Details

analyze596.0ms

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample42.0ms

Algorithm

intervals

Results

8.0ms	186×	body	80	valid
7.0ms	29×	body	2560	valid
3.0ms	16×	body	1280	valid
3.0ms	12×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	27×	body	80	nan
1.0ms	5×	body	320	valid
0.0ms	8×	body	80	invalid
0.0ms	3×	body	160	valid

simplify478.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	713	12
1	713	12

prune13.0ms

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: 27.7b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.0b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

28.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify53.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5743	1403

prune146.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	82	12	94
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	13	95

Merged error: 4.7b

Counts

95 → 13

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.0b	(- (* b_2 b_2) (* a c))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 160

Calls

4 calls:

13.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4972	3316
1	4972	3316

prune166.0ms

Filtered

99 candidates to 172 candidates (-73.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	168	4	172
Fresh	4	7	11
Picked	1	0	1
Done	0	1	1
Total	173	12	185

Merged error: 4.7b

Counts

185 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.1b	(sqrt (- (* b_2 b_2) (* a c)))
19.1b	(sqrt (- (* b_2 b_2) (* a c)))
19.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite24.0ms

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:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5078	823

prune174.0ms

Filtered

58 candidates to 71 candidates (-22.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	70	13	83

Merged error: 4.6b

Counts

83 → 13

localize30.0ms

Local error

Found 4 expressions with local error:

19.1b	(sqrt (- (* b_2 b_2) (* a c)))
19.1b	(sqrt (- (* b_2 b_2) (* a c)))
19.8b	(cbrt (- (* b_2 b_2) (* a c)))
19.8b	(cbrt (- (* b_2 b_2) (* a c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(cbrt (- (* b_2 b_2) (* a c)))
4.0ms	(cbrt (- (* b_2 b_2) (* a c)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
23.0ms	(cbrt (- (* b_2 b_2) (* a c)))
25.0ms	(cbrt (- (* b_2 b_2) (* a c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4864	774
1	4864	774

prune137.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	11	11
Picked	1	0	1
Done	0	1	1
Total	68	13	81

Merged error: 4.6b

Counts

81 → 13

regimes364.0ms

Accuracy

84.4% (4.4b remaining)

Error of 10.1b against oracle of 5.6b and baseline of 34.0b

bsearch51.0ms

Steps

Iters	Range		Point
8	3.65432435475854e-45	2.4730087615102232e-42	1.5195718135839158e-43
9	-3.155246831736112e+157	-4.3224285963270155e+152	-9.328589537535776e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	38
1	67	38

end0.0ms

sample1.1s

Algorithm

intervals

Results

261.0ms	1049×	body	2560	valid
227.0ms	5203×	body	80	valid
170.0ms	846×	body	1280	valid
72.0ms	463×	body	640	valid
34.0ms	114×	body	5120	valid
32.0ms	786×	body	80	nan
26.0ms	223×	body	320	valid
11.0ms	210×	body	80	invalid
8.0ms	102×	body	160	valid

Details

analyze596.0ms

sample42.0ms

simplify478.0ms

prune13.0ms

localize11.0ms

rewrite49.0ms

series65.0ms

simplify53.0ms

prune146.0ms

localize10.0ms

rewrite35.0ms

series66.0ms

simplify66.0ms

prune166.0ms

localize17.0ms

rewrite24.0ms

series52.0ms

simplify51.0ms

prune174.0ms

localize30.0ms

rewrite18.0ms

series75.0ms

simplify49.0ms

prune137.0ms

regimes364.0ms

bsearch51.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling