Details

analyze579.0ms

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

sample61.0ms

Algorithm

intervals

Results

15.0ms	32×	body	1280	valid
13.0ms	45×	body	640	valid
8.0ms	141×	body	80	valid
4.0ms	20×	body	320	valid
3.0ms	10×	body	640	invalid
2.0ms	18×	body	160	valid
2.0ms	11×	body	320	invalid
1.0ms	3×	body	1280	invalid
1.0ms	10×	body	80	invalid
0.0ms	4×	body	160	invalid
0.0ms	7×	body	80	nan

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4985	9
1	4985	9

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: 8.8b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
5.1b	(pow (/ x (+ x y)) x)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
118×	`*-un-lft-identity`
90×	`unpow-prod-down`
80×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
19×	`distribute-lft-out`
16×	`add-exp-log`
12×	`associate-/r/`
7×	`div-exp` `associate-/r*` `add-cbrt-cube` `div-inv`
6×	`flip3-+` `flip-+`
5×	`sqr-pow`
4×	`pow1` `pow-exp`
3×	`pow-unpow` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 172

Calls

3 calls:

11.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))
7.0ms	(pow (/ x (+ x y)) x)

series44.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(/ (pow (/ x (+ x y)) x) x)
5.0ms	(/ x (+ x y))
18.0ms	(pow (/ x (+ x y)) x)

simplify65.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5011	2849

prune191.0ms

Filtered

134 candidates to 181 candidates (-35.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	175	6	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	176	6	182

Merged error: 0.4b

Counts

182 → 6

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ x (+ x y))
5.1b	(pow (/ x (+ x y)) x)

rewrite14.0ms

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))
7.0ms	(pow (/ x (+ x y)) x)

series23.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(/ x (+ x y))
18.0ms	(pow (/ x (+ x y)) x)

simplify49.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5028	860

prune88.0ms

Filtered

51 candidates to 72 candidates (-41.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	72	6	78

Merged error: 0.4b

Counts

78 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt x) (sqrt (+ x y)))
0.1b	(/ (sqrt x) (sqrt (+ x y)))
0.7b	(pow (/ (sqrt x) (sqrt (+ x y))) x)
0.7b	(pow (/ (sqrt x) (sqrt (+ x y))) x)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

194×	`sqrt-prod`
172×	`*-un-lft-identity`
168×	`times-frac`
120×	`add-sqr-sqrt` `add-cube-cbrt`
96×	`unpow-prod-down`
26×	`distribute-lft-out`
14×	`add-exp-log` `associate-/r*`
12×	`associate-/l*`
8×	`sqrt-div` `associate-/r/` `add-cbrt-cube`
6×	`pow1` `pow-unpow`
4×	`sqrt-undiv` `flip3-+` `div-exp` `pow-exp` `flip-+` `div-inv` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqrt-pow2` `sqr-pow`

Counts

4 → 268

Calls

4 calls:

7.0ms	(/ (sqrt x) (sqrt (+ x y)))
10.0ms	(/ (sqrt x) (sqrt (+ x y)))
12.0ms	(pow (/ (sqrt x) (sqrt (+ x y))) x)
11.0ms	(pow (/ (sqrt x) (sqrt (+ x y))) x)

series97.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (sqrt x) (sqrt (+ x y)))
13.0ms	(/ (sqrt x) (sqrt (+ x y)))
37.0ms	(pow (/ (sqrt x) (sqrt (+ x y))) x)
33.0ms	(pow (/ (sqrt x) (sqrt (+ x y))) x)

simplify57.0ms

Algorithm

egg-herbie

Counts

280 → 280

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5006	4636

prune197.0ms

Filtered

144 candidates to 280 candidates (-94.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	280	0	280
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	280	6	286

Merged error: 0.4b

Counts

286 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (pow (/ x (+ x y)) x) x))
0.2b	(* (sqrt (/ (pow (/ x (+ x y)) x) x)) (sqrt (/ (pow (/ x (+ x y)) x) x)))
5.1b	(pow (/ x (+ x y)) x)
5.1b	(pow (/ x (+ x y)) x)

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

671×	`times-frac`
456×	`*-un-lft-identity`
448×	`sqrt-prod`
433×	`add-sqr-sqrt`
368×	`unpow-prod-down`
300×	`add-cube-cbrt`
93×	`swap-sqr`
73×	`associate-r` `associate-l`
69×	`distribute-lft-out`
36×	`unswap-sqr`
34×	`associate-/r/`
30×	`sqr-pow`
22×	`pow1` `div-inv`
17×	`flip3-+` `flip-+`
12×	`add-exp-log`
9×	`sqrt-pow1` `pow1/2`
6×	`pow-unpow` `add-cbrt-cube`
5×	`rem-sqrt-square` `sqrt-div` `pow-prod-up`
4×	`pow-exp` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`pow-to-exp` `pow-pow` `div-exp`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 454

Calls

4 calls:

13.0ms	(sqrt (/ (pow (/ x (+ x y)) x) x))
96.0ms	(* (sqrt (/ (pow (/ x (+ x y)) x) x)) (sqrt (/ (pow (/ x (+ x y)) x) x)))
7.0ms	(pow (/ x (+ x y)) x)
7.0ms	(pow (/ x (+ x y)) x)

series96.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (/ (pow (/ x (+ x y)) x) x))
29.0ms	(* (sqrt (/ (pow (/ x (+ x y)) x) x)) (sqrt (/ (pow (/ x (+ x y)) x) x)))
18.0ms	(pow (/ x (+ x y)) x)
18.0ms	(pow (/ x (+ x y)) x)

simplify97.0ms

Algorithm

egg-herbie

Counts

466 → 466

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4982	10280
1	4982	10280

prune437.0ms

Filtered

314 candidates to 466 candidates (-48.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	466	0	466
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	466	6	472

Merged error: 0.4b

Counts

472 → 6

regimes125.0ms

Accuracy

58.2% (4.3b remaining)

Error of 5.0b against oracle of 0.7b and baseline of 10.9b

bsearch242.0ms

Steps

Iters	Range		Point
7	7.378468937869517e+100	5.047046899323127e+102	3.860084631978537e+102
10	4781.5983133701375	6358589967702337.0	4862.087329763204
10	-8.115155012966615e+39	-3.487506546511078e+21	-3.992462048211031e+29

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	100	107
1	100	107

end0.0ms

sample1.8s

Algorithm

intervals

Results

679.0ms	1349×	body	1280	valid
370.0ms	1229×	body	640	valid
242.0ms	4398×	body	80	valid
135.0ms	672×	body	320	valid
66.0ms	219×	body	640	invalid
49.0ms	111×	body	1280	invalid
45.0ms	352×	body	160	valid
32.0ms	169×	body	320	invalid
11.0ms	92×	body	160	invalid
9.0ms	156×	body	80	invalid
8.0ms	186×	body	80	nan

Details

analyze579.0ms

sample61.0ms

simplify36.0ms

prune8.0ms

localize6.0ms

rewrite34.0ms

series44.0ms

simplify65.0ms

prune191.0ms

localize7.0ms

rewrite14.0ms

series23.0ms

simplify49.0ms

prune88.0ms

localize10.0ms

rewrite52.0ms

series97.0ms

simplify57.0ms

prune197.0ms

localize9.0ms

rewrite167.0ms

series96.0ms

simplify97.0ms

prune437.0ms

regimes125.0ms

bsearch242.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling