Details

analyze961.0ms (8.5%)

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)

sample81.0ms (0.7%)

Algorithm

1×

intervals

Results

19.0ms	55×	body	1024	valid
14.0ms	39×	body	1024	invalid
11.0ms	150×	body	128	valid
8.0ms	32×	body	512	valid
6.0ms	24×	body	512	invalid
3.0ms	19×	body	256	valid
2.0ms	26×	body	128	invalid
2.0ms	11×	body	256	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify179.0ms (1.6%)

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

Merged error: 0.6b

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)))
0.6b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite34.0ms (0.3%)

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)))
8.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
5.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series493.0ms (4.4%)

Counts

3 → 9

Calls

3 calls:

341.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
110.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
42.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify61.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	6033	2380

prune127.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	98	7	105

Merged error: 0.3b

Counts

105 → 7

Compiler

Compiled 2444 to 950 computations (61.1% saved)

localize16.0ms (0.1%)

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))))
5.9b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.9b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite96.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

149×	`add-sqr-sqrt_binary64_435`
146×	`times-frac_binary64_420`
127×	`sqrt-prod_binary64_429`
90×	`cbrt-prod_binary64_442`
87×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
58×	`associate-r_binary64_356`
27×	`add-exp-log_binary64_449`
21×	`unswap-sqr_binary64_382`
19×	`add-cbrt-cube_binary64_447`
10×	`associate-l_binary64_357`
9×	`associate-/r*_binary64_360`
8×	`pow1_binary64_472` `cbrt-undiv_binary64_445` `prod-exp_binary64_460` `cbrt-unprod_binary64_444` `div-exp_binary64_462`
6×	`sqrt-div_binary64_430` `associate-/l*_binary64_361`
4×	`add-log-exp_binary64_450`
3×	`flip3-+_binary64_417` `div-inv_binary64_411` `flip-+_binary64_388`
2×	`sqrt-pow1_binary64_431` `pow1/2_binary64_491` `associate-/l/_binary64_363` `rem-sqrt-square_binary64_427`
1×	`clear-num_binary64_413` `associate-l/_binary64_359` `-commutative_binary64_347` `pow-prod-down_binary64_482` `frac-2neg_binary64_425` `frac-times_binary64_424` `associate-*r/_binary64_358`

Counts

4 → 226

Calls

4 calls:

36.0ms	(.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))))
10.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (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)))

series471.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
123.0ms	(.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))))
53.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
46.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify154.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4905	8058
1	4905	8058

prune437.0ms (3.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	238	7	245

Merged error: 0.3b

Counts

245 → 7

Compiler

Compiled 9564 to 4317 computations (54.9% saved)

localize15.0ms (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)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2)) (cbrt.f64 (sqrt.f64 2))))
0.3b	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2)) (cbrt.f64 (sqrt.f64 2)))
0.5b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2))

rewrite395.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

1707×	`times-frac_binary64_420`
944×	`cbrt-prod_binary64_442`
906×	`add-sqr-sqrt_binary64_435`
829×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
558×	`unpow-prod-down_binary64_490`
472×	`sqrt-prod_binary64_429`
418×	`associate-r_binary64_356`
64×	`sqr-pow_binary64_386` `unpow2_binary64_476`
49×	`associate-/l*_binary64_361`
35×	`add-exp-log_binary64_449`
23×	`associate-/r*_binary64_360`
22×	`div-inv_binary64_411` `unswap-sqr_binary64_382`
17×	`div-exp_binary64_462`
16×	`add-cbrt-cube_binary64_447`
7×	`cbrt-undiv_binary64_445`
6×	`pow1_binary64_472` `add-log-exp_binary64_450`
5×	`prod-exp_binary64_460`
3×	`pow-exp_binary64_479` `pow-to-exp_binary64_480` `associate-l_binary64_357` `cbrt-unprod_binary64_444` `associate-/l/_binary64_363`
2×	`clear-num_binary64_413` `flip3-+_binary64_417` `flip-+_binary64_388` `frac-2neg_binary64_425`
1×	`-commutative_binary64_347` `+-commutative_binary64_346` `pow-prod-down_binary64_482` `sum-log_binary64_502` `associate-r/_binary64_358`

Counts

4 → 1033

Calls

4 calls:

126.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2)) (cbrt.f64 (sqrt.f64 2))))
27.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2)) (cbrt.f64 (sqrt.f64 2)))
14.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2))
5.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series834.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

345.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2))
329.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2)) (cbrt.f64 (sqrt.f64 2))))
118.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2)) (cbrt.f64 (sqrt.f64 2)))
41.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify380.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1045 → 1045

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5361	43863

prune3.1s (27.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	1044	1	1045
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	1045	7	1052

Merged error: 0.3b

Counts

1052 → 7

Compiler

Compiled 39406 to 21601 computations (45.2% 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 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
0.6b	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

rewrite26.0ms (0.2%)

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:

10.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
7.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series416.0ms (3.7%)

Counts

3 → 9

Calls

3 calls:

229.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
144.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
43.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify93.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4932	1293
1	4932	1293

prune57.0ms (0.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	69	7	76

Merged error: 0.3b

Counts

76 → 7

Compiler

Compiled 1266 to 440 computations (65.2% saved)

regimes109.0ms (1%)

Compiler: Compiled 1114 to 858 computations (23% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	52
1	20	52

end0.0ms (0%)

sample2.8s (24.4%)

Algorithm

1×

intervals

Results

664.0ms	1810×	body	1024	valid
564.0ms	1566×	body	1024	invalid
386.0ms	4818×	body	128	valid
213.0ms	889×	body	512	valid
184.0ms	749×	body	512	invalid
77.0ms	480×	body	256	valid
63.0ms	395×	body	256	invalid
59.0ms	660×	body	128	invalid
4.0ms	3×	body	2048	valid

Compiler

Compiled 234 to 177 computations (24.4% saved)

Details

analyze961.0ms (8.5%)

sample81.0ms (0.7%)

simplify179.0ms (1.6%)

prune5.0ms (0%)

localize10.0ms (0.1%)

rewrite34.0ms (0.3%)

series493.0ms (4.4%)

simplify61.0ms (0.5%)

prune127.0ms (1.1%)

localize16.0ms (0.1%)

rewrite96.0ms (0.8%)

series471.0ms (4.2%)

simplify154.0ms (1.4%)

prune437.0ms (3.9%)

localize15.0ms (0.1%)

rewrite395.0ms (3.5%)

series834.0ms (7.4%)

simplify380.0ms (3.4%)

prune3.1s (27.1%)

localize10.0ms (0.1%)

rewrite26.0ms (0.2%)

series416.0ms (3.7%)

simplify93.0ms (0.8%)

prune57.0ms (0.5%)

regimes109.0ms (1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.8s (24.4%)

Profiling