0ms	19×	body	640	valid
1.0ms	21×	body	80	nan
1.0ms	6×	body	320	valid
1.0ms	13×	body	80	invalid
0.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify197.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (196.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune8.0ms

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: 33.8b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
0.2b	(- (* b b) (* 4.0 (* a c)))
0.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

11.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
4.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series63.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify38.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5340	1316

prune162.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 7.1b

Counts

83 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
0.2b	(- (* b b) (* 4.0 (* a c)))
0.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `div-exp`
8×	`pow1` `add-log-exp`
7×	`add-cube-cbrt`
6×	`prod-exp`
4×	`cbrt-undiv` `sqrt-prod`
3×	`rec-exp` `flip3--` `times-frac` `1-exp` `flip--` `associate-/l*`
2×	`sub-neg` `pow-flip` `sqrt-div` `diff-log` `cbrt-unprod` `difference-of-squares`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `div-inv` `distribute-lft-out--` `inv-pow`

Counts

4 → 73

Calls

4 calls:

13.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
4.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series74.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
8.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify38.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4995	1244
1	4995	1244

prune123.0ms

Filtered

57 candidates to 85 candidates (-49.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	82	10	92

Merged error: 6.9b

Counts

92 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite22.0ms

Algorithm

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:

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

17.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms	(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))))

simplify38.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4973	975
1	4973	975

prune242.0ms

Filtered

58 candidates to 71 candidates (-22.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	69	12	81

Merged error: 6.9b

Counts

81 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite21.0ms

Algorithm

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:

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

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

simplify39.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4973	975
1	4973	975

prune172.0ms

Filtered

58 candidates to 71 candidates (-22.4%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	70	13	83

Merged error: 6.9b

Counts

83 → 13

regimes369.0ms

Accuracy

82.3% (5.1b remaining)

Error of 10.9b against oracle of 5.8b and baseline of 34.4b

bsearch48.0ms

Steps

Iters	Range		Point
6	2.041973028102089e-153	1.0173100248620036e-152	9.997495995248066e-153
8	-3.235288621317844e+118	-1.6397235269475537e+115	-9.877954748696237e+117

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	92	40
1	92	40

end0.0ms

sample1.2s

Algorithm

intervals

Results

314.0ms	1022×	body	2560	valid
267.0ms	5125×	body	80	valid
227.0ms	899×	body	1280	valid
99.0ms	501×	body	640	valid
40.0ms	111×	body	5120	valid
35.0ms	663×	body	80	nan
32.0ms	219×	body	320	valid
19.0ms	377×	body	80	invalid
12.0ms	123×	body	160	valid

Details

analyze480.0ms

sample42.0ms

simplify197.0ms

prune8.0ms

localize14.0ms

rewrite28.0ms

series63.0ms

simplify38.0ms

prune162.0ms

localize12.0ms

rewrite31.0ms

series74.0ms

simplify38.0ms

prune123.0ms

localize19.0ms

rewrite22.0ms

series58.0ms

simplify38.0ms

prune242.0ms

localize16.0ms

rewrite21.0ms

series58.0ms

simplify39.0ms

prune172.0ms

regimes369.0ms

bsearch48.0ms

simplify2.0ms

end0.0ms

sample1.2s

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