Details

analyze1.1s (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)

sample97.0ms (0.8%)

Algorithm

1×

intervals

Results

23.0ms	60×	body	1024	valid
17.0ms	52×	body	1024	invalid
13.0ms	161×	body	128	valid
7.0ms	29×	body	512	invalid
5.0ms	20×	body	512	valid
2.0ms	15×	body	256	valid
2.0ms	10×	body	256	invalid
2.0ms	19×	body	128	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune5.0ms (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

0.3b

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

rewrite152.0ms (1.2%)

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:

13.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
8.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

Compiler

Compiled 2362 to 862 computations (63.5% saved)

series670.0ms (5.3%)

Error

0.3b

Counts

3 → 40

Calls

3 calls:

361.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
185.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
87.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1429 to 1264 computations (11.5% saved)

simplify81.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5013	2823

prune144.0ms (1.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	125	9	134
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	126	10	136

Error

Counts

136 → 10

Compiler

Compiled 2847 to 1150 computations (59.6% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
0.1b	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
0.3b	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))

rewrite76.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

3 → 60

Calls

3 calls:

9.0ms	(/.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))
4.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 1347 to 424 computations (68.5% saved)

series732.0ms (5.8%)

Error

Counts

3 → 44

Calls

3 calls:

372.0ms	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
238.0ms	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
89.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 1637 to 1411 computations (13.8% saved)

simplify80.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5001	1788

prune87.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	106	8	114

Error

Counts

114 → 8

Compiler

Compiled 1831 to 724 computations (60.5% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
0.2b	(/.f64 (sqrt.f64 2) (cos.f64 th))
0.3b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))

rewrite210.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

156×	`times-frac_binary64_425`
93×	`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`
10×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
9×	`associate-/l*_binary64_364`
6×	`div-inv_binary64_416`
5×	`add-log-exp_binary64_458`
4×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
3×	`pow1_binary64_480`
2×	`frac-2neg_binary64_430` `clear-num_binary64_418` `flip3-+_binary64_422` `associate-/l/_binary64_366` `flip-+_binary64_393`
1×	`associate-/r/_binary64_365` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

3 → 158

Calls

3 calls:

12.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
4.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))
4.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 4249 to 1613 computations (62% saved)

series519.0ms (4.1%)

Error

Counts

3 → 32

Calls

3 calls:

375.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
82.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
38.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))

Compiler

Compiled 1197 to 1024 computations (14.5% saved)

simplify107.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5041	5364

prune192.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	190	8	198

Error

Counts

198 → 8

Compiler

Compiled 4428 to 1644 computations (62.9% saved)

localize14.0ms (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 a2 a2) (.f64 a1 a1)))))
0.4b	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
5.7b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.7b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite708.0ms (5.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

540×	`times-frac_binary64_425`
429×	`sqrt-prod_binary64_435`
297×	`add-sqr-sqrt_binary64_441`
295×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
48×	`associate-/r*_binary64_363`
22×	`sqrt-div_binary64_436`
17×	`associate-/r/_binary64_365`
12×	`associate-/l*_binary64_364`
11×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `flip3-+_binary64_422` `flip-+_binary64_393`
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×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `frac-2neg_binary64_430` `clear-num_binary64_418` `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 a2 a2) (.f64 a1 a1)))))
8.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 18617 to 4886 computations (73.8% saved)

series553.0ms (4.3%)

Error

Counts

4 → 52

Calls

4 calls:

179.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
153.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
87.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
82.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 2946 to 2119 computations (28.1% saved)

simplify233.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4967	18597
1	4967	18597

prune641.0ms (5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	463	0	463
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	463	8	471

Error

Counts

471 → 8

Compiler

Compiled 15797 to 4712 computations (70.2% saved)

regimes1.6s (12.8%)

Accuracy

Total 0.5b remaining (95.2%)

Threshold costs 0.5b (95.2%)

Compiler

Compiled 19938 to 14498 computations (27.3% saved)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	25
1	15	25

Remove

(sort a1 a2)

Compiler

Compiled 32 to 28 computations (12.5% saved)

end0.0ms (0%)

sample4.7s (36.8%)

Algorithm

1×

intervals

Results

592.0ms	1782×	body	1024	valid
545.0ms	1622×	body	1024	invalid
393.0ms	4890×	body	128	valid
213.0ms	874×	body	512	valid
197.0ms	821×	body	512	invalid
71.0ms	453×	body	256	valid
64.0ms	408×	body	256	invalid
51.0ms	618×	body	128	invalid
0.0ms	1×	body	2048	valid

Compiler

Compiled 2506 to 1822 computations (27.3% saved)

Details

analyze1.1s (8.4%)

sample97.0ms (0.8%)

simplify9.0ms (0.1%)

prune5.0ms (0%)

localize10.0ms (0.1%)

rewrite152.0ms (1.2%)

series670.0ms (5.3%)

simplify81.0ms (0.6%)

prune144.0ms (1.1%)

localize10.0ms (0.1%)

rewrite76.0ms (0.6%)

series732.0ms (5.8%)

simplify80.0ms (0.6%)

prune87.0ms (0.7%)

localize10.0ms (0.1%)

rewrite210.0ms (1.7%)

series519.0ms (4.1%)

simplify107.0ms (0.8%)

prune192.0ms (1.5%)

localize14.0ms (0.1%)

rewrite708.0ms (5.6%)

series553.0ms (4.3%)

simplify233.0ms (1.8%)

prune641.0ms (5%)

regimes1.6s (12.8%)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample4.7s (36.8%)

Profiling