Details

analyze729.0ms

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

sample84.0ms

Algorithm

intervals

Results

21.0ms	63×	body	1024	invalid
19.0ms	54×	body	1024	valid
11.0ms	146×	body	128	valid
9.0ms	37×	body	512	valid
6.0ms	25×	body	512	invalid
3.0ms	19×	body	256	valid
2.0ms	14×	body	256	invalid
2.0ms	24×	body	128	invalid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.4b

Counts

2 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
22×	`associate-r_binary64` `sqrt-prod_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r*_binary64`
4×	`pow1_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64` `associate-/l*_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

2 → 83

Calls

2 calls:

13.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
8.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

series449.0ms

Counts

2 → 6

Calls

2 calls:

339.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
110.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

simplify68.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5014	2187

prune93.0ms

Filtered

59 candidates to 89 candidates (-50.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	81	8	89
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	82	9	91

Merged error: 0.0b

Counts

91 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
5.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

149×	`add-sqr-sqrt_binary64`
146×	`times-frac_binary64`
127×	`sqrt-prod_binary64`
90×	`cbrt-prod_binary64`
87×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
58×	`associate-r_binary64`
27×	`add-exp-log_binary64`
21×	`unswap-sqr_binary64`
19×	`add-cbrt-cube_binary64`
10×	`associate-l_binary64`
9×	`associate-/r*_binary64`
8×	`pow1_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
6×	`associate-/l*_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 226

Calls

4 calls:

13.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
38.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series450.0ms

Counts

4 → 12

Calls

4 calls:

238.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
126.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
41.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
44.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify154.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4906	8058
1	4906	8058

prune249.0ms

Filtered

141 candidates to 238 candidates (-68.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	238	9	247

Merged error: 0b

Counts

247 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
0.4b	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
5.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

540×	`times-frac_binary64`
429×	`sqrt-prod_binary64`
297×	`add-sqr-sqrt_binary64`
295×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
48×	`associate-/r*_binary64`
22×	`sqrt-div_binary64`
17×	`associate-/r/_binary64`
12×	`associate-/l*_binary64`
11×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
9×	`div-inv_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`sqrt-undiv_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 411

Calls

4 calls:

23.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
9.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
100.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
46.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
44.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify202.0ms

Algorithm

egg-herbie

Counts

423 → 423

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5056	17836

prune206.0ms

Filtered

162 candidates to 423 candidates (-161.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	421	2	423
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	423	9	432

Merged error: 0b

Counts

432 → 9

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
0.4b	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
4×	`pow1_binary64` `associate-*l/_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

2 → 49

Calls

2 calls:

7.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
10.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

series379.0ms

Counts

2 → 6

Calls

2 calls:

131.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
248.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

simplify83.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4926	1110
1	4926	1110

prune39.0ms

Filtered

38 candidates to 55 candidates (-44.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	56	8	64

Merged error: 0b

Counts

64 → 8

regimes139.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	36
1	16	36

end0.0ms

sample2.4s

Algorithm

intervals

Results

611.0ms	1741×	body	1024	valid
541.0ms	1563×	body	1024	invalid
346.0ms	4870×	body	128	valid
211.0ms	923×	body	512	valid
185.0ms	796×	body	512	invalid
69.0ms	459×	body	256	valid
66.0ms	416×	body	256	invalid
54.0ms	659×	body	128	invalid
5.0ms	7×	body	2048	valid

Details

analyze729.0ms

sample84.0ms

simplify10.0ms

prune8.0ms

localize10.0ms

rewrite29.0ms

series449.0ms

simplify68.0ms

prune93.0ms

localize16.0ms

rewrite98.0ms

series450.0ms

simplify154.0ms

prune249.0ms

localize16.0ms

rewrite119.0ms

series299.0ms

simplify202.0ms

prune206.0ms

localize10.0ms

rewrite24.0ms

series379.0ms

simplify83.0ms

prune39.0ms

regimes139.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.4s

Profiling