Details

analyze754.0ms (10.5%)

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)

sample97.0ms (1.3%)

Algorithm

1×

intervals

Results

20.0ms	47×	body	1280	invalid
15.0ms	37×	body	640	invalid
13.0ms	31×	body	1280	valid
12.0ms	167×	body	80	valid
10.0ms	32×	body	640	valid
4.0ms	18×	body	320	valid
4.0ms	17×	body	320	invalid
2.0ms	12×	body	160	invalid
2.0ms	21×	body	80	invalid
1.0ms	8×	body	160	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify24.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

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 (0.1%)

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))

rewrite36.0ms (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` `insert-posit16`
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 → 97

Calls

3 calls:

15.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
9.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
5.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series443.0ms (6.2%)

Counts

3 → 9

Calls

3 calls:

306.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
97.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
40.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify86.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	6038	2431

prune129.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	98	8	106
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	99	9	108

Merged error: 0b

Counts

108 → 9

Compiler

Compiled 2494 to 983 computations (60.6% 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 (+.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))

rewrite30.0ms (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` `insert-posit16` `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 → 63

Calls

3 calls:

14.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
9.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
5.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series403.0ms (5.6%)

Counts

3 → 9

Calls

3 calls:

225.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
131.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
47.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify154.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (127.0ms)

Iter	Nodes	Cost
0	4933	1344
1	4933	1344

prune73.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	72	9	81

Merged error: 0b

Counts

81 → 9

Compiler

Compiled 1487 to 592 computations (60.2% 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 (sqrt.f64 2) (cos.f64 th))
0.3b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`times-frac_binary64`
93×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
48×	`sqrt-prod_binary64`
25×	`associate-/r*_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-/l*_binary64`
6×	`div-inv_binary64`
5×	`add-log-exp_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64` `insert-posit16`
2×	`flip3-+_binary64` `associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`associate-/r/_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 161

Calls

3 calls:

14.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
5.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))
5.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series321.0ms (4.5%)

Counts

3 → 9

Calls

3 calls:

215.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
67.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))
38.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify125.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5107	5085

prune171.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	172	7	179

Merged error: 0b

Counts

179 → 7

Compiler

Compiled 4195 to 1550 computations (63.1% saved)

localize15.0ms (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))))
8.0b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
8.0b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite77.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

540×	`times-frac_binary64`
429×	`sqrt-prod_binary64`
297×	`add-sqr-sqrt_binary64`
295×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
48×	`associate-/r*_binary64`
22×	`sqrt-div_binary64`
17×	`associate-/r/_binary64`
12×	`associate-/l*_binary64`
11×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
9×	`div-inv_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `insert-posit16`
3×	`sqrt-undiv_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 415

Calls

4 calls:

25.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
10.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
5.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series278.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

100.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
82.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
52.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
43.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify281.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

427 → 427

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	4943	16840
1	4943	16840

prune516.0ms (7.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	427	0	427
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	427	7	434

Merged error: 0b

Counts

434 → 7

Compiler

Compiled 14268 to 4413 computations (69.1% saved)

regimes102.0ms (1.4%)

Compiler: Compiled 868 to 744 computations (14.3% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	20
1	14	20

end0.0ms (0%)

sample3.0s (41.7%)

Algorithm

1×

intervals

Results

583.0ms	1334×	body	1280	valid
551.0ms	1238×	body	1280	invalid
358.0ms	1160×	body	640	valid
353.0ms	4690×	body	80	valid
303.0ms	1004×	body	640	invalid
121.0ms	547×	body	320	valid
109.0ms	498×	body	320	invalid
41.0ms	517×	body	80	invalid
41.0ms	269×	body	160	valid
36.0ms	225×	body	160	invalid

Compiler

Compiled 174 to 147 computations (15.5% saved)

Details

analyze754.0ms (10.5%)

sample97.0ms (1.3%)

simplify24.0ms (0.3%)

prune5.0ms (0.1%)

localize10.0ms (0.1%)

rewrite36.0ms (0.5%)

series443.0ms (6.2%)

simplify86.0ms (1.2%)

prune129.0ms (1.8%)

localize10.0ms (0.1%)

rewrite30.0ms (0.4%)

series403.0ms (5.6%)

simplify154.0ms (2.2%)

prune73.0ms (1%)

localize10.0ms (0.1%)

rewrite34.0ms (0.5%)

series321.0ms (4.5%)

simplify125.0ms (1.7%)

prune171.0ms (2.4%)

localize15.0ms (0.2%)

rewrite77.0ms (1.1%)

series278.0ms (3.9%)

simplify281.0ms (3.9%)

prune516.0ms (7.2%)

regimes102.0ms (1.4%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample3.0s (41.7%)

Profiling