Details

analyze1.2s

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
25%	74.9%	0.1%	8
54.6%	45.2%	0.1%	9
56.2%	43.7%	0.1%	10
62.4%	37.4%	0.1%	11
65.9%	33.9%	0.1%	12
66.3%	33.5%	0.1%	13
69%	30.8%	0.1%	14

sample195.0ms

Algorithm

intervals

Results

127.0ms	123×	body	1280	valid
37.0ms	51×	body	640	valid
12.0ms	29×	body	320	valid
6.0ms	45×	body	80	valid
2.0ms	8×	body	160	valid

simplify167.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (153.0ms)

Iter	Nodes	Cost
0	5013	26

prune5.0ms

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: 3.4b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
3.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
25×	`sqrt-prod_binary64`
24×	`times-frac_binary64`
16×	`unpow-prod-down_binary64`
10×	`distribute-lft-out_binary64`
8×	`associate-/r*_binary64` `add-exp-log_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`associate-/l*_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 106

Calls

4 calls:

16.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
4.0ms	(pow.f64 (sin.f64 kx) 2)
4.0ms	(pow.f64 (sin.f64 ky) 2)
10.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

332.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
186.0ms	(pow.f64 (sin.f64 kx) 2)
184.0ms	(pow.f64 (sin.f64 ky) 2)
393.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	621	723
1	621	723
0	621	723
1	621	723
0	4858	14
1	4858	14
0	617	408
1	617	408
0	617	408
1	617	408
0	1	3
1	1	3
0	617	408
1	617	408
0	617	408
1	617	408
0	1	3
1	1	3
0	864	1392
1	864	1392
0	864	1392
1	864	1392
0	1	3
1	1	3

simplify74.0ms

Counts

118 → 118

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5121	2201

prune127.0ms

Filtered

71 candidates to 118 candidates (-66.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	109	9	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	9	119

Merged error: 2.9b

Counts

119 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
3.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac_binary64`
150×	`*-un-lft-identity_binary64`
99×	`add-sqr-sqrt_binary64`
98×	`add-cube-cbrt_binary64`
65×	`sqrt-prod_binary64`
32×	`unpow-prod-down_binary64`
28×	`associate-/r*_binary64`
26×	`distribute-lft-out_binary64`
17×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
7×	`div-exp_binary64`
6×	`pow-unpow_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`pow-to-exp_binary64` `1-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `rec-exp_binary64` `pow-exp_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64` `flip-+_binary64`

Counts

4 → 193

Calls

4 calls:

24.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
4.0ms	(pow.f64 (sin.f64 kx) 2)
4.0ms	(pow.f64 (sin.f64 ky) 2)
10.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series1.4s

Counts

4 → 12

Calls

4 calls:

594.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
185.0ms	(pow.f64 (sin.f64 kx) 2)
181.0ms	(pow.f64 (sin.f64 ky) 2)
392.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	621	723
1	621	723
0	621	723
1	621	723
0	4858	14
1	4858	14
0	617	408
1	617	408
0	617	408
1	617	408
0	1	3
1	1	3
0	617	408
1	617	408
0	617	408
1	617	408
0	1	3
1	1	3
0	1500	1425
1	1500	1425
0	1500	1425
1	1500	1425
0	5187	16

simplify167.0ms

Counts

205 → 205

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4971	5561
1	4971	5561

prune154.0ms

Filtered

95 candidates to 205 candidates (-115.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	206	8	214

Merged error: 2.9b

Counts

214 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (/.f64 1 (sin.f64 ky)))
0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
3.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

1005×	`times-frac_binary64`
608×	`*-un-lft-identity_binary64`
437×	`add-sqr-sqrt_binary64`
436×	`add-cube-cbrt_binary64`
215×	`sqrt-prod_binary64`
92×	`unpow-prod-down_binary64`
86×	`distribute-lft-out_binary64`
46×	`add-exp-log_binary64` `div-inv_binary64`
32×	`div-exp_binary64`
30×	`associate-/l*_binary64` `sqrt-div_binary64`
29×	`associate-/r/_binary64`
16×	`add-cbrt-cube_binary64`
15×	`flip3-+_binary64` `flip-+_binary64`
13×	`associate-/r*_binary64`
8×	`1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
2×	`pow-to-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow-exp_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 522

Calls

4 calls:

32.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (/.f64 1 (sin.f64 ky)))
4.0ms	(pow.f64 (sin.f64 kx) 2)
4.0ms	(pow.f64 (sin.f64 ky) 2)
10.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

434.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (/.f64 1 (sin.f64 ky)))
188.0ms	(pow.f64 (sin.f64 kx) 2)
190.0ms	(pow.f64 (sin.f64 ky) 2)
397.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	621	723
1	621	723
0	621	723
1	621	723
0	4858	14
1	4858	14
0	617	408
1	617	408
0	617	408
1	617	408
0	1	3
1	1	3
0	617	408
1	617	408
0	617	408
1	617	408
0	1	3
1	1	3
0	1986	1336
1	1986	1336
0	1986	1336
1	1986	1336
0	84	14
1	84	14

simplify308.0ms

Counts

534 → 534

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	5123	21919

prune527.0ms

Filtered

178 candidates to 534 candidates (-200.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	534	0	534
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	534	8	542

Merged error: 2.9b

Counts

542 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
30×	`sqrt-prod_binary64` `cbrt-prod_binary64`
25×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out_binary64` `unpow-prod-down_binary64`
8×	`sqrt-div_binary64`
7×	`pow1_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip-+_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`associate-/r/_binary64`
1×	`cbrt-div_binary64` `pow1/3_binary64` `div-inv_binary64`

Counts

4 → 94

Calls

4 calls:

14.0ms	(cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
10.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series1.3s

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
391.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
395.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
393.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	621	723
1	621	723
0	621	723
1	621	723
0	4858	14
1	4858	14
0	621	723
1	621	723
0	621	723
1	621	723
0	4858	14
1	4858	14
0	621	723
1	621	723
0	621	723
1	621	723
0	4858	14
1	4858	14
0	160	1908
1	160	1908
0	160	1908
1	160	1908
0	1	3
1	1	3

simplify87.0ms

Counts

106 → 106

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5352	2773

prune189.0ms

Filtered

72 candidates to 106 candidates (-47.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	106	8	114

Merged error: 2.9b

Counts

114 → 8

regimes205.0ms

Accuracy

0% (0.5b remaining)

Error of 4.1b against oracle of 3.6b and baseline of 4.1b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	32
1	21	32

end0.0ms

sample6.1s

Algorithm

intervals

Results

4.0s	3728×	body	1280	valid
1.3s	2040×	body	640	valid
313.0ms	688×	body	320	valid
153.0ms	1261×	body	80	valid
78.0ms	283×	body	160	valid

Details

analyze1.2s

sample195.0ms

simplify167.0ms

prune5.0ms

localize15.0ms

rewrite37.0ms

series1.1s

simplify74.0ms

prune127.0ms

localize16.0ms

rewrite55.0ms

series1.4s

simplify167.0ms

prune154.0ms

localize17.0ms

rewrite108.0ms

series1.2s

simplify308.0ms

prune527.0ms

localize20.0ms

rewrite49.0ms

series1.3s

simplify87.0ms

prune189.0ms

regimes205.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample6.1s

Profiling