Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

sample19.0ms

Algorithm

intervals

Results

6.0ms	51×	body	1280	valid
4.0ms	151×	body	80	valid
3.0ms	32×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	9×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	70	7
1	70	7

prune1.0ms

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: 25.3b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `difference-of-squares_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `distribute-lft-out--_binary64`
2×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

2 → 34

Calls

2 calls:

3.0ms	(sqrt.f64 (+.f64 x 1))
9.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series16.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
12.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify58.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5006	484

prune34.0ms

Filtered

30 candidates to 40 candidates (-33.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	2	41

Merged error: 0.1b

Counts

41 → 2

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
24×	`sqrt-prod_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
7×	`add-exp-log_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/r/_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

3 → 75

Calls

3 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
9.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series24.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
6.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
14.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

simplify63.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4999	966
1	4999	966

prune60.0ms

Filtered

56 candidates to 84 candidates (-50.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	79	7	86

Merged error: 0.0b

Counts

86 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

742×	`*-un-lft-identity_binary64`
700×	`sqrt-prod_binary64`
594×	`times-frac_binary64`
280×	`distribute-lft-out_binary64`
254×	`add-sqr-sqrt_binary64`
252×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
28×	`sqrt-div_binary64`
24×	`associate-/r/_binary64`
18×	`associate-/r*_binary64`
17×	`add-exp-log_binary64`
14×	`flip3-+_binary64` `flip-+_binary64`
12×	`div-inv_binary64`
11×	`add-cbrt-cube_binary64`
8×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `pow-flip_binary64`
2×	`1-exp_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`associate-/l/_binary64` `inv-pow_binary64`

Counts

4 → 453

Calls

4 calls:

9.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
12.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
32.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
11.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
13.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
20.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

simplify121.0ms

Algorithm

egg-herbie

Counts

465 → 465

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4926	10751
1	4926	10751

prune179.0ms

Filtered

131 candidates to 465 candidates (-255.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	461	4	465
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	463	9	472

Merged error: 0b

Counts

472 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b	(/.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
0.2b	(/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))

rewrite3.3s

Algorithm

rewrite-expression-head

Rules

56169×	`sqrt-prod_binary64`
42381×	`times-frac_binary64`
38028×	`*-un-lft-identity_binary64`
14256×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
13584×	`distribute-lft-out_binary64`
1391×	`sqrt-div_binary64`
1389×	`associate-/r/_binary64`
714×	`div-inv_binary64`
676×	`flip3-+_binary64` `flip-+_binary64`
383×	`associate-/r*_binary64`
51×	`associate-/l*_binary64`
48×	`sqrt-pow1_binary64`
35×	`pow1_binary64`
31×	`pow-flip_binary64`
30×	`pow-div_binary64`
19×	`add-exp-log_binary64`
18×	`pow1/2_binary64`
15×	`add-cbrt-cube_binary64`
8×	`div-exp_binary64`
7×	`inv-pow_binary64`
6×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64`
3×	`associate-/l/_binary64` `sqrt-undiv_binary64`
2×	`1-exp_binary64` `rec-exp_binary64`

Counts

4 → 12747

Calls

4 calls:

13.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
13.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
32.0ms	(/.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
319.0ms	(/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
13.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
20.0ms	(/.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
10.0ms	(/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))

simplify5.2s

Algorithm

egg-herbie

Counts

12759 → 12759

Iterations

Useful iterations: 0 (715.0ms)

Iter	Nodes	Cost
0	5149	679877

prune11.3s

Filtered

985 candidates to 12759 candidates (-1195.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	12758	1	12759
Fresh	2	3	5
Picked	0	1	1
Done	1	2	3
Total	12761	7	12768

Merged error: 0b

Counts

12768 → 7

regimes46.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	9
1	10	9

end0.0ms

sample605.0ms

Algorithm

intervals

Results

214.0ms	1708×	body	1280	valid
129.0ms	1263×	body	640	valid
107.0ms	4105×	body	80	valid
45.0ms	621×	body	320	valid
17.0ms	303×	body	160	valid
0.0ms	2×	body	80	nan

Details

analyze2.0ms

sample19.0ms

simplify8.0ms

prune1.0ms

localize5.0ms

rewrite13.0ms

series16.0ms

simplify58.0ms

prune34.0ms

localize6.0ms

rewrite26.0ms

series24.0ms

simplify63.0ms

prune60.0ms

localize12.0ms

rewrite105.0ms

series55.0ms

simplify121.0ms

prune179.0ms

localize13.0ms

rewrite3.3s

series60.0ms

simplify5.2s

prune11.3s

regimes46.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample605.0ms

Profiling