Details

analyze393.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
15.6%	31.2%	53.2%	6
17.2%	26.5%	56.3%	7
18%	22.6%	59.4%	8
18.3%	19.9%	61.8%	9
18.5%	17.8%	63.7%	10
18.6%	16.3%	65.1%	11
18.7%	15.2%	66.1%	12
18.7%	14.4%	66.9%	13
18.7%	13.8%	67.4%	14

sample75.0ms

Algorithm

intervals

Results

21.0ms	256×	body	80	valid
16.0ms	29×	body	1280	nan
11.0ms	87×	body	80	overflowed
9.0ms	22×	body	640	nan
3.0ms	12×	body	320	nan
2.0ms	10×	body	160	nan
1.0ms	22×	body	80	nan
1.0ms	8×	body	80	invalid

simplify105.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4909	22
1	4909	22

prune5.0ms

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: 0.3b

Counts

2 → 2

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.3b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac_binary64`
42×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
33×	`add-cube-cbrt_binary64`
26×	`add-exp-log_binary64`
22×	`pow-unpow_binary64`
18×	`sqrt-prod_binary64`
14×	`pow1_binary64`
10×	`add-cbrt-cube_binary64`
9×	`prod-exp_binary64`
8×	`sqr-pow_binary64` `unpow-prod-down_binary64`
6×	`pow-prod-down_binary64` `associate-/r*_binary64` `difference-of-squares_binary64` `pow-exp_binary64`
5×	`associate-/l*_binary64` `div-exp_binary64`
3×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `pow-pow_binary64` `distribute-lft-out--_binary64` `insert-posit16`
2×	`pow-to-exp_binary64` `div-sub_binary64` `pow-sub_binary64` `div-inv_binary64`
1×	`associate-/l/_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

3 → 118

Calls

3 calls:

12.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
9.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
6.0ms	(.f64 (.f64 2 PI.f64) n)

series1.3s

Counts

3 → 9

Calls

3 calls:

466.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
370.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
460.0ms	(.f64 (.f64 2 PI.f64) n)

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	284	1957
1	284	1957
0	4845	1079
1	4845	1079
0	284	1957
1	284	1957
0	4845	1079
1	4845	1079
0	4792	9
1	4792	9
0	696	2740
1	696	2740
0	4957	2340
1	4957	2340
0	696	2740
1	696	2740
0	4957	2340
1	4957	2340
0	605	6
1	605	6
0	504	2673
1	504	2673
0	4938	2277
1	4938	2277
0	504	2673
1	504	2673
0	4938	2277
1	4938	2277
0	5287	14

simplify131.0ms

Counts

127 → 127

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4923	3084
1	4923	3084

prune146.0ms

Filtered

84 candidates to 127 candidates (-51.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	118	9	127
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	119	10	129

Merged error: 0.0b

Counts

129 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.2b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(/.f64 1 (sqrt.f64 k))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
62×	`times-frac_binary64`
57×	`*-un-lft-identity_binary64`
44×	`add-cube-cbrt_binary64`
38×	`prod-exp_binary64`
25×	`sqrt-prod_binary64`
23×	`associate-l_binary64`
22×	`pow-unpow_binary64`
17×	`pow1_binary64`
16×	`add-cbrt-cube_binary64`
15×	`pow-exp_binary64`
12×	`div-exp_binary64`
10×	`unswap-sqr_binary64`
8×	`associate-r_binary64`
7×	`sqr-pow_binary64`
6×	`pow-prod-down_binary64` `associate-/r*_binary64` `1-exp_binary64` `difference-of-squares_binary64` `rec-exp_binary64`
5×	`pow-to-exp_binary64` `cbrt-unprod_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`pow-pow_binary64` `div-sub_binary64` `pow-sub_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `pow-flip_binary64`
2×	`cbrt-undiv_binary64` `unpow-prod-down_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 176

Calls

4 calls:

13.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
16.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
6.0ms	(.f64 (.f64 2 PI.f64) n)
5.0ms	(/.f64 1 (sqrt.f64 k))

series1.8s

Counts

4 → 12

Calls

4 calls:

474.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
412.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
457.0ms	(.f64 (.f64 2 PI.f64) n)
437.0ms	(/.f64 1 (sqrt.f64 k))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	435	849
1	435	849
0	19	9
1	19	9
0	435	849
1	435	849
0	19	9
1	19	9
0	5063	42
0	284	1957
1	284	1957
0	4845	1079
1	4845	1079
0	284	1957
1	284	1957
0	4845	1079
1	4845	1079
0	4792	9
1	4792	9
0	725	2759
1	725	2759
0	39	1989
1	39	1989
0	725	2759
1	725	2759
0	39	1989
1	39	1989
0	1	3
1	1	3
0	504	2673
1	504	2673
0	4938	2277
1	4938	2277
0	504	2673
1	504	2673
0	4938	2277
1	4938	2277
0	5287	14

simplify173.0ms

Counts

188 → 188

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	4914	3513
1	4914	3513

prune151.0ms

Filtered

110 candidates to 188 candidates (-70.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	187	11	198

Merged error: 0.0b

Counts

198 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
0.2b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.2b	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac_binary64`
147×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
138×	`add-cube-cbrt_binary64`
78×	`sqrt-prod_binary64`
72×	`add-exp-log_binary64`
40×	`associate-/r*_binary64`
32×	`sqr-pow_binary64` `unpow-prod-down_binary64` `div-exp_binary64`
22×	`pow-unpow_binary64`
18×	`prod-exp_binary64`
16×	`pow1_binary64` `add-cbrt-cube_binary64`
15×	`pow-exp_binary64`
9×	`associate-/l*_binary64`
7×	`div-inv_binary64`
6×	`pow-prod-down_binary64` `1-exp_binary64` `associate-/r/_binary64` `div-sub_binary64` `pow-sub_binary64` `difference-of-squares_binary64` `rec-exp_binary64`
5×	`pow-to-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `insert-posit16`
3×	`cbrt-unprod_binary64` `associate-r_binary64` `pow-pow_binary64` `distribute-lft-out--_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-l_binary64` `inv-pow_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 295

Calls

4 calls:

15.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
13.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
11.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
6.0ms	(.f64 (.f64 2 PI.f64) n)

series1.9s

Counts

4 → 12

Calls

4 calls:

562.0ms	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
464.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
405.0ms	(/.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
470.0ms	(.f64 (.f64 2 PI.f64) n)

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	284	1957
1	284	1957
0	4845	1079
1	4845	1079
0	284	1957
1	284	1957
0	4845	1079
1	4845	1079
0	4792	9
1	4792	9
0	682	2732
1	682	2732
0	139	2098
1	139	2098
0	682	2732
1	682	2732
0	139	2098
1	139	2098
0	1	3
1	1	3
0	504	2673
1	504	2673
0	4938	2277
1	4938	2277
0	504	2673
1	504	2673
0	4938	2277
1	4938	2277
0	5287	14
0	817	2759
1	817	2759
0	5081	2455
0	817	2759
1	817	2759
0	5081	2455
0	605	6
1	605	6

simplify217.0ms

Counts

307 → 307

Iterations

Useful iterations: 0 (117.0ms)

Iter	Nodes	Cost
0	5388	10120

prune243.0ms

Filtered

163 candidates to 307 candidates (-88.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	306	1	307
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	308	10	318

Merged error: 0b

Counts

318 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k)))
0.2b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

954×	`times-frac_binary64` `sqrt-prod_binary64`
452×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
443×	`add-cube-cbrt_binary64`
101×	`sqr-pow_binary64` `unpow-prod-down_binary64`
54×	`associate-/l*_binary64`
46×	`add-exp-log_binary64`
22×	`pow-unpow_binary64`
18×	`associate-/r*_binary64`
16×	`add-cbrt-cube_binary64` `div-exp_binary64`
15×	`pow1_binary64`
13×	`div-inv_binary64`
12×	`prod-exp_binary64`
9×	`pow-exp_binary64`
6×	`pow-prod-down_binary64` `difference-of-squares_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `pow-pow_binary64` `distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `div-sub_binary64` `clear-num_binary64` `pow-sub_binary64` `frac-2neg_binary64`
1×	`associate-l_binary64` `*-commutative_binary64`

Counts

4 → 655

Calls

4 calls:

27.0ms	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
10.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k)))
12.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
6.0ms	(.f64 (.f64 2 PI.f64) n)

series2.2s

Counts

4 → 12

Calls

4 calls:

626.0ms	(/.f64 (/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
661.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k)))
463.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
457.0ms	(.f64 (.f64 2 PI.f64) n)

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	284	1957
1	284	1957
0	4845	1079
1	4845	1079
0	284	1957
1	284	1957
0	4845	1079
1	4845	1079
0	4792	9
1	4792	9
0	504	2673
1	504	2673
0	4938	2277
1	4938	2277
0	504	2673
1	504	2673
0	4938	2277
1	4938	2277
0	5287	14
0	756	2758
1	756	2758
0	5475	1942
0	756	2758
1	756	2758
0	5475	1942
0	5030	21
0	883	2843
1	883	2843
0	4924	1917
1	4924	1917
0	883	2843
1	883	2843
0	4924	1917
1	4924	1917
0	5146	9

simplify396.0ms

Counts

667 → 667

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	4952	32485
1	4952	32485

prune406.0ms

Filtered

231 candidates to 667 candidates (-188.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	667	0	667
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	667	10	677

Merged error: 0b

Counts

677 → 10

regimes101.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	25
1	28	25

end0.0ms

sample2.7s

Algorithm

intervals

Results

883.0ms	8000×	body	80	valid
599.0ms	1015×	body	1280	nan
368.0ms	851×	body	640	nan
324.0ms	2434×	body	80	overflowed
134.0ms	452×	body	320	nan
41.0ms	770×	body	80	nan
38.0ms	223×	body	160	nan
21.0ms	238×	body	80	invalid

Details

analyze393.0ms

sample75.0ms

simplify105.0ms

prune5.0ms

localize12.0ms

rewrite33.0ms

series1.3s

simplify131.0ms

prune146.0ms

localize14.0ms

rewrite49.0ms

series1.8s

simplify173.0ms

prune151.0ms

localize14.0ms

rewrite64.0ms

series1.9s

simplify217.0ms

prune243.0ms

localize17.0ms

rewrite125.0ms

series2.2s

simplify396.0ms

prune406.0ms

regimes101.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample2.7s

Profiling