Details

analyze752.0ms (8.1%)

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)

sample80.0ms (0.9%)

Algorithm

1×

intervals

Results

16.0ms	53×	body	1024	valid
15.0ms	49×	body	1024	invalid
13.0ms	165×	body	128	valid
12.0ms	31×	body	512	valid
7.0ms	30×	body	512	invalid
2.0ms	13×	body	256	invalid
2.0ms	20×	body	128	invalid
1.0ms	7×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify94.0ms (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 (0.1%)

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

Merged error: 0.3b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize11.0ms (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))

rewrite37.0ms (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:

13.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
12.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series249.0ms (2.7%)

Counts

3 → 9

Calls

3 calls:

176.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
51.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
21.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify80.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4977	2380
1	4977	2380

prune127.0ms (1.4%)

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

Merged error: 0b

Counts

105 → 8

Compiler

Compiled 2433 to 953 computations (60.8% saved)

localize16.0ms (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 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
8.1b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
8.1b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite83.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 201

Calls

4 calls:

31.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.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)))

series272.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
104.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
25.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
22.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify144.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4964	6988
1	4964	6988

prune368.0ms (4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	213	8	221

Merged error: 0b

Counts

221 → 8

Compiler

Compiled 8410 to 3723 computations (55.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite247.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

1137×	`sqrt-prod_binary64_435`
1119×	`times-frac_binary64_425`
625×	`add-sqr-sqrt_binary64_441`
578×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
283×	`associate-r_binary64_359`
34×	`associate-/l*_binary64_364`
22×	`div-inv_binary64_416`
20×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
18×	`associate-/r*_binary64_363`
13×	`unswap-sqr_binary64_387`
7×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
6×	`add-log-exp_binary64_458` `pow1_binary64_480`
3×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l_binary64_360` `associate-/l/_binary64_366`
2×	`flip3-+_binary64_422` `clear-num_binary64_418` `frac-2neg_binary64_430` `flip-+_binary64_393`
1×	`pow-prod-down_binary64_490` `sum-log_binary64_510` `associate-r/_binary64_361` `-commutative_binary64_350` `+-commutative_binary64_349`

Counts

4 → 713

Calls

4 calls:

82.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
20.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
9.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series294.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

151.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
68.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))
54.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
21.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify275.0ms (3%)

Algorithm

1×	egg-herbie

Counts

725 → 725

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5147	26176

prune1.4s (15.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	725	0	725
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	725	8	733

Merged error: 0b

Counts

733 → 8

Compiler

Compiled 23981 to 11851 computations (50.6% 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))))
8.1b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
8.1b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite107.0ms (1.2%)

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:

21.0ms	(/.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)))

series141.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
47.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
22.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
22.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify232.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

423 → 423

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4922	16317
1	4922	16317

prune509.0ms (5.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	423	0	423
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	423	8	431

Merged error: 0b

Counts

431 → 8

Compiler

Compiled 13899 to 4227 computations (69.6% saved)

regimes587.0ms (6.3%)

Compiler: Compiled 7248 to 5367 computations (26% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	32
1	17	32

end0.0ms (0%)

sample3.1s (33.8%)

Algorithm

1×

intervals

Results

553.0ms	1775×	body	1024	valid
479.0ms	1515×	body	1024	invalid
371.0ms	4878×	body	128	valid
208.0ms	916×	body	512	valid
168.0ms	766×	body	512	invalid
72.0ms	428×	body	256	valid
60.0ms	386×	body	256	invalid
58.0ms	669×	body	128	invalid
1.0ms	3×	body	2048	valid

Compiler

Compiled 932 to 692 computations (25.8% saved)

Details

analyze752.0ms (8.1%)

sample80.0ms (0.9%)

simplify94.0ms (1%)

prune5.0ms (0.1%)

localize11.0ms (0.1%)

rewrite37.0ms (0.4%)

series249.0ms (2.7%)

simplify80.0ms (0.9%)

prune127.0ms (1.4%)

localize16.0ms (0.2%)

rewrite83.0ms (0.9%)

series272.0ms (2.9%)

simplify144.0ms (1.6%)

prune368.0ms (4%)

localize11.0ms (0.1%)

rewrite247.0ms (2.7%)

series294.0ms (3.2%)

simplify275.0ms (3%)

prune1.4s (15.1%)

localize12.0ms (0.1%)

rewrite107.0ms (1.2%)

series141.0ms (1.5%)

simplify232.0ms (2.5%)

prune509.0ms (5.5%)

regimes587.0ms (6.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.1s (33.8%)

Profiling