Details

analyze761.0ms

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

sample89.0ms

Algorithm

intervals

Results

19.0ms	36×	body	1280	invalid
13.0ms	29×	body	1280	valid
13.0ms	42×	body	640	valid
12.0ms	155×	body	80	valid
9.0ms	30×	body	640	invalid
5.0ms	21×	body	320	valid
2.0ms	9×	body	320	invalid
1.0ms	10×	body	160	invalid
1.0ms	18×	body	80	invalid
1.0ms	9×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	105	13
1	105	13

prune10.0ms

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: 0.6b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.6b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 94

Calls

3 calls:

8.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
12.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

series68.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
46.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
14.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

simplify40.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5138	1529

prune117.0ms

Filtered

69 candidates to 103 candidates (-49.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	99	6	105

Merged error: 0.3b

Counts

105 → 6

localize15.0ms

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 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
5.7b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.7b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac_binary64`
102×	`sqrt-prod_binary64`
86×	`add-sqr-sqrt_binary64`
84×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
78×	`cbrt-prod_binary64`
58×	`associate-r_binary64`
38×	`add-exp-log_binary64`
29×	`add-cbrt-cube_binary64`
16×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`pow1_binary64`
9×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
6×	`associate-/l*_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-*l/_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`
1×	`associate-r/_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `-commutative_binary64`

Counts

4 → 201

Calls

4 calls:

11.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
28.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.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)))

series81.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
32.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
7.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
7.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify89.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4958	4503
1	4958	4503

prune205.0ms

Filtered

126 candidates to 213 candidates (-69.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	212	1	213
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	213	6	219

Merged error: 0.3b

Counts

219 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
0.2b	(/.f64 (.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 2)))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
13.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
14.0ms	(/.f64 (.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 2)))
10.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

series192.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
91.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
46.0ms	(/.f64 (.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 2)))
47.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

simplify47.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5016	1745

prune118.0ms

Filtered

79 candidates to 112 candidates (-41.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	112	6	118

Merged error: 0.3b

Counts

118 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
0.6b	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 60

Calls

3 calls:

4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
7.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
9.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

series61.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
20.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
34.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

simplify51.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4986	841
1	4986	841

prune51.0ms

Filtered

46 candidates to 69 candidates (-50.0%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	69	6	75

Merged error: 0.3b

Counts

75 → 6

regimes307.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	22
1	16	22

end0.0ms

sample2.7s

Algorithm

intervals

Results

585.0ms	1324×	body	1280	valid
506.0ms	1133×	body	1280	invalid
370.0ms	1198×	body	640	valid
357.0ms	4664×	body	80	valid
285.0ms	942×	body	640	invalid
123.0ms	546×	body	320	valid
104.0ms	471×	body	320	invalid
41.0ms	268×	body	160	valid
37.0ms	474×	body	80	invalid
32.0ms	211×	body	160	invalid

Details

analyze761.0ms

sample89.0ms

simplify7.0ms

prune10.0ms

localize10.0ms

rewrite30.0ms

series68.0ms

simplify40.0ms

prune117.0ms

localize15.0ms

rewrite56.0ms

series81.0ms

simplify89.0ms

prune205.0ms

localize13.0ms

rewrite45.0ms

series192.0ms

simplify47.0ms

prune118.0ms

localize10.0ms

rewrite22.0ms

series61.0ms

simplify51.0ms

prune51.0ms

regimes307.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling