Details

analyze459.0ms

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

sample43.0ms

Algorithm

intervals

Results

8.0ms	165×	body	80	valid
8.0ms	29×	body	2560	valid
7.0ms	29×	body	1280	valid
4.0ms	21×	body	640	valid
1.0ms	28×	body	80	nan
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	16×	body	80	invalid
0.0ms	4×	body	160	valid

simplify206.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (205.0ms)

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: 31.3b

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))
1.0b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.6b	(- (* b b) (* 4.0 (* a c)))
20.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite26.0ms

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:

10.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

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

prune155.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 4.9b

Counts

83 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
1.0b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.6b	(- (* b b) (* 4.0 (* a c)))
20.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

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:

12.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
16.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify37.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4995	1244
1	4995	1244

prune126.0ms

Filtered

58 candidates to 85 candidates (-46.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	82	11	93

Merged error: 4.8b

Counts

93 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b b) (* 4.0 (* a c)))
10.3b	(- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b)
21.5b	(cbrt (- (* b b) (* 4.0 (* a c))))
21.5b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b)
4.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series88.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
31.0ms	(- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b)
23.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
25.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify35.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5044	1083

prune168.0ms

Filtered

53 candidates to 60 candidates (-13.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	60	11	71

Merged error: 4.8b

Counts

71 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

15.4b	(- (* (* (cbrt (sqrt (- (* b b) (* 4.0 (* a c))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))) b)
20.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

10×	`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`

Counts

4 → 56

Calls

4 calls:

21.0ms	(- (* (* (cbrt (sqrt (- (* b b) (* 4.0 (* a c))))) (cbrt (sqrt (- (* b b) (* 4.0 (* a c)))))) (cbrt (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))))

series57.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify41.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5056	868

prune160.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	6	7
Picked	0	1	1
Done	0	3	3
Total	68	11	79

Merged error: 4.8b

Counts

79 → 11

regimes310.0ms

Accuracy

88.7% (3.1b remaining)

Error of 8.6b against oracle of 5.6b and baseline of 32.6b

bsearch78.0ms

Steps

Iters	Range	Point
10	2.5312074942013306e+65	2.4839001300170943e+77	4.4076190914119784e+69
2	2.8395686309221393e-123	3.041035527734523e-123	2.9121987620533157e-123
9	-1.3801073068520631e+159	-1.436433112909709e+151	-2.282303906287587e+153

Iters

Range

Point

2.5312074942013306e+65

2.4839001300170943e+77

4.4076190914119784e+69

2.8395686309221393e-123

3.041035527734523e-123

2.9121987620533157e-123

-1.3801073068520631e+159

-1.436433112909709e+151

-2.282303906287587e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	109	71
1	109	71

end0.0ms

sample1.2s

Algorithm

intervals

Results

292.0ms	973×	body	2560	valid
270.0ms	5247×	body	80	valid
213.0ms	880×	body	1280	valid
92.0ms	478×	body	640	valid
38.0ms	101×	body	5120	valid
35.0ms	674×	body	80	nan
29.0ms	199×	body	320	valid
21.0ms	421×	body	80	invalid
12.0ms	122×	body	160	valid

Details

analyze459.0ms

sample43.0ms

simplify206.0ms

prune8.0ms

localize14.0ms

rewrite26.0ms

series62.0ms

simplify38.0ms

prune155.0ms

localize12.0ms

rewrite29.0ms

series71.0ms

simplify37.0ms

prune126.0ms

localize20.0ms

rewrite22.0ms

series88.0ms

simplify35.0ms

prune168.0ms

localize15.0ms

rewrite34.0ms

series57.0ms

simplify41.0ms

prune160.0ms

regimes310.0ms

bsearch78.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling