Details

analyze770.0ms (9.8%)

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)

sample84.0ms (1.1%)

Algorithm

1×

intervals

Results

23.0ms	65×	body	1024	valid
18.0ms	58×	body	1024	invalid
11.0ms	146×	body	128	valid
6.0ms	24×	body	512	invalid
5.0ms	24×	body	512	valid
3.0ms	21×	body	256	valid
3.0ms	16×	body	256	invalid
1.0ms	14×	body	128	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify104.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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

0.3b

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))
0.2b	(.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))

rewrite32.0ms (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:

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

series256.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

177.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
55.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
23.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify76.0ms (1%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4977	2380
1	4977	2380

prune124.0ms (1.6%)

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

Error

Counts

105 → 8

Compiler

Compiled 2448 to 963 computations (60.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
0.4b	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
6.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite109.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

540×	`times-frac_binary64_425`
429×	`sqrt-prod_binary64_435`
297×	`add-sqr-sqrt_binary64_441`
295×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
48×	`associate-/r*_binary64_363`
22×	`sqrt-div_binary64_436`
17×	`associate-/r/_binary64_365`
12×	`associate-/l*_binary64_364`
11×	`flip3-+_binary64_422` `flip-+_binary64_393` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
9×	`div-inv_binary64_416`
6×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
3×	`sqrt-undiv_binary64_440`
2×	`clear-num_binary64_418` `pow1/2_binary64_499` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `associate-/l/_binary64_366`

Counts

4 → 411

Calls

4 calls:

22.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
8.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series160.0ms (2%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
52.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
25.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
24.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify242.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

423 → 423

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4922	16317
1	4922	16317

prune496.0ms (6.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	423	0	423
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	423	8	431

Error

Counts

431 → 8

Compiler

Compiled 14071 to 4356 computations (69% 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 (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))))
6.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite93.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

149×	`add-sqr-sqrt_binary64_441`
146×	`times-frac_binary64_425`
127×	`sqrt-prod_binary64_435`
90×	`cbrt-prod_binary64_450`
87×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
58×	`associate-r_binary64_359`
27×	`add-exp-log_binary64_457`
21×	`unswap-sqr_binary64_387`
19×	`add-cbrt-cube_binary64_455`
10×	`associate-l_binary64_360`
9×	`associate-/r*_binary64_363`
8×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `pow1_binary64_480` `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` `div-inv_binary64_416` `flip-+_binary64_393`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `associate-/l/_binary64_366`
1×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `clear-num_binary64_418` `frac-times_binary64_429` `associate-r/_binary64_361` `*-commutative_binary64_350` `frac-2neg_binary64_430`

Counts

4 → 226

Calls

4 calls:

40.0ms	(.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)))

series221.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
62.0ms	(.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))))
24.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
24.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify115.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5181	8434

prune412.0ms (5.2%)

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

Error

Counts

246 → 8

Compiler

Compiled 9735 to 4507 computations (53.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.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))

rewrite47.0ms (0.6%)

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

series217.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
73.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
35.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
34.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

simplify113.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4964	2940
1	4964	2940

prune221.0ms (2.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	180	8	188

Error

Counts

188 → 8

Compiler

Compiled 4606 to 2431 computations (47.2% saved)

regimes651.0ms (8.3%)

Accuracy

Total 0.5b remaining (99.4%)

Threshold costs 0.5b (99.4%)

Compiler

Compiled 8401 to 5991 computations (28.7% 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%)

sample3.3s (41.5%)

Algorithm

1×

intervals

Results

582.0ms	1799×	body	1024	valid
483.0ms	1522×	body	1024	invalid
393.0ms	4912×	body	128	valid
202.0ms	843×	body	512	valid
189.0ms	823×	body	512	invalid
69.0ms	441×	body	256	valid
66.0ms	393×	body	256	invalid
51.0ms	622×	body	128	invalid
2.0ms	5×	body	2048	valid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 1065 to 760 computations (28.6% saved)

Details

analyze770.0ms (9.8%)

sample84.0ms (1.1%)

simplify104.0ms (1.3%)

prune8.0ms (0.1%)

localize10.0ms (0.1%)

rewrite32.0ms (0.4%)

series256.0ms (3.3%)

simplify76.0ms (1%)

prune124.0ms (1.6%)

localize12.0ms (0.1%)

rewrite109.0ms (1.4%)

series160.0ms (2%)

simplify242.0ms (3.1%)

prune496.0ms (6.3%)

localize15.0ms (0.2%)

rewrite93.0ms (1.2%)

series221.0ms (2.8%)

simplify115.0ms (1.5%)

prune412.0ms (5.2%)

localize11.0ms (0.1%)

rewrite47.0ms (0.6%)

series217.0ms (2.8%)

simplify113.0ms (1.4%)

prune221.0ms (2.8%)

regimes651.0ms (8.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.3s (41.5%)

Profiling