Details

analyze766.0ms (5.9%)

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)

sample72.0ms (0.6%)

Algorithm

1×

intervals

Results

16.0ms	54×	body	1024	valid
13.0ms	43×	body	1024	invalid
12.0ms	159×	body	128	valid
9.0ms	29×	body	512	valid
4.0ms	19×	body	512	invalid
2.0ms	14×	body	256	valid
1.0ms	18×	body	128	invalid
1.0ms	7×	body	256	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify92.0ms (0.7%)

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: 0.4b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite48.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64_425`
70×	`add-sqr-sqrt_binary64_441`
60×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
44×	`associate-l_binary64_360` `sqrt-prod_binary64_435`
32×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
14×	`pow1_binary64_480`
12×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-/r*_binary64_363`
6×	`pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `div-exp_binary64_470` `associate-/l*_binary64_364` `cbrt-undiv_binary64_453`
4×	`add-log-exp_binary64_458` `div-inv_binary64_416`
2×	`associate-l/_binary64_362` `clear-num_binary64_418` `associate-r_binary64_359` `-commutative_binary64_350` `frac-2neg_binary64_430`

Counts

4 → 168

Calls

4 calls:

10.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
10.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
8.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
5.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

series426.0ms (3.3%)

Counts

4 → 26

Calls

4 calls:

179.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
148.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
57.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
42.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 1000 to 876 computations (12.4% saved)

simplify88.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4969	3256
1	4969	3256

prune299.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	185	9	194
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	186	10	196

Merged error: 0.0b

Counts

196 → 10

Compiler

Compiled 5216 to 2836 computations (45.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a1 a1))
0.6b	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))

rewrite223.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

1149×	`sqrt-prod_binary64_435`
1137×	`times-frac_binary64_425`
626×	`add-sqr-sqrt_binary64_441`
592×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
283×	`associate-l_binary64_360`
37×	`associate-/l*_binary64_364`
34×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
24×	`associate-/r*_binary64_363`
23×	`div-inv_binary64_416`
13×	`unswap-sqr_binary64_387`
11×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
9×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `pow1_binary64_480`
4×	`add-log-exp_binary64_458`
3×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `frac-2neg_binary64_430`
1×	`associate-l/_binary64_362` `associate-r_binary64_359` `-commutative_binary64_350` `associate-/l/_binary64_366`

Counts

4 → 744

Calls

4 calls:

57.0ms	(.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a1 a1))
18.0ms	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
6.0ms	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))
5.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

series360.0ms (2.8%)

Counts

4 → 25

Calls

4 calls:

184.0ms	(.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (.f64 a1 a1))
73.0ms	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))
55.0ms	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
47.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 1026 to 911 computations (11.2% saved)

simplify225.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

769 → 769

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5029	20086

prune2.4s (18.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	767	2	769
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	768	11	779

Merged error: 0b

Counts

779 → 11

Compiler

Compiled 27362 to 17189 computations (37.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
0.6b	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))

rewrite116.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

616×	`sqrt-prod_binary64_435`
614×	`times-frac_binary64_425`
345×	`add-sqr-sqrt_binary64_441`
340×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
37×	`associate-/l*_binary64_364`
25×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
24×	`associate-/r*_binary64_363`
22×	`associate-l_binary64_360`
14×	`div-inv_binary64_416`
9×	`pow1_binary64_480`
7×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
6×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
4×	`add-log-exp_binary64_458`
3×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `unswap-sqr_binary64_387` `frac-2neg_binary64_430`
1×	`associate-l/_binary64_362` `associate-r_binary64_359` `-commutative_binary64_350` `associate-/l/_binary64_366`

Counts

4 → 469

Calls

4 calls:

20.0ms	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
10.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
6.0ms	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))
4.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

series325.0ms (2.5%)

Counts

4 → 23

Calls

4 calls:

173.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
59.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
55.0ms	(/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2)))
37.0ms	(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

Compiler

Compiled 1042 to 932 computations (10.6% saved)

simplify166.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

492 → 492

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4974	13543
1	4974	13543

prune1.1s (8.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	492	0	492
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	492	11	503

Merged error: 0b

Counts

503 → 11

Compiler

Compiled 16649 to 10228 computations (38.6% saved)

localize12.0ms (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))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 83

Calls

2 calls:

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))

series673.0ms (5.2%)

Counts

2 → 30

Calls

2 calls:

487.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
186.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

Compiler

Compiled 817 to 785 computations (3.9% saved)

simplify115.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4955	2796
1	4955	2796

prune118.0ms (0.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	4	4	8
Picked	0	1	1
Done	0	2	2
Total	115	9	124

Merged error: 0b

Counts

124 → 9

Compiler

Compiled 2427 to 945 computations (61.1% saved)

regimes1.2s (9.6%)

Compiler: Compiled 16351 to 12853 computations (21.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	29
1	16	29

end0.0ms (0%)

sample4.0s (30.9%)

Algorithm

1×

intervals

Results

544.0ms	1744×	body	1024	valid
474.0ms	1517×	body	1024	invalid
381.0ms	4903×	body	128	valid
205.0ms	897×	body	512	valid
174.0ms	775×	body	512	invalid
70.0ms	450×	body	256	valid
61.0ms	407×	body	256	invalid
53.0ms	619×	body	128	invalid
3.0ms	6×	body	2048	valid

Compiler

Compiled 2013 to 1582 computations (21.4% saved)

Details

analyze766.0ms (5.9%)

sample72.0ms (0.6%)

simplify92.0ms (0.7%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite48.0ms (0.4%)

series426.0ms (3.3%)

simplify88.0ms (0.7%)

prune299.0ms (2.3%)

localize14.0ms (0.1%)

rewrite223.0ms (1.7%)

series360.0ms (2.8%)

simplify225.0ms (1.7%)

prune2.4s (18.3%)

localize14.0ms (0.1%)

rewrite116.0ms (0.9%)

series325.0ms (2.5%)

simplify166.0ms (1.3%)

prune1.1s (8.7%)

localize12.0ms (0.1%)

rewrite26.0ms (0.2%)

series673.0ms (5.2%)

simplify115.0ms (0.9%)

prune118.0ms (0.9%)

regimes1.2s (9.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.0s (30.9%)

Profiling