Details

analyze475.0ms

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

sample47.0ms

Algorithm

intervals

Results

11.0ms	36×	body	2560	valid
9.0ms	29×	body	1280	valid
9.0ms	166×	body	80	valid
3.0ms	13×	body	640	valid
1.0ms	24×	body	80	nan
1.0ms	3×	body	5120	valid
1.0ms	14×	body	80	invalid
1.0ms	6×	body	160	valid
0.0ms	3×	body	320	valid

simplify204.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (202.0ms)

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: 33.9b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

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))
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))))

series67.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
9.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify39.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5340	1316

prune173.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 6.0b

Counts

83 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

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))
6.0ms	(- (* 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))))

series75.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1 (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
9.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify39.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4995	1244
1	4995	1244

prune137.0ms

Filtered

58 candidates to 85 candidates (-46.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	84	11	95

Merged error: 5.9b

Counts

95 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
34×	`times-frac`
32×	`*-un-lft-identity`
26×	`add-exp-log`
22×	`add-cube-cbrt` `associate-r`
16×	`add-cbrt-cube`
13×	`associate-l`
8×	`div-exp` `prod-exp` `add-log-exp` `difference-of-squares`
7×	`pow1` `sqrt-prod`
6×	`unswap-sqr`
4×	`cbrt-undiv` `cbrt-unprod` `distribute-lft-out--`
3×	`flip3--` `flip--`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 105

Calls

4 calls:

17.0ms	(* (/ 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))))

series75.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0))
8.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4968	1950
1	4968	1950

prune188.0ms

Filtered

82 candidates to 117 candidates (-42.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	118	10	128

Merged error: 5.9b

Counts

128 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

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

series60.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify40.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4973	1018
1	4973	1018

prune144.0ms

Filtered

56 candidates to 70 candidates (-25.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	70	10	80

Merged error: 5.9b

Counts

80 → 10

regimes356.0ms

Accuracy

84.1% (4.6b remaining)

Error of 10.3b against oracle of 5.7b and baseline of 34.5b

bsearch51.0ms

Steps

Iters	Range		Point
8	3.1096354915926662e-37	1.0074983651851025e-34	3.1404660646488194e-37
7	-5.770706226479995e+116	-2.1889815760753618e+115	-1.642943447623613e+116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	92	40
1	92	40

end0.0ms

sample1.3s

Algorithm

intervals

Results

321.0ms	1034×	body	2560	valid
282.0ms	5085×	body	80	valid
237.0ms	943×	body	1280	valid
93.0ms	458×	body	640	valid
57.0ms	138×	body	5120	valid
35.0ms	656×	body	80	nan
30.0ms	202×	body	320	valid
20.0ms	374×	body	80	invalid
14.0ms	140×	body	160	valid

Details

analyze475.0ms

sample47.0ms

simplify204.0ms

prune8.0ms

localize11.0ms

rewrite27.0ms

series67.0ms

simplify39.0ms

prune173.0ms

localize13.0ms

rewrite32.0ms

series75.0ms

simplify39.0ms

prune137.0ms

localize13.0ms

rewrite35.0ms

series75.0ms

simplify57.0ms

prune188.0ms

localize15.0ms

rewrite24.0ms

series60.0ms

simplify40.0ms

prune144.0ms

regimes356.0ms

bsearch51.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling