Details

analyze1.3s (8.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	279	80
1	279	80
0	3	3
1	3	3

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

Symmetry

(sort a1 a2)

Compiler

Compiled 20 to 16 computations (20% saved)

sample111.0ms (0.7%)

Algorithm

1×

intervals

Results

26.0ms	65×	body	1024	invalid
21.0ms	60×	body	1024	valid
12.0ms	153×	body	128	valid
9.0ms	32×	body	512	valid
7.0ms	29×	body	512	invalid
2.0ms	12×	body	256	invalid
2.0ms	23×	body	128	invalid
2.0ms	10×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune8.0ms (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

Error

0.4b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize9.0ms (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))

rewrite152.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

39×	`add-sqr-sqrt_binary64_441`
38×	`times-frac_binary64_425`
31×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
22×	`sqrt-prod_binary64_435` `associate-r_binary64_359`
9×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
6×	`associate-/r*_binary64_363`
4×	`pow1_binary64_480`
3×	`associate-/l_binary64_364` `unswap-sqr_binary64_387` `associate-l*_binary64_360`
2×	`div-exp_binary64_470` `add-log-exp_binary64_458` `cbrt-undiv_binary64_453` `div-inv_binary64_416` `associate-/l/_binary64_366` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
1×	`frac-2neg_binary64_430` `clear-num_binary64_418` `flip3-+_binary64_422` `flip-+_binary64_393` `pow-prod-down_binary64_490` `associate-r/_binary64_361` `-commutative_binary64_350`

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))

Compiler

Compiled 2118 to 796 computations (62.4% saved)

series753.0ms (4.9%)

Error

0.3b

Counts

2 → 30

Calls

2 calls:

470.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
250.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

Compiler

Compiled 1334 to 1170 computations (12.3% saved)

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5339	2746

prune163.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	105	8	113
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	107	8	115

Error

Counts

115 → 8

Compiler

Compiled 2579 to 1063 computations (58.8% saved)

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.2b	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
0.4b	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))

rewrite75.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

2 → 49

Calls

2 calls:

10.0ms	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
7.0ms	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))

Compiler

Compiled 1103 to 358 computations (67.5% saved)

series848.0ms (5.5%)

Error

Counts

2 → 36

Calls

2 calls:

476.0ms	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
321.0ms	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))

Compiler

Compiled 1732 to 1472 computations (15% saved)

simplify85.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4973	1803
1	4973	1803

prune98.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	85	8	93

Error

Counts

93 → 8

Compiler

Compiled 1686 to 705 computations (58.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 (sqrt.f64 2) (cos.f64 th))
0.4b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))

rewrite207.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

156×	`times-frac_binary64_425`
92×	`add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419`
48×	`sqrt-prod_binary64_435`
25×	`associate-/r*_binary64_363`
9×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `associate-/l*_binary64_364`
6×	`div-inv_binary64_416`
4×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`pow1_binary64_480` `add-log-exp_binary64_458` `frac-2neg_binary64_430` `clear-num_binary64_418` `associate-/l/_binary64_366`
1×	`flip3-+_binary64_422` `flip-+_binary64_393` `associate-/r/_binary64_365`

Counts

2 → 147

Calls

2 calls:

13.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
4.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))

Compiler

Compiled 4005 to 1547 computations (61.4% saved)

series572.0ms (3.7%)

Error

Counts

2 → 24

Calls

2 calls:

474.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
71.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))

Compiler

Compiled 1204 to 1009 computations (16.2% saved)

simplify135.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4972	5346
1	4972	5346

prune212.0ms (1.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	168	3	171
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	171	8	179

Error

Counts

179 → 8

Compiler

Compiled 4251 to 1611 computations (62.1% saved)

localize19.0ms (0.1%)

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 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.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))))
6.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.4b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite587.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

4 → 201

Calls

4 calls:

35.0ms	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.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))))
10.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 9640 to 4180 computations (56.6% saved)

series1.3s (8.6%)

Error

Counts

4 → 60

Calls

4 calls:

575.0ms	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.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))))
390.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
124.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
117.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 4679 to 3717 computations (20.6% saved)

simplify160.0ms (1%)

Algorithm

1×	egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4973	8454
1	4973	8454

prune530.0ms (3.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	261	0	261
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	261	8	269

Error

Counts

269 → 8

Compiler

Compiled 9921 to 4609 computations (53.5% saved)

regimes2.1s (14.1%)

Accuracy

Total 0.4b remaining (93.4%)

Threshold costs 0.4b (93.4%)

Compiler

Compiled 21682 to 16066 computations (25.9% saved)

bsearch0.0ms (0%)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	20
1	14	20

Remove

(sort a1 a2)

Compiler

Compiled 26 to 22 computations (15.4% saved)

end0.0ms (0%)

sample5.7s (37.2%)

Algorithm

1×

intervals

Results

649.0ms	1733×	body	1024	valid
608.0ms	1603×	body	1024	invalid
435.0ms	4952×	body	128	valid
239.0ms	877×	body	512	valid
232.0ms	839×	body	512	invalid
77.0ms	435×	body	256	valid
76.0ms	389×	body	256	invalid
63.0ms	633×	body	128	invalid
2.0ms	3×	body	2048	valid

Compiler

Compiled 2721 to 2015 computations (25.9% saved)

Details

analyze1.3s (8.4%)

sample111.0ms (0.7%)

simplify13.0ms (0.1%)

prune8.0ms (0.1%)

localize9.0ms (0.1%)

rewrite152.0ms (1%)

series753.0ms (4.9%)

simplify80.0ms (0.5%)

prune163.0ms (1.1%)

localize15.0ms (0.1%)

rewrite75.0ms (0.5%)

series848.0ms (5.5%)

simplify85.0ms (0.6%)

prune98.0ms (0.6%)

localize9.0ms (0.1%)

rewrite207.0ms (1.4%)

series572.0ms (3.7%)

simplify135.0ms (0.9%)

prune212.0ms (1.4%)

localize19.0ms (0.1%)

rewrite587.0ms (3.8%)

series1.3s (8.6%)

simplify160.0ms (1%)

prune530.0ms (3.5%)

regimes2.1s (14.1%)

bsearch0.0ms (0%)

simplify14.0ms (0.1%)

end0.0ms (0%)

sample5.7s (37.2%)

Profiling