Details

analyze736.0ms

Algorithm

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

sample86.0ms

Algorithm

intervals

Results

19.0ms	44×	body	1280	valid
15.0ms	35×	body	1280	invalid
11.0ms	151×	body	80	valid
11.0ms	36×	body	640	valid
8.0ms	28×	body	640	invalid
4.0ms	18×	body	320	valid
3.0ms	13×	body	320	invalid
1.0ms	9×	body	160	invalid
1.0ms	17×	body	80	invalid
1.0ms	7×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.4b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.5b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite35.0ms

Algorithm

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:

6.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
15.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
10.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

series1.2s

Counts

3 → 9

Calls

3 calls:

185.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
631.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
388.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	728	897
1	728	897
0	728	897
1	728	897
0	5243	3
0	1238	1201
1	1238	1201
0	1238	1201
1	1238	1201
0	4867	3
1	4867	3
0	573	257
1	573	257
0	573	257
1	573	257
0	1	3
1	1	3

simplify85.0ms

Counts

106 → 106

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5863	2290

prune102.0ms

Filtered

73 candidates to 106 candidates (-45.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	95	11	106
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	96	12	108

Merged error: 0.3b

Counts

108 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(.f64 (cos.f64 th) (/.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))))
5.5b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.5b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

522×	`times-frac_binary64`
403×	`sqrt-prod_binary64`
312×	`add-sqr-sqrt_binary64`
270×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
257×	`associate-r_binary64`
18×	`sqrt-div_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
11×	`unswap-sqr_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`pow1_binary64` `div-inv_binary64`
6×	`associate-/r_binary64` `associate-/l_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `insert-posit16`
3×	`cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `sqrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 384

Calls

4 calls:

88.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
11.0ms	(/.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)))

series2.0s

Counts

4 → 12

Calls

4 calls:

914.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
318.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
367.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
370.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	645	567
1	645	567
0	645	567
1	645	567
0	4858	14
1	4858	14
0	645	567
1	645	567
0	645	567
1	645	567
0	4858	14
1	4858	14
0	856	1422
1	856	1422
0	856	1422
1	856	1422
0	1	3
1	1	3
0	2453	1705
1	2453	1705
0	2453	1705
1	2453	1705
0	1	3
1	1	3

simplify217.0ms

Counts

396 → 396

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4981	11869
1	4981	11869

prune241.0ms

Filtered

171 candidates to 396 candidates (-131.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	393	3	396
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	397	11	408

Merged error: 0.2b

Counts

408 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
0.5b	(/.f64 2 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.5b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.6b	(sqrt.f64 (/.f64 2 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac_binary64`
169×	`sqrt-prod_binary64`
132×	`add-sqr-sqrt_binary64`
113×	`associate-r_binary64`
106×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
17×	`associate-/r/_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
8×	`pow1_binary64`
7×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`associate-/r_binary64` `associate-l_binary64` `rem-sqrt-square_binary64` `associate-/l_binary64`
2×	`pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

4 → 212

Calls

4 calls:

46.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
8.0ms	(/.f64 2 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
8.0ms	(sqrt.f64 (/.f64 2 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))

series1.9s

Counts

4 → 12

Calls

4 calls:

720.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))))
289.0ms	(/.f64 2 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
382.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
531.0ms	(sqrt.f64 (/.f64 2 (+.f64 (.f64 a1 a1) (.f64 a2 a2))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	900	1024
1	900	1024
0	900	1024
1	900	1024
0	1	3
1	1	3
0	645	567
1	645	567
0	645	567
1	645	567
0	4858	14
1	4858	14
0	832	591
1	832	591
0	832	591
1	832	591
0	1	3
1	1	3
0	2007	2042
1	2007	2042
0	2007	2042
1	2007	2042
0	1	3
1	1	3

simplify129.0ms

Counts

224 → 224

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5114	6483

prune183.0ms

Filtered

143 candidates to 224 candidates (-56.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	223	1	224
Fresh	1	8	9
Picked	0	1	1
Done	1	0	1
Total	225	10	235

Merged error: 0.2b

Counts

235 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac_binary64`
70×	`add-sqr-sqrt_binary64`
60×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
44×	`associate-l_binary64` `sqrt-prod_binary64`
32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`pow1_binary64`
12×	`associate-/r*_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
6×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `associate-/l*_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64` `insert-posit16`
2×	`associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 172

Calls

4 calls:

13.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
13.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
7.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
7.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

244.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
240.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
421.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
422.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	471	1165
1	471	1165
0	471	1165
1	471	1165
0	5627	14
0	471	1165
1	471	1165
0	471	1165
1	471	1165
0	5627	14
0	665	797
1	665	797
0	665	797
1	665	797
0	1	3
1	1	3
0	665	797
1	665	797
0	665	797
1	665	797
0	1	3
1	1	3

simplify124.0ms

Counts

184 → 184

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5502	2818

prune153.0ms

Filtered

122 candidates to 184 candidates (-50.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	182	2	184
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	186	8	194

Merged error: 0b

Counts

194 → 8

regimes119.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	39
1	19	39

end0.0ms

sample2.7s

Algorithm

intervals

Results

566.0ms	1295×	body	1280	valid
498.0ms	1138×	body	1280	invalid
349.0ms	1166×	body	640	valid
344.0ms	4669×	body	80	valid
286.0ms	947×	body	640	invalid
130.0ms	583×	body	320	valid
102.0ms	474×	body	320	invalid
45.0ms	287×	body	160	valid
43.0ms	542×	body	80	invalid
39.0ms	265×	body	160	invalid

Details

analyze736.0ms

sample86.0ms

simplify28.0ms

prune4.0ms

localize10.0ms

rewrite35.0ms

series1.2s

simplify85.0ms

prune102.0ms

localize14.0ms

rewrite146.0ms

series2.0s

simplify217.0ms

prune241.0ms

localize12.0ms

rewrite83.0ms

series1.9s

simplify129.0ms

prune183.0ms

localize12.0ms

rewrite48.0ms

series1.3s

simplify124.0ms

prune153.0ms

regimes119.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample2.7s

Profiling