Details

analyze763.0ms (13.5%)

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

sample88.0ms (1.6%)

Algorithm

1×

intervals

Results

16.0ms	36×	body	1280	invalid
14.0ms	155×	body	80	valid
13.0ms	29×	body	1280	valid
13.0ms	42×	body	640	valid
9.0ms	30×	body	640	invalid
5.0ms	21×	body	320	valid
2.0ms	9×	body	320	invalid
1.0ms	10×	body	160	invalid
1.0ms	18×	body	80	invalid
1.0ms	9×	body	160	valid

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	105	13
1	105	13

prune11.0ms (0.2%)

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

localize10.0ms (0.2%)

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)))
0.6b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2.0))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
22×	`associate-r_binary64` `sqrt-prod_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64` `associate-/l*_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 94

Calls

3 calls:

14.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2.0)))
8.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2.0))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series68.0ms (1.2%)

Counts

3 → 9

Calls

3 calls:

47.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2.0)))
14.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2.0))
7.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify69.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4965	1529
1	4965	1529

prune157.0ms (2.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	99	6	105

Merged error: 0.3b

Counts

105 → 6

localize16.0ms (0.3%)

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)))
0.3b	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2.0)) (cbrt.f64 (sqrt.f64 2.0)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2.0))))
5.7b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.7b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite55.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64`
102×	`sqrt-prod_binary64`
86×	`add-sqr-sqrt_binary64`
84×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
78×	`cbrt-prod_binary64`
58×	`associate-r_binary64`
38×	`add-exp-log_binary64`
29×	`add-cbrt-cube_binary64`
16×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`pow1_binary64`
9×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
6×	`associate-/l*_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-*l/_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`
1×	`associate-r/_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `-commutative_binary64`

Counts

4 → 201

Calls

4 calls:

28.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2.0)) (cbrt.f64 (sqrt.f64 2.0)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2.0))))
9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2.0)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series81.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2.0)) (cbrt.f64 (sqrt.f64 2.0)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2.0))))
29.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2.0)))
10.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
8.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify98.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4970	4143
1	4970	4143

prune343.0ms (6.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	213	6	219

Merged error: 0.3b

Counts

219 → 6

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.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 2.0))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
4×	`associate-*l/_binary64`
3×	`flip3-+_binary64` `associate-r_binary64` `associate-l_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 60

Calls

3 calls:

9.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2.0))
7.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
5.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series62.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

34.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2.0))
20.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
7.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify54.0ms (1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5036	853

prune91.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	69	6	75

Merged error: 0.3b

Counts

75 → 6

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)))
0.4b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2.0))
5.7b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.7b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`sqrt-prod_binary64`
72×	`times-frac_binary64`
61×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
40×	`associate-r_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64`
10×	`sqrt-div_binary64`
6×	`associate-/r_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l_binary64` `associate-*l/_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `frac-times_binary64`
1×	`associate-r/_binary64` `associate-l_binary64` `sqrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

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 2.0)))
8.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2.0))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series62.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(.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 2.0)))
14.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2.0))
7.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
7.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify55.0ms (1%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5477	2865

prune189.0ms (3.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	168	7	175

Merged error: 0.0b

Counts

175 → 7

regimes461.0ms (8.2%)

Accuracy

Total 0.4b remaining (92.4%)

Threshold costs 0.4b (92.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	32
1	19	32

end0.0ms (0%)

sample2.8s (49.2%)

Algorithm

1×

intervals

Results

596.0ms	1324×	body	1280	valid
515.0ms	1133×	body	1280	invalid
372.0ms	1198×	body	640	valid
353.0ms	4664×	body	80	valid
287.0ms	942×	body	640	invalid
121.0ms	546×	body	320	valid
107.0ms	471×	body	320	invalid
40.0ms	268×	body	160	valid
37.0ms	474×	body	80	invalid
32.0ms	211×	body	160	invalid

Details

analyze763.0ms (13.5%)

sample88.0ms (1.6%)

simplify7.0ms (0.1%)

prune11.0ms (0.2%)

localize10.0ms (0.2%)

rewrite30.0ms (0.5%)

series68.0ms (1.2%)

simplify69.0ms (1.2%)

prune157.0ms (2.8%)

localize16.0ms (0.3%)

rewrite55.0ms (1%)

series81.0ms (1.4%)

simplify98.0ms (1.7%)

prune343.0ms (6.1%)

localize11.0ms (0.2%)

rewrite23.0ms (0.4%)

series62.0ms (1.1%)

simplify54.0ms (1%)

prune91.0ms (1.6%)

localize13.0ms (0.2%)

rewrite44.0ms (0.8%)

series62.0ms (1.1%)

simplify55.0ms (1%)

prune189.0ms (3.4%)

regimes461.0ms (8.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.8s (49.2%)

Profiling