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

sample27.0ms

Algorithm

intervals

Results

7.0ms	49×	body	1280	valid
6.0ms	56×	body	640	valid
6.0ms	27×	body	320	valid
3.0ms	117×	body	80	valid
0.0ms	7×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

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: 33.6b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.0b	(-.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))

series55.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(sqrt.f64 (+.f64 x 1))
40.0ms	(-.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)))

series69.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(sqrt.f64 (+.f64 x 1))
24.0ms	(+.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 (70.0ms)

Iter	Nodes	Cost
0	4955	1536
1	4955	1536

prune79.0ms

Filtered

56 candidates to 84 candidates (-50.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	81	7	88

Merged error: 0.0b

Counts

88 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.0b	(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:

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)))
13.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
35.0ms	(/.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))))

series219.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
44.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
55.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
78.0ms	(/.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))))

simplify193.0ms

Algorithm

egg-herbie

Counts

465 → 465

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4912	17620
1	4912	17620

prune274.0ms

Filtered

131 candidates to 465 candidates (-255.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	461	4	465
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	464	8	472

Merged error: 0b

Counts

472 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(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 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.3b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

334×	`*-un-lft-identity_binary64`
284×	`sqrt-prod_binary64`
238×	`times-frac_binary64`
200×	`add-sqr-sqrt_binary64`
117×	`add-cube-cbrt_binary64`
108×	`distribute-lft-out_binary64`
53×	`swap-sqr_binary64`
52×	`add-exp-log_binary64`
33×	`associate-r_binary64` `associate-l_binary64`
32×	`pow1_binary64`
30×	`pow-flip_binary64`
25×	`unswap-sqr_binary64`
20×	`add-cbrt-cube_binary64` `div-exp_binary64`
18×	`associate-/r*_binary64`
16×	`prod-exp_binary64`
14×	`sqrt-div_binary64`
12×	`associate-/r/_binary64`
11×	`pow1/2_binary64` `sqrt-pow1_binary64`
10×	`1-exp_binary64` `inv-pow_binary64` `rec-exp_binary64`
9×	`pow-prod-up_binary64`
8×	`div-inv_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`cbrt-undiv_binary64` `associate-/l*_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-r/_binary64` `pow-plus_binary64` `rem-sqrt-square_binary64` `un-div-inv_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 333

Calls

4 calls:

8.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
12.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
12.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
45.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
46.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
48.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
35.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

simplify158.0ms

Algorithm

egg-herbie

Counts

345 → 345

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4909	9778
1	4909	9778

prune250.0ms

Filtered

136 candidates to 345 candidates (-153.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	345	0	345
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	345	8	353

Merged error: 0b

Counts

353 → 8

regimes23.0ms

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

sample669.0ms

Algorithm

intervals

Results

240.0ms	1656×	body	1280	valid
137.0ms	1251×	body	640	valid
122.0ms	4148×	body	80	valid
54.0ms	635×	body	320	valid
17.0ms	310×	body	160	valid
0.0ms	2×	body	80	nan

Details

analyze3.0ms

sample27.0ms

simplify15.0ms

prune1.0ms

localize5.0ms

rewrite13.0ms

series55.0ms

simplify84.0ms

prune38.0ms

localize6.0ms

rewrite26.0ms

series69.0ms

simplify92.0ms

prune79.0ms

localize12.0ms

rewrite105.0ms

series219.0ms

simplify193.0ms

prune274.0ms

localize9.0ms

rewrite104.0ms

series174.0ms

simplify158.0ms

prune250.0ms

regimes23.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample669.0ms

Profiling