Details

analyze599.0ms

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
0%	99.9%	0.1%	5
3.1%	90.5%	6.3%	6
4.7%	85.9%	9.5%	7
21.1%	64%	14.9%	8
23.4%	58.9%	17.7%	9
27.7%	51.3%	21%	10
28.9%	48.5%	22.6%	11
31.1%	44.4%	24.5%	12
31.7%	42.9%	25.4%	13
32.7%	41%	26.3%	14

sample71.0ms

Algorithm

intervals

Results

23.0ms	47×	body	1280	valid
15.0ms	46×	body	640	valid
10.0ms	130×	body	80	valid
5.0ms	25×	body	320	valid
3.0ms	6×	body	1280	invalid
2.0ms	8×	body	320	invalid
1.0ms	4×	body	640	invalid
1.0ms	8×	body	160	valid
0.0ms	3×	body	160	invalid
0.0ms	7×	body	80	nan
0.0ms	4×	body	80	invalid

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4985	9
1	4985	9

prune7.0ms

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: 12.8b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
6.6b	(pow (/ x (+ x y)) x)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
24×	`times-frac`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`unpow-prod-down`
7×	`add-exp-log` `distribute-lft-out`
4×	`associate-/r*` `associate-/r/` `add-cbrt-cube`
3×	`pow1` `pow-unpow` `associate-/l*`
2×	`flip3-+` `div-exp` `pow-exp` `flip-+` `div-inv` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

2 → 66

Calls

2 calls:

5.0ms	(/ x (+ x y))
6.0ms	(pow (/ x (+ x y)) x)

series27.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(/ x (+ x y))
18.0ms	(pow (/ x (+ x y)) x)

simplify42.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5028	860

prune101.0ms

Filtered

51 candidates to 72 candidates (-41.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	5	73

Merged error: 1.3b

Counts

73 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
1.2b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.9b	(pow (* (/ (cbrt x) (cbrt (+ x y))) (/ (cbrt x) (cbrt (+ x y)))) x)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

51×	`cbrt-prod`
49×	`unpow-prod-down`
47×	`*-un-lft-identity`
42×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
13×	`pow1`
7×	`pow-pow` `pow-exp`
6×	`pow-unpow` `distribute-lft-out`
5×	`div-exp`
4×	`prod-exp` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `cbrt-div` `pow1/3` `associate-/r/` `sqr-pow`
1×	`pow2` `flip3-+` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip-+` `div-inv`

Counts

4 → 109

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
10.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
17.0ms	(pow (* (/ (cbrt x) (cbrt (+ x y))) (/ (cbrt x) (cbrt (+ x y)))) x)

series115.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt x)
23.0ms	(cbrt x)
28.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
40.0ms	(pow (* (/ (cbrt x) (cbrt (+ x y))) (/ (cbrt x) (cbrt (+ x y)))) x)

simplify39.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5310	1999

prune165.0ms

Filtered

90 candidates to 121 candidates (-34.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	122	4	126

Merged error: 0.8b

Counts

126 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
1.2b	(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.2b	(pow (/ (cbrt x) (cbrt (+ x y))) (* x 2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod` `unpow-prod-down`
85×	`*-un-lft-identity`
84×	`times-frac`
61×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`distribute-lft-out`
10×	`add-exp-log`
6×	`pow1`
4×	`pow-unpow` `cbrt-div` `pow-exp` `associate-/r/` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow1/3` `div-exp` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 146

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
10.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
10.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) (* x 2))

series105.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt x)
23.0ms	(cbrt x)
31.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) x)
29.0ms	(pow (/ (cbrt x) (cbrt (+ x y))) (* x 2))

simplify49.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5050	3075

prune233.0ms

Filtered

125 candidates to 158 candidates (-26.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	158	4	162

Merged error: 0.8b

Counts

162 → 4

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
1.2b	(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
1.9b	(pow (* (/ (cbrt x) (cbrt (+ x y))) (/ (cbrt x) (cbrt (+ x y)))) x)
15.0b	(pow (* (/ (cbrt (cbrt x)) (cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))) (cbrt (cbrt x))) x)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

198×	`cbrt-prod`
98×	`unpow-prod-down`
90×	`times-frac`
85×	`*-un-lft-identity`
67×	`add-sqr-sqrt` `add-cube-cbrt`
26×	`add-exp-log`
16×	`pow1`
10×	`pow-exp`
9×	`pow-unpow` `pow-pow` `distribute-lft-out`
6×	`div-exp` `prod-exp`
4×	`cbrt-div` `add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `sqr-pow`
2×	`pow-prod-down` `associate-/r/`
1×	`pow2` `flip3-+` `pow-plus` `pow1/3` `pow-sqr` `pow-prod-up` `flip-+` `div-inv`

Counts

4 → 167

Calls

4 calls:

2.0ms	(cbrt (cbrt x))
16.0ms	(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
17.0ms	(pow (* (/ (cbrt x) (cbrt (+ x y))) (/ (cbrt x) (cbrt (+ x y)))) x)
11.0ms	(pow (* (/ (cbrt (cbrt x)) (cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))) (cbrt (cbrt x))) x)

series136.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(cbrt (cbrt x))
31.0ms	(pow (/ (cbrt (cbrt x)) (cbrt (cbrt (+ x y)))) x)
36.0ms	(pow (* (/ (cbrt x) (cbrt (+ x y))) (/ (cbrt x) (cbrt (+ x y)))) x)
37.0ms	(pow (* (/ (cbrt (cbrt x)) (cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))) (cbrt (cbrt x))) x)

simplify69.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4987	4191
1	4987	4191

prune248.0ms

Filtered

141 candidates to 179 candidates (-27.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	179	4	183

Merged error: 0.8b

Counts

183 → 4

regimes91.0ms

Accuracy

23.5% (3.5b remaining)

Error of 4.8b against oracle of 1.3b and baseline of 5.9b

bsearch66.0ms

Steps

Iters	Range		Point
10	0.0025637095939271496	607190829057.0403	231.81783700568812

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	79
1	35	79

end0.0ms

sample1.9s

Algorithm

intervals

Results

720.0ms	1418×	body	1280	valid
373.0ms	1190×	body	640	valid
255.0ms	4339×	body	80	valid
140.0ms	679×	body	320	valid
67.0ms	224×	body	640	invalid
50.0ms	374×	body	160	valid
47.0ms	104×	body	1280	invalid
35.0ms	178×	body	320	invalid
15.0ms	117×	body	160	invalid
10.0ms	165×	body	80	invalid
8.0ms	199×	body	80	nan

Details

analyze599.0ms

sample71.0ms

simplify34.0ms

prune7.0ms

localize6.0ms

rewrite13.0ms

series27.0ms

simplify42.0ms

prune101.0ms

localize18.0ms

rewrite34.0ms

series115.0ms

simplify39.0ms

prune165.0ms

localize17.0ms

rewrite29.0ms

series105.0ms

simplify49.0ms

prune233.0ms

localize34.0ms

rewrite58.0ms

series136.0ms

simplify69.0ms

prune248.0ms

regimes91.0ms

bsearch66.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling