Details

analyze757.0ms (11.4%)

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)

sample87.0ms (1.3%)

Algorithm

1×

intervals

Results

24.0ms	57×	body	1024	invalid
17.0ms	49×	body	1024	valid
13.0ms	164×	body	128	valid
7.0ms	28×	body	512	valid
6.0ms	24×	body	512	invalid
2.0ms	14×	body	256	valid
2.0ms	14×	body	256	invalid
1.0ms	15×	body	128	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify161.0ms (2.4%)

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)

localize10.0ms (0.2%)

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))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_435`
38×	`times-frac_binary64_420`
32×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
22×	`sqrt-prod_binary64_429` `associate-r_binary64_356`
10×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
6×	`associate-/r*_binary64_360`
5×	`pow1_binary64_472` `add-log-exp_binary64_450`
3×	`associate-l_binary64_357` `unswap-sqr_binary64_382` `associate-/l*_binary64_361`
2×	`flip3-+_binary64_417` `div-inv_binary64_411` `cbrt-undiv_binary64_445` `prod-exp_binary64_460` `flip-+_binary64_388` `cbrt-unprod_binary64_444` `associate-/l/_binary64_363` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `-commutative_binary64_347` `+-commutative_binary64_346` `pow-prod-down_binary64_482` `frac-2neg_binary64_425` `sum-log_binary64_502` `associate-r/_binary64_358`

Counts

3 → 94

Calls

3 calls:

13.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
11.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series466.0ms (7%)

Counts

3 → 9

Calls

3 calls:

325.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
102.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
39.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify57.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	6033	2380

prune126.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	96	9	105

Merged error: 0b

Counts

105 → 9

Compiler

Compiled 2447 to 964 computations (60.6% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite219.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_435`
10×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
9×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
6×	`times-frac_binary64_420` `sqrt-prod_binary64_429` `associate-/r*_binary64_360`
5×	`pow1_binary64_472` `add-log-exp_binary64_450`
4×	`associate-*l/_binary64_359`
3×	`flip3-+_binary64_417` `associate-l_binary64_357` `flip-+_binary64_388` `associate-r_binary64_356`
2×	`cbrt-undiv_binary64_445` `prod-exp_binary64_460` `cbrt-unprod_binary64_444` `associate-/l/_binary64_363` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `div-inv_binary64_411` `-commutative_binary64_347` `+-commutative_binary64_346` `pow-prod-down_binary64_482` `frac-2neg_binary64_425` `unswap-sqr_binary64_382` `associate-/l_binary64_361` `sum-log_binary64_502`

Counts

3 → 60

Calls

3 calls:

199.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
9.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series418.0ms (6.3%)

Counts

3 → 9

Calls

3 calls:

239.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
137.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
41.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify97.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4932	1293
1	4932	1293

prune67.0ms (1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	72	6	78

Merged error: 0b

Counts

78 → 6

Compiler

Compiled 1390 to 536 computations (61.4% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite40.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`times-frac_binary64_420`
93×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414` `add-sqr-sqrt_binary64_435`
48×	`sqrt-prod_binary64_429`
25×	`associate-/r*_binary64_360`
10×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
9×	`associate-/l*_binary64_361`
6×	`div-inv_binary64_411`
5×	`add-log-exp_binary64_450`
4×	`cbrt-undiv_binary64_445` `div-exp_binary64_462`
3×	`pow1_binary64_472`
2×	`clear-num_binary64_413` `flip3-+_binary64_417` `flip-+_binary64_388` `frac-2neg_binary64_425` `associate-/l/_binary64_363`
1×	`associate-/r/_binary64_362` `+-commutative_binary64_346` `sum-log_binary64_502`

Counts

3 → 158

Calls

3 calls:

12.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
5.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series341.0ms (5.1%)

Counts

3 → 9

Calls

3 calls:

237.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
61.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))
42.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify85.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5102	5041

prune174.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	167	6	173

Merged error: 0b

Counts

173 → 6

Compiler

Compiled 4133 to 1511 computations (63.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
0.4b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
5.3b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.3b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite60.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`sqrt-prod_binary64_429`
72×	`times-frac_binary64_420`
61×	`add-sqr-sqrt_binary64_435`
59×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
40×	`associate-r_binary64_356`
18×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
11×	`pow1_binary64_472`
10×	`sqrt-div_binary64_430`
6×	`associate-l/_binary64_359` `prod-exp_binary64_460` `associate-/l_binary64_361` `cbrt-unprod_binary64_444` `associate-/r*_binary64_360`
5×	`flip3-+_binary64_417` `flip-+_binary64_388`
4×	`add-log-exp_binary64_450`
3×	`cbrt-undiv_binary64_445` `pow-prod-down_binary64_482` `div-exp_binary64_462`
2×	`div-inv_binary64_411` `sqrt-pow1_binary64_431` `pow1/2_binary64_491` `frac-times_binary64_424` `associate-/l/_binary64_363` `rem-sqrt-square_binary64_427`
1×	`clear-num_binary64_413` `-commutative_binary64_347` `sqrt-undiv_binary64_434` `associate-l_binary64_357` `frac-2neg_binary64_425` `associate-r/_binary64_358`

Counts

4 → 157

Calls

4 calls:

21.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
5.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series441.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
101.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
47.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
43.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify83.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5072	4501

prune173.0ms (2.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	169	6	175

Merged error: 0b

Counts

175 → 6

Compiler

Compiled 5156 to 1365 computations (73.5% saved)

regimes89.0ms (1.3%)

Compiler: Compiled 730 to 588 computations (19.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	34
1	17	34

end0.0ms (0%)

sample2.6s (39.5%)

Algorithm

1×

intervals

Results

643.0ms	1793×	body	1024	valid
542.0ms	1502×	body	1024	invalid
377.0ms	4845×	body	128	valid
219.0ms	904×	body	512	valid
193.0ms	805×	body	512	invalid
75.0ms	455×	body	256	valid
60.0ms	381×	body	256	invalid
57.0ms	650×	body	128	invalid
2.0ms	3×	body	2048	valid

Compiler

Compiled 160 to 123 computations (23.1% saved)

Details

analyze757.0ms (11.4%)

sample87.0ms (1.3%)

simplify161.0ms (2.4%)

prune5.0ms (0.1%)

localize10.0ms (0.2%)

rewrite38.0ms (0.6%)

series466.0ms (7%)

simplify57.0ms (0.9%)

prune126.0ms (1.9%)

localize10.0ms (0.2%)

rewrite219.0ms (3.3%)

series418.0ms (6.3%)

simplify97.0ms (1.5%)

prune67.0ms (1%)

localize10.0ms (0.2%)

rewrite40.0ms (0.6%)

series341.0ms (5.1%)

simplify85.0ms (1.3%)

prune174.0ms (2.6%)

localize13.0ms (0.2%)

rewrite60.0ms (0.9%)

series441.0ms (6.6%)

simplify83.0ms (1.3%)

prune173.0ms (2.6%)

regimes89.0ms (1.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.6s (39.5%)

Profiling