Details

analyze1.6s (5.9%)

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)

sample146.0ms (0.5%)

Algorithm

1×

intervals

Results

25.0ms	48×	body	1024	invalid
24.0ms	49×	body	1024	valid
19.0ms	167×	body	128	valid
14.0ms	39×	body	512	invalid
7.0ms	20×	body	512	valid
5.0ms	20×	body	256	valid
4.0ms	14×	body	256	invalid
2.0ms	18×	body	128	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune9.0ms (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

Error

0.4b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize20.0ms (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))

rewrite224.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

40×	`add-sqr-sqrt_binary64_441`
38×	`times-frac_binary64_425`
32×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
22×	`sqrt-prod_binary64_435` `associate-r_binary64_359`
10×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
6×	`associate-/r*_binary64_363`
5×	`pow1_binary64_480` `add-log-exp_binary64_458`
3×	`associate-/l_binary64_364` `unswap-sqr_binary64_387` `associate-l*_binary64_360`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `div-inv_binary64_416` `flip3-+_binary64_422` `associate-/l/_binary64_366` `flip-+_binary64_393` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
1×	`frac-2neg_binary64_430` `clear-num_binary64_418` `pow-prod-down_binary64_490` `associate-r/_binary64_361` `-commutative_binary64_350` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

3 → 94

Calls

3 calls:

14.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
13.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 2362 to 862 computations (63.5% saved)

series1.0s (3.8%)

Error

0.3b

Counts

3 → 41

Calls

3 calls:

553.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
287.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
120.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1585 to 1399 computations (11.7% saved)

simplify87.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5689	2865

prune255.0ms (0.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	126	9	135
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	128	9	137

Error

Counts

137 → 9

Compiler

Compiled 2863 to 1143 computations (60.1% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
0.1b	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
0.2b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
0.2b	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

rewrite848.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

195×	`times-frac_binary64_425`
111×	`add-sqr-sqrt_binary64_441`
94×	`cbrt-prod_binary64_450`
91×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
67×	`associate-r_binary64_359`
47×	`sqrt-prod_binary64_435`
32×	`add-exp-log_binary64_457`
22×	`div-inv_binary64_416`
20×	`add-cbrt-cube_binary64_455`
12×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
10×	`associate-/l_binary64_364` `associate-/r_binary64_363`
7×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `unswap-sqr_binary64_387`
6×	`pow1_binary64_480` `add-log-exp_binary64_458`
3×	`associate-/l/_binary64_366` `associate-l_binary64_360`
2×	`frac-2neg_binary64_430` `clear-num_binary64_418` `flip3-+_binary64_422` `flip-+_binary64_393`
1×	`pow-prod-down_binary64_490` `associate-r/_binary64_361` `-commutative_binary64_350` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

4 → 225

Calls

4 calls:

57.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
25.0ms	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
19.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
4.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 8603 to 5119 computations (40.5% saved)

series2.1s (7.9%)

Error

Counts

4 → 53

Calls

4 calls:

952.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
669.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
283.0ms	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
154.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 2659 to 2437 computations (8.3% saved)

simplify248.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	5050	8675

prune656.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	277	1	278
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	280	7	287

Error

Counts

287 → 7

Compiler

Compiled 8301 to 4649 computations (44% saved)

localize30.0ms (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 (cbrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
0.2b	(/.f64 (.f64 (cbrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
0.4b	(.f64 (cbrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

rewrite291.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

24×	`add-sqr-sqrt_binary64_441`
22×	`cbrt-prod_binary64_450`
20×	`add-exp-log_binary64_457`
18×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419` `times-frac_binary64_425`
16×	`associate-r_binary64_359`
13×	`add-cbrt-cube_binary64_455`
9×	`associate-l_binary64_360` `sqrt-prod_binary64_435` `associate-/r*_binary64_363`
8×	`pow1_binary64_480`
6×	`prod-exp_binary64_468` `add-log-exp_binary64_458` `cbrt-unprod_binary64_452`
5×	`associate-*r/_binary64_361`
4×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
3×	`unswap-sqr_binary64_387` `flip3-+_binary64_422` `flip-+_binary64_393`
2×	`pow-prod-down_binary64_490` `*-commutative_binary64_350` `div-inv_binary64_416` `associate-/l/_binary64_366`
1×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `frac-2neg_binary64_430` `clear-num_binary64_418` `associate-/l*_binary64_364` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

4 → 105

Calls

4 calls:

23.0ms	(.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
18.0ms	(/.f64 (.f64 (cbrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
15.0ms	(.f64 (cbrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
7.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 2769 to 1381 computations (50.1% saved)

series3.0s (11.1%)

Error

Counts

4 → 53

Calls

4 calls:

1.6s	(.f64 (cos.f64 th) (/.f64 (.f64 (cbrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
944.0ms	(/.f64 (.f64 (cbrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
218.0ms	(.f64 (cbrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
156.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 3145 to 2923 computations (7.1% saved)

simplify113.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4971	3436
1	4971	3436

prune301.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	158	7	165

Error

Counts

165 → 7

Compiler

Compiled 3535 to 1903 computations (46.2% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
0.1b	(.f64 (cos.f64 th) (.f64 (cbrt.f64 1/2) (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))))
0.2b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))
0.4b	(.f64 (cbrt.f64 1/2) (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2))))

rewrite396.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

70×	`add-sqr-sqrt_binary64_441`
60×	`times-frac_binary64_425`
53×	`cbrt-prod_binary64_450`
48×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
32×	`associate-r_binary64_359`
23×	`sqrt-prod_binary64_435`
20×	`add-exp-log_binary64_457`
13×	`add-cbrt-cube_binary64_455`
11×	`pow1_binary64_480`
9×	`associate-l_binary64_360` `associate-/r*_binary64_363`
8×	`unswap-sqr_binary64_387`
7×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
6×	`add-log-exp_binary64_458`
4×	`pow-prod-down_binary64_490`
3×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-r/_binary64_361` `associate-/l_binary64_364`
2×	`div-inv_binary64_416` `*-commutative_binary64_350` `flip3-+_binary64_422` `associate-/l/_binary64_366` `flip-+_binary64_393`
1×	`frac-2neg_binary64_430` `clear-num_binary64_418` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

4 → 144

Calls

4 calls:

19.0ms	(.f64 (cbrt.f64 1/2) (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2))))
19.0ms	(.f64 (cos.f64 th) (.f64 (cbrt.f64 1/2) (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))))
8.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))
8.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 4282 to 2053 computations (52.1% saved)

series3.5s (13%)

Error

Counts

4 → 53

Calls

4 calls:

1.5s	(.f64 (cos.f64 th) (.f64 (cbrt.f64 1/2) (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))))
894.0ms	(.f64 (cbrt.f64 1/2) (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2))))
781.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))
181.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 3307 to 3085 computations (6.7% saved)

simplify192.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	5013	5136

prune341.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	197	7	204

Error

Counts

204 → 7

Compiler

Compiled 4877 to 2446 computations (49.8% saved)

regimes3.2s (11.7%)

Accuracy

Total 0.4b remaining (91.1%)

Threshold costs 0.4b (91.1%)

Compiler

Compiled 24415 to 18599 computations (23.8% saved)

bsearch0.0ms (0%)

simplify20.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	27
1	22	27

Remove

(sort a1 a2)

Compiler

Compiled 34 to 30 computations (11.8% saved)

end0.0ms (0%)

sample8.3s (30.8%)

Algorithm

1×

intervals

Results

918.0ms	1785×	body	1024	valid
732.0ms	1469×	body	1024	invalid
560.0ms	4763×	body	128	valid
345.0ms	967×	body	512	valid
271.0ms	767×	body	512	invalid
119.0ms	481×	body	256	valid
95.0ms	401×	body	256	invalid
81.0ms	669×	body	128	invalid
3.0ms	4×	body	2048	valid
3.0ms	3×	body	2048	invalid

Compiler

Compiled 3074 to 2342 computations (23.8% saved)

Details

analyze1.6s (5.9%)

sample146.0ms (0.5%)

simplify17.0ms (0.1%)

prune9.0ms (0%)

localize20.0ms (0.1%)

rewrite224.0ms (0.8%)

series1.0s (3.8%)

simplify87.0ms (0.3%)

prune255.0ms (0.9%)

localize26.0ms (0.1%)

rewrite848.0ms (3.1%)

series2.1s (7.9%)

simplify248.0ms (0.9%)

prune656.0ms (2.4%)

localize30.0ms (0.1%)

rewrite291.0ms (1.1%)

series3.0s (11.1%)

simplify113.0ms (0.4%)

prune301.0ms (1.1%)

localize26.0ms (0.1%)

rewrite396.0ms (1.5%)

series3.5s (13%)

simplify192.0ms (0.7%)

prune341.0ms (1.3%)

regimes3.2s (11.7%)

bsearch0.0ms (0%)

simplify20.0ms (0.1%)

end0.0ms (0%)

sample8.3s (30.8%)

Profiling