Details

analyze8.0ms

Algorithm

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

sample62.0ms

Algorithm

intervals

Results

49.0ms	256×	body	80	valid
3.0ms	260×	pre	80	true
1.0ms	4×	body	80	invalid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5216	49

prune18.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 1.6b

Counts

2 → 2

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.1b	(pow (/ 1.0 (fabs x)) 5)
1.1b	(pow (exp (fabs x)) (fabs x))
1.4b	(pow (/ 1.0 (fabs x)) 7)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

29×	`unpow-prod-down`
25×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
10×	`add-exp-log`
9×	`pow-unpow`
8×	`pow1`
6×	`pow-pow`
5×	`pow-exp`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `exp-prod` `sqrt-prod` `sqr-pow`
2×	`div-exp` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 89

Calls

4 calls:

1.0ms	(sqrt PI)
4.0ms	(pow (/ 1.0 (fabs x)) 5)
3.0ms	(pow (exp (fabs x)) (fabs x))
5.0ms	(pow (/ 1.0 (fabs x)) 7)

series58.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(sqrt PI)
12.0ms	(pow (/ 1.0 (fabs x)) 5)
30.0ms	(pow (exp (fabs x)) (fabs x))
15.0ms	(pow (/ 1.0 (fabs x)) 7)

simplify53.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4987	897
1	4987	897

prune349.0ms

Filtered

70 candidates to 99 candidates (-41.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	85	14	99
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	86	15	101

Merged error: 0.8b

Counts

101 → 15

localize33.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)
1.1b	(pow (/ 1.0 (fabs x)) 5)
1.1b	(pow (exp (fabs x)) (fabs x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `*-un-lft-identity`
29×	`unpow-prod-down`
27×	`times-frac`
13×	`cube-prod`
10×	`add-exp-log`
9×	`pow-unpow`
8×	`pow1`
7×	`add-cbrt-cube`
6×	`pow-pow`
5×	`pow-exp`
4×	`add-log-exp`
3×	`pow-to-exp` `exp-prod` `sqrt-prod` `div-inv` `sqr-pow`
2×	`div-exp` `rem-cube-cbrt`
1×	`cbrt-undiv` `cube-div` `cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3`

Counts

4 → 107

Calls

4 calls:

5.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)
4.0ms	(pow (/ 1.0 (fabs x)) 5)
5.0ms	(pow (exp (fabs x)) (fabs x))

series49.0ms

Counts

4 → 10

Calls

4 calls:

9.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)
12.0ms	(pow (/ 1.0 (fabs x)) 5)
28.0ms	(pow (exp (fabs x)) (fabs x))

simplify46.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5099	967

prune318.0ms

Filtered

70 candidates to 117 candidates (-67.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	111	6	117
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	116	16	132

Merged error: 0.7b

Counts

132 → 16

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (exp (fabs x)) (/ (fabs x) 2))
0.8b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)
1.1b	(pow (/ 1.0 (fabs x)) 5)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`add-cube-cbrt` `*-un-lft-identity`
36×	`times-frac`
29×	`unpow-prod-down`
19×	`pow-unpow`
13×	`cube-prod`
10×	`add-exp-log`
8×	`pow1`
7×	`add-cbrt-cube`
6×	`pow-pow`
5×	`pow-exp`
4×	`div-inv` `add-log-exp`
3×	`pow-to-exp` `exp-prod` `sqrt-prod` `sqr-pow`
2×	`div-exp` `rem-cube-cbrt`
1×	`cbrt-undiv` `cube-div` `cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow3`

Counts

4 → 117

Calls

4 calls:

5.0ms	(pow (exp (fabs x)) (/ (fabs x) 2))
5.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)
5.0ms	(pow (/ 1.0 (fabs x)) 5)

series54.0ms

Counts

4 → 10

Calls

4 calls:

30.0ms	(pow (exp (fabs x)) (/ (fabs x) 2))
9.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)
15.0ms	(pow (/ 1.0 (fabs x)) 5)

simplify59.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5832	1131

prune458.0ms

Filtered

79 candidates to 127 candidates (-60.8%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	116	11	127
Fresh	3	12	15
Picked	0	1	1
Done	0	0	0
Total	119	24	143

Merged error: 0.5b

Counts

143 → 24

localize40.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (/ 1.0 (fabs x)) 3)
1.0b	(sqrt PI)
1.1b	(pow (/ 1.0 (fabs x)) 5)
5.0b	(log (exp (pow (/ 1.0 (fabs x)) 3)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt` `times-frac`
44×	`add-cube-cbrt` `*-un-lft-identity`
39×	`unpow-prod-down`
33×	`log-pow`
32×	`exp-prod`
26×	`cube-prod`
10×	`add-exp-log`
8×	`pow1`
7×	`add-cbrt-cube`
6×	`pow-unpow`
5×	`div-inv`
4×	`pow-exp` `add-log-exp`
3×	`log-prod` `sqrt-prod` `sqr-pow`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `div-exp` `rem-cube-cbrt`
1×	`cbrt-undiv` `cube-div` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp`

Counts

4 → 131

Calls

4 calls:

5.0ms	(pow (/ 1.0 (fabs x)) 3)
1.0ms	(sqrt PI)
5.0ms	(pow (/ 1.0 (fabs x)) 5)
8.0ms	(log (exp (pow (/ 1.0 (fabs x)) 3)))

series31.0ms

Counts

4 → 10

Calls

4 calls:

9.0ms	(pow (/ 1.0 (fabs x)) 3)
0.0ms	(sqrt PI)
12.0ms	(pow (/ 1.0 (fabs x)) 5)
9.0ms	(log (exp (pow (/ 1.0 (fabs x)) 3)))

simplify32.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5061	1097

prune365.0ms

Filtered

81 candidates to 141 candidates (-74.1%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	2	20	22
Picked	1	0	1
Done	0	1	1
Total	141	24	165

Merged error: 0.5b

Counts

165 → 24

regimes536.0ms

Accuracy

0% (1.0b remaining)

Error of 1.3b against oracle of 0.3b and baseline of 1.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	60
1	43	60

end0.0ms

analyze7.0ms

Algorithm

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

sample1.8s

Algorithm

intervals

Results

1.6s	8000×	body	80	valid
91.0ms	8113×	pre	80	true
22.0ms	113×	body	80	invalid

Details

analyze8.0ms

sample62.0ms

simplify19.0ms

prune18.0ms

localize32.0ms

rewrite16.0ms

series58.0ms

simplify53.0ms

prune349.0ms

localize33.0ms

rewrite19.0ms

series49.0ms

simplify46.0ms

prune318.0ms

localize35.0ms

rewrite19.0ms

series54.0ms

simplify59.0ms

prune458.0ms

localize40.0ms

rewrite26.0ms

series31.0ms

simplify32.0ms

prune365.0ms

regimes536.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze7.0ms

sample1.8s

Profiling