Details

analyze746.0ms (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

21.0ms	61×	body	1024	valid
17.0ms	49×	body	1024	invalid
11.0ms	150×	body	128	valid
7.0ms	31×	body	512	invalid
7.0ms	29×	body	512	valid
2.0ms	16×	body	256	valid
2.0ms	16×	body	256	invalid
1.0ms	19×	body	128	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify180.0ms (1.8%)

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)

localize10.0ms (0.1%)

Local error

Found 3 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)) (sqrt.f64 2)))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_441`
38×	`times-frac_binary64_425`
32×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
22×	`associate-r_binary64_359` `sqrt-prod_binary64_435`
10×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
6×	`associate-/r*_binary64_363`
5×	`add-log-exp_binary64_458` `pow1_binary64_480`
3×	`unswap-sqr_binary64_387` `associate-l_binary64_360` `associate-/l*_binary64_364`
2×	`flip3-+_binary64_422` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `flip-+_binary64_393` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `sum-log_binary64_510` `associate-r/_binary64_361` `-commutative_binary64_350` `frac-2neg_binary64_430` `+-commutative_binary64_349`

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))
5.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series484.0ms (4.9%)

Counts

3 → 9

Calls

3 calls:

340.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
104.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
41.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify75.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4965	2380
1	4965	2380

prune125.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Merged error: 0b

Counts

105 → 8

Compiler

Compiled 2420 to 947 computations (60.9% saved)

localize10.0ms (0.1%)

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

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_441`
10×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
9×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
6×	`times-frac_binary64_425` `sqrt-prod_binary64_435` `associate-/r*_binary64_363`
5×	`add-log-exp_binary64_458` `pow1_binary64_480`
4×	`associate-*l/_binary64_362`
3×	`flip3-+_binary64_422` `associate-r_binary64_359` `associate-l_binary64_360` `flip-+_binary64_393`
2×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `div-inv_binary64_416` `unswap-sqr_binary64_387` `sum-log_binary64_510` `-commutative_binary64_350` `frac-2neg_binary64_430` `+-commutative_binary64_349` `associate-/l_binary64_364`

Counts

3 → 60

Calls

3 calls:

10.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
8.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series427.0ms (4.3%)

Counts

3 → 9

Calls

3 calls:

244.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
146.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
38.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5282	1293

prune68.0ms (0.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	69	8	77

Merged error: 0b

Counts

77 → 8

Compiler

Compiled 1413 to 550 computations (61.1% saved)

localize19.0ms (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))))
4.7b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.7b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite86.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64_425`
102×	`sqrt-prod_binary64_435`
86×	`add-sqr-sqrt_binary64_441`
84×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
78×	`cbrt-prod_binary64_450`
58×	`associate-r_binary64_359`
38×	`add-exp-log_binary64_457`
29×	`add-cbrt-cube_binary64_455`
16×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
11×	`pow1_binary64_480`
9×	`associate-/r*_binary64_363` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
6×	`sqrt-div_binary64_436` `associate-/l*_binary64_364`
4×	`add-log-exp_binary64_458`
3×	`flip3-+_binary64_422` `associate-*l/_binary64_362` `pow-prod-down_binary64_490` `flip-+_binary64_393`
2×	`pow1/2_binary64_499` `div-inv_binary64_416` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `frac-times_binary64_429` `associate-r/_binary64_361` `-commutative_binary64_350` `associate-l_binary64_360` `frac-2neg_binary64_430`

Counts

4 → 201

Calls

4 calls:

33.0ms	(.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))))
10.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
5.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series606.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

262.0ms	(.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))))
242.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
53.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
49.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify142.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4949	6988
1	4949	6988

prune361.0ms (3.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	213	8	221

Merged error: 0b

Counts

221 → 8

Compiler

Compiled 8377 to 3701 computations (55.8% saved)

localize15.0ms (0.1%)

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

rewrite277.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

1137×	`sqrt-prod_binary64_435`
1119×	`times-frac_binary64_425`
625×	`add-sqr-sqrt_binary64_441`
578×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
283×	`associate-r_binary64_359`
34×	`associate-/l*_binary64_364`
22×	`div-inv_binary64_416`
20×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
18×	`associate-/r*_binary64_363`
13×	`unswap-sqr_binary64_387`
7×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
6×	`add-log-exp_binary64_458` `pow1_binary64_480`
3×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l_binary64_360` `associate-/l/_binary64_366`
2×	`flip3-+_binary64_422` `clear-num_binary64_418` `frac-2neg_binary64_430` `flip-+_binary64_393`
1×	`pow-prod-down_binary64_490` `sum-log_binary64_510` `associate-r/_binary64_361` `-commutative_binary64_350` `+-commutative_binary64_349`

Counts

4 → 713

Calls

4 calls:

90.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
21.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
10.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series606.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

319.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
140.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
106.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
40.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify267.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

725 → 725

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5120	26166

prune1.4s (14.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	725	0	725
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	725	8	733

Merged error: 0b

Counts

733 → 8

Compiler

Compiled 23845 to 11749 computations (50.7% saved)

regimes606.0ms (6.1%)

Compiler: Compiled 6986 to 5207 computations (25.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	20
1	14	20

end0.0ms (0%)

sample3.2s (32.3%)

Algorithm

1×

intervals

Results

643.0ms	1829×	body	1024	valid
526.0ms	1506×	body	1024	invalid
359.0ms	4792×	body	128	valid
210.0ms	913×	body	512	valid
175.0ms	756×	body	512	invalid
71.0ms	465×	body	256	valid
60.0ms	391×	body	256	invalid
53.0ms	616×	body	128	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 891 to 664 computations (25.5% saved)

Details

analyze746.0ms (7.5%)

sample82.0ms (0.8%)

simplify180.0ms (1.8%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite38.0ms (0.4%)

series484.0ms (4.9%)

simplify75.0ms (0.8%)

prune125.0ms (1.3%)

localize10.0ms (0.1%)

rewrite27.0ms (0.3%)

series427.0ms (4.3%)

simplify71.0ms (0.7%)

prune68.0ms (0.7%)

localize19.0ms (0.2%)

rewrite86.0ms (0.9%)

series606.0ms (6.1%)

simplify142.0ms (1.4%)

prune361.0ms (3.6%)

localize15.0ms (0.1%)

rewrite277.0ms (2.8%)

series606.0ms (6.1%)

simplify267.0ms (2.7%)

prune1.4s (14.1%)

regimes606.0ms (6.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.2s (32.3%)

Profiling