Details

analyze3.0ms

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

sample25.0ms

Algorithm

intervals

Results

9.0ms	137×	body	80	valid
6.0ms	46×	body	1280	valid
3.0ms	35×	body	640	valid
2.0ms	24×	body	320	valid
1.0ms	14×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

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: 28.4b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
4.0b	(-.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))
8.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series58.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(sqrt.f64 (+.f64 x 1))
43.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify84.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4986	774
1	4986	774

prune38.0ms

Filtered

30 candidates to 40 candidates (-33.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	4	41

Merged error: 0.1b

Counts

41 → 4

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))
0.2b	(/.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:

3.0ms	(sqrt.f64 (+.f64 x 1))
8.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series63.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(sqrt.f64 (+.f64 x 1))
20.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
31.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

simplify92.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4955	1536
1	4955	1536

prune78.0ms

Filtered

56 candidates to 84 candidates (-50.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	78	10	88

Merged error: 0.0b

Counts

88 → 10

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))))

rewrite102.0ms

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:

8.0ms	(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))))

series197.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
44.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
48.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
66.0ms	(/.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))))

simplify200.0ms

Algorithm

egg-herbie

Counts

465 → 465

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4912	17620
1	4912	17620

prune270.0ms

Filtered

131 candidates to 465 candidates (-255.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	461	4	465
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	465	10	475

Merged error: 0b

Counts

475 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

21574×	`sqrt-prod_binary64`
15023×	`*-un-lft-identity_binary64`
14958×	`times-frac_binary64`
5512×	`distribute-lft-out_binary64`
5378×	`add-sqr-sqrt_binary64`
5377×	`add-cube-cbrt_binary64`
584×	`sqrt-div_binary64`
555×	`associate-/l*_binary64`
292×	`associate-/r/_binary64`
147×	`flip3-+_binary64` `flip-+_binary64`
146×	`div-inv_binary64`
33×	`associate-/r*_binary64`
32×	`add-exp-log_binary64`
21×	`sqrt-pow1_binary64`
20×	`add-cbrt-cube_binary64`
19×	`pow1_binary64` `div-exp_binary64`
14×	`pow-flip_binary64`
11×	`pow1/2_binary64`
10×	`pow-div_binary64` `cbrt-undiv_binary64`
4×	`add-log-exp_binary64`
3×	`1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
2×	`associate-/l/_binary64` `inv-pow_binary64`
1×	`rem-sqrt-square_binary64`

Counts

4 → 5808

Calls

4 calls:

8.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
196.0ms	(/.f64 (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
37.0ms	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
13.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

series228.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
70.0ms	(/.f64 (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
50.0ms	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
64.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

simplify3.8s

Algorithm

egg-herbie

Counts

5820 → 5820

Iterations

Useful iterations: 0 (286.0ms)

Iter	Nodes	Cost
0	5015	379967

prune3.1s

Filtered

606 candidates to 5820 candidates (-860.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	5820	0	5820
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	5820	10	5830

Merged error: 0b

Counts

5830 → 10

regimes27.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

end0.0ms

sample609.0ms

Algorithm

intervals

Results

231.0ms	1743×	body	1280	valid
120.0ms	1235×	body	640	valid
109.0ms	4135×	body	80	valid
44.0ms	600×	body	320	valid
14.0ms	287×	body	160	valid
0.0ms	2×	body	80	nan

Details

analyze3.0ms

sample25.0ms

simplify16.0ms

prune1.0ms

localize5.0ms

rewrite13.0ms

series58.0ms

simplify84.0ms

prune38.0ms

localize6.0ms

rewrite26.0ms

series63.0ms

simplify92.0ms

prune78.0ms

localize12.0ms

rewrite102.0ms

series197.0ms

simplify200.0ms

prune270.0ms

localize18.0ms

rewrite1.2s

series228.0ms

simplify3.8s

prune3.1s

regimes27.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample609.0ms

Profiling