Details

analyze750.0ms (7.5%)

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)

sample82.0ms (0.8%)

Algorithm

1×

intervals

Results

18.0ms	41×	body	1024	invalid
16.0ms	45×	body	1024	valid
12.0ms	153×	body	128	valid
9.0ms	38×	body	512	valid
8.0ms	33×	body	512	invalid
3.0ms	20×	body	256	valid
3.0ms	34×	body	128	invalid
1.0ms	8×	body	256	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify168.0ms (1.7%)

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%)

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: 0.3b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize13.0ms (0.1%)

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))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

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))

series447.0ms (4.5%)

Counts

2 → 6

Calls

2 calls:

340.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
107.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

simplify50.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5606	2187

prune113.0ms (1.1%)

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

Compiler

Compiled 2224 to 886 computations (60.2% saved)

localize15.0ms (0.2%)

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)))

rewrite85.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64_420`
102×	`sqrt-prod_binary64_429`
86×	`add-sqr-sqrt_binary64_435`
84×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
78×	`cbrt-prod_binary64_442`
58×	`associate-r_binary64_356`
38×	`add-exp-log_binary64_449`
29×	`add-cbrt-cube_binary64_447`
16×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
11×	`pow1_binary64_472`
9×	`cbrt-undiv_binary64_445` `div-exp_binary64_462` `associate-/r*_binary64_360`
6×	`sqrt-div_binary64_430` `associate-/l*_binary64_361`
4×	`add-log-exp_binary64_450`
3×	`associate-*l/_binary64_359` `flip3-+_binary64_417` `pow-prod-down_binary64_482` `flip-+_binary64_388`
2×	`div-inv_binary64_411` `sqrt-pow1_binary64_431` `pow1/2_binary64_491` `associate-/l/_binary64_363` `rem-sqrt-square_binary64_427`
1×	`clear-num_binary64_413` `-commutative_binary64_347` `associate-l_binary64_357` `frac-2neg_binary64_425` `frac-times_binary64_424` `associate-r/_binary64_358`

Counts

4 → 201

Calls

4 calls:

35.0ms	(.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))))
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)))

series593.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

257.0ms	(.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))))
243.0ms	(/.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)))
46.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify138.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4936	6988
1	4936	6988

prune364.0ms (3.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	210	3	213
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	214	8	222

Merged error: 0b

Counts

222 → 8

Compiler

Compiled 8483 to 3766 computations (55.6% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b

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

0.2b

(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2))

0.2b

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

rewrite78.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`times-frac_binary64_420`
86×	`add-sqr-sqrt_binary64_435`
68×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
66×	`unpow-prod-down_binary64_490`
56×	`cbrt-prod_binary64_442`
46×	`associate-r_binary64_356`
34×	`add-exp-log_binary64_449`
28×	`sqrt-prod_binary64_429`
23×	`associate-/r*_binary64_360`
16×	`add-cbrt-cube_binary64_447`
14×	`div-exp_binary64_462`
8×	`sqr-pow_binary64_386` `prod-exp_binary64_460` `unpow2_binary64_476`
7×	`unswap-sqr_binary64_382`
6×	`cbrt-undiv_binary64_445`
5×	`pow1_binary64_472`
4×	`associate-/l*_binary64_361` `cbrt-unprod_binary64_444`
3×	`div-inv_binary64_411` `pow-exp_binary64_479` `pow-to-exp_binary64_480` `associate-l_binary64_357` `add-log-exp_binary64_450` `associate-/l/_binary64_363`
2×	`clear-num_binary64_413` `frac-2neg_binary64_425` `associate-*r/_binary64_358`
1×	`flip3-+_binary64_417` `*-commutative_binary64_347` `pow-prod-down_binary64_482` `flip-+_binary64_388`

Counts

3 → 185

Calls

3 calls:

21.0ms

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

17.0ms

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

15.0ms

(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2))

series1.3s (13.3%)

Counts

3 → 9

Calls

3 calls:

683.0ms

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

336.0ms

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

318.0ms

(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2))

simplify94.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4996	5765
1	4996	5765

prune274.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	194	8	202

Merged error: 0b

Counts

202 → 8

Compiler

Compiled 5860 to 3064 computations (47.7% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b

(*.f64 (cos.f64 th) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)))

0.2b

(/.f64 (*.f64 (cos.f64 th) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))) (cbrt.f64 (sqrt.f64 2)))

0.5b

(*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64_449`
17×	`add-sqr-sqrt_binary64_435`
16×	`cbrt-prod_binary64_442`
13×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414` `add-cbrt-cube_binary64_447`
10×	`pow1_binary64_472`
9×	`times-frac_binary64_420` `associate-/r*_binary64_360`
7×	`prod-exp_binary64_460` `associate-r_binary64_356` `cbrt-unprod_binary64_444`
6×	`associate-l/_binary64_359` `sqrt-prod_binary64_429` `associate-l*_binary64_357`
4×	`pow-prod-down_binary64_482` `associate-*r/_binary64_358`
3×	`flip3-+_binary64_417` `cbrt-undiv_binary64_445` `add-log-exp_binary64_450` `flip-+_binary64_388` `div-exp_binary64_462`
2×	`*-commutative_binary64_347` `unswap-sqr_binary64_382` `associate-/l/_binary64_363`
1×	`clear-num_binary64_413` `div-inv_binary64_411` `frac-2neg_binary64_425` `associate-/l*_binary64_361`

Counts

3 → 81

Calls

3 calls:

12.0ms

(/.f64 (*.f64 (cos.f64 th) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))) (cbrt.f64 (sqrt.f64 2)))

10.0ms

(*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))

9.0ms

(*.f64 (cos.f64 th) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)))

series963.0ms (9.6%)

Counts

3 → 9

Calls

3 calls:

637.0ms

(/.f64 (*.f64 (cos.f64 th) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))) (cbrt.f64 (sqrt.f64 2)))

252.0ms

(*.f64 (cos.f64 th) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)))

73.0ms

(*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))

simplify59.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4977	2177
1	4977	2177

prune102.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	91	7	98

Merged error: 0b

Counts

98 → 7

Compiler

Compiled 2056 to 1075 computations (47.7% saved)

regimes728.0ms (7.3%)

Compiler: Compiled 9137 to 6752 computations (26.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	27
1	19	27

end0.0ms (0%)

sample3.5s (34.7%)

Algorithm

1×

intervals

Results

630.0ms	1798×	body	1024	valid
555.0ms	1565×	body	1024	invalid
379.0ms	4884×	body	128	valid
207.0ms	869×	body	512	valid
195.0ms	819×	body	512	invalid
74.0ms	443×	body	256	valid
57.0ms	369×	body	256	invalid
55.0ms	629×	body	128	invalid
4.0ms	6×	body	2048	valid

Compiler

Compiled 1165 to 862 computations (26% saved)

Details

analyze750.0ms (7.5%)

sample82.0ms (0.8%)

simplify168.0ms (1.7%)

prune4.0ms (0%)

localize13.0ms (0.1%)

rewrite29.0ms (0.3%)

series447.0ms (4.5%)

simplify50.0ms (0.5%)

prune113.0ms (1.1%)

localize15.0ms (0.2%)

rewrite85.0ms (0.9%)

series593.0ms (5.9%)

simplify138.0ms (1.4%)

prune364.0ms (3.6%)

localize14.0ms (0.1%)

rewrite78.0ms (0.8%)

series1.3s (13.3%)

simplify94.0ms (0.9%)

prune274.0ms (2.7%)

localize14.0ms (0.1%)

rewrite40.0ms (0.4%)

series963.0ms (9.6%)

simplify59.0ms (0.6%)

prune102.0ms (1%)

regimes728.0ms (7.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.5s (34.7%)

Profiling