Details

analyze758.0ms (9.9%)

Algorithm

1×

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

Compiler

Compiled 20 to 16 computations (20% saved)

sample83.0ms (1.1%)

Algorithm

1×

intervals

Results

21.0ms	52×	body	1024	invalid
19.0ms	56×	body	1024	valid
12.0ms	165×	body	128	valid
6.0ms	28×	body	512	invalid
6.0ms	26×	body	512	valid
2.0ms	13×	body	256	invalid
1.0ms	18×	body	128	invalid
1.0ms	9×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify180.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune4.0ms (0.1%)

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

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize11.0ms (0.1%)

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

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_435`
38×	`times-frac_binary64_420`
32×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
22×	`sqrt-prod_binary64_429` `associate-r_binary64_356`
10×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
6×	`associate-/r*_binary64_360`
5×	`pow1_binary64_472` `add-log-exp_binary64_450`
3×	`associate-l_binary64_357` `unswap-sqr_binary64_382` `associate-/l*_binary64_361`
2×	`flip3-+_binary64_417` `div-inv_binary64_411` `cbrt-undiv_binary64_445` `prod-exp_binary64_460` `flip-+_binary64_388` `cbrt-unprod_binary64_444` `associate-/l/_binary64_363` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `-commutative_binary64_347` `+-commutative_binary64_346` `pow-prod-down_binary64_482` `frac-2neg_binary64_425` `sum-log_binary64_502` `associate-r/_binary64_358`

Counts

3 → 94

Calls

3 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))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series493.0ms (6.5%)

Counts

3 → 9

Calls

3 calls:

346.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
105.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
42.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify56.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	6033	2380

prune123.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	96	9	105

Merged error: 0b

Counts

105 → 9

Compiler

Compiled 2441 to 964 computations (60.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
0.2b	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
0.3b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
0.3b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))

rewrite51.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64_414`
16×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `add-sqr-sqrt_binary64_435`
14×	`add-cube-cbrt_binary64_446`
12×	`times-frac_binary64_420` `sqrt-prod_binary64_429` `associate-/r*_binary64_360`
6×	`pow1_binary64_472` `div-inv_binary64_411` `add-log-exp_binary64_450`
5×	`associate-r_binary64_356`
4×	`cbrt-undiv_binary64_445` `div-exp_binary64_462`
3×	`prod-exp_binary64_460` `associate-l_binary64_357` `cbrt-unprod_binary64_444` `associate-*r/_binary64_358`
2×	`clear-num_binary64_413` `flip3-+_binary64_417` `distribute-rgt-out_binary64_369` `frac-add_binary64_422` `flip-+_binary64_388` `frac-2neg_binary64_425` `distribute-lft-out_binary64_367` `associate-/l*_binary64_361`
1×	`distribute-lft-in_binary64_365` `distribute-rgt-in_binary64_366` `*-commutative_binary64_347` `+-commutative_binary64_346` `pow-prod-down_binary64_482` `unswap-sqr_binary64_382` `sum-log_binary64_502`

Counts

4 → 93

Calls

4 calls:

17.0ms	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
13.0ms	(+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
6.0ms	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
6.0ms	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))

series640.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

343.0ms	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
125.0ms	(+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
86.0ms	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
85.0ms	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))

simplify72.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4959	1731
1	4959	1731

prune121.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	106	8	114

Merged error: 0b

Counts

114 → 8

Compiler

Compiled 2313 to 1327 computations (42.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
0.2b	(.f64 (cos.f64 th) (+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 (.f64 a2 a2) (sqrt.f64 2))))
0.3b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
0.5b	(/.f64 (sqrt.f64 2) a1)

rewrite97.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`times-frac_binary64_420`
102×	`*-un-lft-identity_binary64_414` `add-sqr-sqrt_binary64_435`
100×	`add-cube-cbrt_binary64_446`
54×	`sqrt-prod_binary64_429`
31×	`associate-/r*_binary64_360`
18×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
10×	`associate-/l*_binary64_361`
7×	`div-inv_binary64_411`
6×	`pow1_binary64_472` `cbrt-undiv_binary64_445` `div-exp_binary64_462`
4×	`add-log-exp_binary64_450` `associate-r_binary64_356`
3×	`clear-num_binary64_413` `associate-l_binary64_357` `frac-2neg_binary64_425` `associate-*r/_binary64_358`
2×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
1×	`associate-/r/_binary64_362` `distribute-lft-in_binary64_365` `flip3-+_binary64_417` `distribute-rgt-in_binary64_366` `*-commutative_binary64_347` `pow-prod-down_binary64_482` `frac-add_binary64_422` `flip-+_binary64_388` `distribute-lft-out_binary64_367` `unswap-sqr_binary64_382`

Counts

4 → 196

Calls

4 calls:

51.0ms	(.f64 (cos.f64 th) (+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 (.f64 a2 a2) (sqrt.f64 2))))
8.0ms	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
6.0ms	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
5.0ms	(/.f64 (sqrt.f64 2) a1)

series584.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

367.0ms	(.f64 (cos.f64 th) (+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 (.f64 a2 a2) (sqrt.f64 2))))
84.0ms	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
83.0ms	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
49.0ms	(/.f64 (sqrt.f64 2) a1)

simplify101.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4958	3586
1	4958	3586

prune251.0ms (3.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	208	8	216

Merged error: 0b

Counts

216 → 8

Compiler

Compiled 4871 to 2956 computations (39.3% saved)

localize19.0ms (0.3%)

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))))
6.7b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.7b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite100.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

149×	`add-sqr-sqrt_binary64_435`
146×	`times-frac_binary64_420`
127×	`sqrt-prod_binary64_429`
90×	`cbrt-prod_binary64_442`
87×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
58×	`associate-r_binary64_356`
27×	`add-exp-log_binary64_449`
21×	`unswap-sqr_binary64_382`
19×	`add-cbrt-cube_binary64_447`
10×	`associate-l_binary64_357`
9×	`associate-/r*_binary64_360`
8×	`pow1_binary64_472` `cbrt-undiv_binary64_445` `prod-exp_binary64_460` `cbrt-unprod_binary64_444` `div-exp_binary64_462`
6×	`sqrt-div_binary64_430` `associate-/l*_binary64_361`
4×	`add-log-exp_binary64_450`
3×	`flip3-+_binary64_417` `div-inv_binary64_411` `flip-+_binary64_388`
2×	`sqrt-pow1_binary64_431` `pow1/2_binary64_491` `associate-/l/_binary64_363` `rem-sqrt-square_binary64_427`
1×	`clear-num_binary64_413` `associate-l/_binary64_359` `-commutative_binary64_347` `pow-prod-down_binary64_482` `frac-2neg_binary64_425` `frac-times_binary64_424` `associate-*r/_binary64_358`

Counts

4 → 226

Calls

4 calls:

37.0ms	(.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))))
9.0ms	(/.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)))

series441.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

236.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
115.0ms	(.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))))
46.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
44.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify156.0ms (2%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4905	8058
1	4905	8058

prune424.0ms (5.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	238	8	246

Merged error: 0b

Counts

246 → 8

Compiler

Compiled 9407 to 4212 computations (55.2% saved)

regimes142.0ms (1.9%)

Compiler: Compiled 1294 to 1058 computations (18.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	15	25

end0.0ms (0%)

sample2.7s (34.9%)

Algorithm

1×

intervals

Results

631.0ms	1759×	body	1024	valid
539.0ms	1517×	body	1024	invalid
378.0ms	4891×	body	128	valid
216.0ms	889×	body	512	valid
184.0ms	774×	body	512	invalid
71.0ms	455×	body	256	valid
67.0ms	409×	body	256	invalid
52.0ms	632×	body	128	invalid
4.0ms	6×	body	2048	valid

Compiler

Compiled 195 to 159 computations (18.5% saved)

Details

analyze758.0ms (9.9%)

sample83.0ms (1.1%)

simplify180.0ms (2.4%)

prune4.0ms (0.1%)

localize11.0ms (0.1%)

rewrite34.0ms (0.4%)

series493.0ms (6.5%)

simplify56.0ms (0.7%)

prune123.0ms (1.6%)

localize12.0ms (0.2%)

rewrite51.0ms (0.7%)

series640.0ms (8.4%)

simplify72.0ms (0.9%)

prune121.0ms (1.6%)

localize12.0ms (0.2%)

rewrite97.0ms (1.3%)

series584.0ms (7.7%)

simplify101.0ms (1.3%)

prune251.0ms (3.3%)

localize19.0ms (0.3%)

rewrite100.0ms (1.3%)

series441.0ms (5.8%)

simplify156.0ms (2%)

prune424.0ms (5.6%)

regimes142.0ms (1.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (34.9%)

Profiling