Details

analyze798.0ms

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

sample102.0ms

Algorithm

intervals

Results

18.0ms	41×	body	1280	valid
18.0ms	40×	body	1280	invalid
14.0ms	157×	body	80	valid
11.0ms	36×	body	640	valid
10.0ms	32×	body	640	invalid
3.0ms	15×	body	320	invalid
3.0ms	14×	body	320	valid
1.0ms	8×	body	160	valid
1.0ms	15×	body	80	invalid
1.0ms	6×	body	160	invalid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune25.0ms

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

localize16.0ms

Local error

Found 2 expressions with local error:

0.2b	(.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))

rewrite22.0ms

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:

11.0ms	(.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))

series222.0ms

Counts

2 → 6

Calls

2 calls:

166.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
56.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

simplify64.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5432	2187

prune370.0ms

Filtered

59 candidates to 89 candidates (-50.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	82	7	89
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	84	7	91

Merged error: 0.0b

Counts

91 → 7

localize27.0ms

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))))
8.1b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
8.1b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite69.0ms

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:

9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
39.0ms	(.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)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
61.0ms	(.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))))
22.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
23.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify147.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5094	8654

prune850.0ms

Filtered

140 candidates to 238 candidates (-70.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	238	7	245

Merged error: 0.0b

Counts

245 → 7

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b	(.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))

rewrite17.0ms

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

series184.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
117.0ms	(/.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 (63.0ms)

Iter	Nodes	Cost
0	5124	1120

prune240.0ms

Filtered

40 candidates to 55 candidates (-37.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	54	8	62

Merged error: 0b

Counts

62 → 8

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b

(*.f64 (cos.f64 th) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))

0.2b

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

0.3b

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

234×	`sqrt-prod_binary64`
216×	`times-frac_binary64`
95×	`add-sqr-sqrt_binary64`
93×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`associate-/r*_binary64`
14×	`associate-/l*_binary64`
12×	`div-inv_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
5×	`pow1_binary64`
4×	`associate-*r/_binary64`
3×	`associate-/l/_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`flip3-+_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

3 → 213

Calls

3 calls:

7.0ms

(*.f64 (cos.f64 th) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))

15.0ms

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

10.0ms

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

series443.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms

(*.f64 (cos.f64 th) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))

159.0ms

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

189.0ms

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

simplify118.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5175	7600

prune537.0ms

Filtered

103 candidates to 222 candidates (-115.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	222	8	230

Merged error: 0b

Counts

230 → 8

regimes665.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	52
1	20	52

end0.0ms

sample2.9s

Algorithm

intervals

Results

641.0ms	1437×	body	1280	valid
519.0ms	1146×	body	1280	invalid
360.0ms	1156×	body	640	valid
354.0ms	4562×	body	80	valid
296.0ms	933×	body	640	invalid
129.0ms	572×	body	320	valid
107.0ms	472×	body	320	invalid
44.0ms	273×	body	160	valid
43.0ms	503×	body	80	invalid
36.0ms	236×	body	160	invalid

Details

analyze798.0ms

sample102.0ms

simplify14.0ms

prune25.0ms

localize16.0ms

rewrite22.0ms

series222.0ms

simplify64.0ms

prune370.0ms

localize27.0ms

rewrite69.0ms

series220.0ms

simplify147.0ms

prune850.0ms

localize16.0ms

rewrite17.0ms

series184.0ms

simplify83.0ms

prune240.0ms

localize20.0ms

rewrite47.0ms

series443.0ms

simplify118.0ms

prune537.0ms

regimes665.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample2.9s

Profiling