Details

analyze744.0ms (9.9%)

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)

sample73.0ms (1%)

Algorithm

1×

intervals

Results

18.0ms	52×	body	1024	invalid
16.0ms	55×	body	1024	valid
11.0ms	156×	body	128	valid
7.0ms	33×	body	512	valid
5.0ms	22×	body	512	invalid
2.0ms	12×	body	256	valid
2.0ms	22×	body	128	invalid
1.0ms	7×	body	256	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify97.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune4.0ms (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: 0.4b

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)))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_782`
38×	`times-frac_binary64_766`
32×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
22×	`sqrt-prod_binary64_776` `associate-r_binary64_700`
10×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
6×	`associate-/r*_binary64_704`
5×	`add-log-exp_binary64_799` `pow1_binary64_821`
3×	`unswap-sqr_binary64_728` `associate-/l_binary64_705` `associate-l*_binary64_701`
2×	`cbrt-undiv_binary64_794` `prod-exp_binary64_809` `flip3-+_binary64_763` `associate-/l/_binary64_707` `div-inv_binary64_757` `flip-+_binary64_734` `cbrt-unprod_binary64_793` `div-exp_binary64_811`
1×	`frac-2neg_binary64_771` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-r/_binary64_702` `clear-num_binary64_759` `pow-prod-down_binary64_831` `-commutative_binary64_691`

Counts

3 → 94

Calls

3 calls:

12.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series243.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

169.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
53.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
20.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify71.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4977	2380
1	4977	2380

prune124.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	95	8	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Merged error: 0b

Counts

105 → 8

Compiler

Compiled 2457 to 958 computations (61% saved)

localize11.0ms (0.1%)

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)))
0.5b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
6.1b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.1b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite57.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`sqrt-prod_binary64_776`
72×	`times-frac_binary64_766`
61×	`add-sqr-sqrt_binary64_782`
59×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
40×	`associate-r_binary64_700`
18×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
11×	`pow1_binary64_821`
10×	`sqrt-div_binary64_777`
6×	`associate-l/_binary64_703` `prod-exp_binary64_809` `associate-/r_binary64_704` `associate-/l*_binary64_705` `cbrt-unprod_binary64_793`
5×	`flip3-+_binary64_763` `flip-+_binary64_734`
4×	`add-log-exp_binary64_799`
3×	`cbrt-undiv_binary64_794` `div-exp_binary64_811` `pow-prod-down_binary64_831`
2×	`rem-sqrt-square_binary64_773` `associate-/l/_binary64_707` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `frac-times_binary64_770` `pow1/2_binary64_840`
1×	`frac-2neg_binary64_771` `sqrt-undiv_binary64_781` `associate-l_binary64_701` `associate-r/_binary64_702` `clear-num_binary64_759` `-commutative_binary64_691`

Counts

4 → 157

Calls

4 calls:

19.0ms	(.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)))
7.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (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)))

series217.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

121.0ms	(.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)))
49.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
24.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
23.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify78.0ms (1%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5484	4501

prune179.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	169	8	177

Merged error: 0b

Counts

177 → 8

Compiler

Compiled 5337 to 1489 computations (72.1% saved)

localize12.0ms (0.2%)

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))))
6.1b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.1b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite107.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

540×	`times-frac_binary64_766`
429×	`sqrt-prod_binary64_776`
297×	`add-sqr-sqrt_binary64_782`
295×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
48×	`associate-/r*_binary64_704`
22×	`sqrt-div_binary64_777`
17×	`associate-/r/_binary64_706`
12×	`associate-/l*_binary64_705`
11×	`flip3-+_binary64_763` `add-exp-log_binary64_798` `flip-+_binary64_734` `add-cbrt-cube_binary64_796`
9×	`div-inv_binary64_757`
6×	`pow1_binary64_821`
4×	`cbrt-undiv_binary64_794` `add-log-exp_binary64_799` `div-exp_binary64_811`
3×	`sqrt-undiv_binary64_781`
2×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `associate-/l/_binary64_707` `sqrt-pow1_binary64_778` `pow1/2_binary64_840` `clear-num_binary64_759`

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)))

series144.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
41.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
29.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
23.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify230.0ms (3%)

Algorithm

1×	egg-herbie

Counts

423 → 423

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4922	16317
1	4922	16317

prune512.0ms (6.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	423	0	423
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	423	8	431

Merged error: 0b

Counts

431 → 8

Compiler

Compiled 14057 to 4338 computations (69.1% saved)

localize14.0ms (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))))
6.1b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.1b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite80.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64_766`
102×	`sqrt-prod_binary64_776`
86×	`add-sqr-sqrt_binary64_782`
84×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
78×	`cbrt-prod_binary64_791`
58×	`associate-r_binary64_700`
38×	`add-exp-log_binary64_798`
29×	`add-cbrt-cube_binary64_796`
16×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
11×	`pow1_binary64_821`
9×	`cbrt-undiv_binary64_794` `associate-/r*_binary64_704` `div-exp_binary64_811`
6×	`sqrt-div_binary64_777` `associate-/l*_binary64_705`
4×	`add-log-exp_binary64_799`
3×	`associate-*l/_binary64_703` `flip3-+_binary64_763` `flip-+_binary64_734` `pow-prod-down_binary64_831`
2×	`rem-sqrt-square_binary64_773` `associate-/l/_binary64_707` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `pow1/2_binary64_840`
1×	`frac-2neg_binary64_771` `frac-times_binary64_770` `associate-l_binary64_701` `associate-r/_binary64_702` `clear-num_binary64_759` `-commutative_binary64_691`

Counts

4 → 201

Calls

4 calls:

32.0ms	(.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))))
8.0ms	(/.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)))

series294.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(.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))))
115.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
23.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
23.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify135.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4964	6988
1	4964	6988

prune337.0ms (4.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	213	8	221

Merged error: 0b

Counts

221 → 8

Compiler

Compiled 8262 to 3613 computations (56.3% saved)

regimes650.0ms (8.6%)

Compiler: Compiled 8370 to 5854 computations (30.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	34
1	17	34

end0.0ms (0%)

sample3.1s (40.8%)

Algorithm

1×

intervals

Results

537.0ms	1760×	body	1024	valid
469.0ms	1552×	body	1024	invalid
361.0ms	4887×	body	128	valid
197.0ms	917×	body	512	valid
165.0ms	779×	body	512	invalid
63.0ms	430×	body	256	valid
57.0ms	397×	body	256	invalid
52.0ms	646×	body	128	invalid
3.0ms	6×	body	2048	valid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 1071 to 745 computations (30.4% saved)

Details

analyze744.0ms (9.9%)

sample73.0ms (1%)

simplify97.0ms (1.3%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

rewrite31.0ms (0.4%)

series243.0ms (3.2%)

simplify71.0ms (0.9%)

prune124.0ms (1.6%)

localize11.0ms (0.1%)

rewrite57.0ms (0.8%)

series217.0ms (2.9%)

simplify78.0ms (1%)

prune179.0ms (2.4%)

localize12.0ms (0.2%)

rewrite107.0ms (1.4%)

series144.0ms (1.9%)

simplify230.0ms (3%)

prune512.0ms (6.8%)

localize14.0ms (0.2%)

rewrite80.0ms (1.1%)

series294.0ms (3.9%)

simplify135.0ms (1.8%)

prune337.0ms (4.5%)

regimes650.0ms (8.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.1s (40.8%)

Profiling