Details

analyze1.1s

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
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

sample202.0ms

Algorithm

intervals

Results

66.0ms	120×	body	1280	valid
34.0ms	27×	body	1280	nan
23.0ms	53×	body	640	valid
16.0ms	23×	body	640	nan
14.0ms	80×	body	80	overflowed
7.0ms	25×	body	320	valid
7.0ms	16×	body	320	nan
6.0ms	9×	body	640	invalid
5.0ms	3×	body	1280	invalid
4.0ms	46×	body	80	valid
2.0ms	12×	body	160	valid
2.0ms	4×	body	320	invalid
2.0ms	23×	body	80	nan
1.0ms	4×	body	160	nan
0.0ms	2×	body	160	invalid
0.0ms	3×	body	80	invalid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5058	13

prune3.0ms

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: 35.2b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
3.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 78

Calls

3 calls:

3.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series70.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(pow x (/ 1.0 n))
17.0ms	(pow (+ x 1.0) (/ 1.0 n))
38.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify38.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4992	1200
1	4992	1200

prune176.0ms

Filtered

71 candidates to 87 candidates (-22.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	82	5	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	5	88

Merged error: 24.7b

Counts

88 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt x) (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
4.3b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
39×	`pow-unpow`
35×	`*-un-lft-identity`
29×	`add-cube-cbrt`
27×	`times-frac`
26×	`unpow-prod-down`
19×	`sqrt-prod`
16×	`difference-of-squares`
11×	`sqr-pow`
8×	`pow1`
7×	`add-exp-log`
6×	`add-log-exp`
5×	`pow-pow`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-exp` `div-inv`
2×	`distribute-lft-out`
1×	`sub-neg` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `sqrt-pow2` `flip--` `distribute-lft-out--`

Counts

4 → 117

Calls

4 calls:

4.0ms	(pow (sqrt x) (/ 1.0 n))
7.0ms	(pow (+ x 1.0) (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
12.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (sqrt x) (/ 1.0 n))
17.0ms	(pow (+ x 1.0) (/ 1.0 n))
19.0ms	(pow (+ x 1.0) (/ 1.0 n))
68.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

simplify54.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5006	1947

prune344.0ms

Filtered

96 candidates to 129 candidates (-34.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	129	5	134

Merged error: 24.7b

Counts

134 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt x) (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
4.3b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
39×	`pow-unpow`
35×	`*-un-lft-identity`
29×	`add-cube-cbrt`
27×	`times-frac`
26×	`unpow-prod-down`
19×	`sqrt-prod`
16×	`difference-of-squares`
11×	`sqr-pow`
8×	`pow1`
7×	`add-exp-log`
6×	`add-log-exp`
5×	`pow-pow`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-exp` `div-inv`
2×	`distribute-lft-out`
1×	`sub-neg` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `sqrt-pow2` `flip--` `distribute-lft-out--`

Counts

4 → 117

Calls

4 calls:

4.0ms	(pow (sqrt x) (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
12.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

series128.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (sqrt x) (/ 1.0 n))
17.0ms	(pow (+ x 1.0) (/ 1.0 n))
17.0ms	(pow (+ x 1.0) (/ 1.0 n))
71.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

simplify56.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5006	1947

prune402.0ms

Filtered

96 candidates to 129 candidates (-34.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	128	6	134

Merged error: 24.7b

Counts

134 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))) 3)
0.0b	(cbrt (pow (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))) 3))
4.3b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

138×	`add-sqr-sqrt`
104×	`unpow-prod-down`
80×	`sqrt-prod` `difference-of-squares`
46×	`cbrt-prod`
43×	`sqr-pow`
40×	`cube-prod`
30×	`*-un-lft-identity`
18×	`add-cube-cbrt`
16×	`pow-unpow`
9×	`times-frac`
6×	`pow1` `add-exp-log` `add-log-exp`
5×	`add-cbrt-cube` `distribute-lft-out--`
4×	`cube-div`
3×	`flip3--` `flip--`
2×	`cube-mult` `pow-to-exp` `cbrt-div` `pow-pow` `unpow3` `pow-exp`
1×	`sub-neg` `pow1/3` `diff-log` `rem-cbrt-cube` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 172

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
19.0ms	(pow (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))) 3)
16.0ms	(cbrt (pow (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))) 3))
12.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

series559.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (+ x 1.0) (/ 1.0 n))
403.0ms	(pow (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))) 3)
67.0ms	(cbrt (pow (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))) 3))
71.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

simplify48.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5237	6062

prune548.0ms

Filtered

97 candidates to 184 candidates (-89.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	183	1	184
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	184	6	190

Merged error: 24.7b

Counts

190 → 6

regimes252.0ms

Accuracy

88.9% (1.1b remaining)

Error of 23.7b against oracle of 22.6b and baseline of 32.6b

bsearch208.0ms

Steps

Iters	Range		Point
11	7.615176259177752e-18	5201930438.109229	4360947995.274645
9	-120759.73963987811	-0.38284730022597174	-119587.8191154939

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	50
1	37	50

end0.0ms

analyze1.1s

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
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

sample6.5s

Algorithm

intervals

Results

2.1s	3750×	body	1280	valid
1.1s	1043×	body	1280	nan
712.0ms	1591×	body	640	valid
626.0ms	902×	body	640	nan
477.0ms	2756×	body	80	overflowed
232.0ms	738×	body	320	valid
204.0ms	488×	body	320	nan
180.0ms	266×	body	640	invalid
140.0ms	1600×	body	80	valid
131.0ms	106×	body	1280	invalid
71.0ms	170×	body	320	invalid
61.0ms	321×	body	160	valid
52.0ms	231×	body	160	nan
34.0ms	527×	body	80	nan
22.0ms	182×	body	80	invalid
22.0ms	93×	body	160	invalid

Details

analyze1.1s

sample202.0ms

simplify40.0ms

prune3.0ms

localize11.0ms

rewrite19.0ms

series70.0ms

simplify38.0ms

prune176.0ms

localize12.0ms

rewrite32.0ms

series127.0ms

simplify54.0ms

prune344.0ms

localize19.0ms

rewrite30.0ms

series128.0ms

simplify56.0ms

prune402.0ms

localize19.0ms

rewrite60.0ms

series559.0ms

simplify48.0ms

prune548.0ms

regimes252.0ms

bsearch208.0ms

simplify1.0ms

end0.0ms

analyze1.1s

sample6.5s

Profiling