Details

analyze1.4s

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

122.0ms	110×	body	1280	valid
42.0ms	65×	body	640	valid
11.0ms	26×	body	320	valid
6.0ms	45×	body	80	valid
3.0ms	10×	body	160	valid

simplify69.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5114	16

prune3.0ms

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: 4.8b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
4.4b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite31.0ms

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` `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 → 102

Calls

4 calls:

13.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
3.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/.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)
26.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify37.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5455	1421

prune124.0ms

Filtered

67 candidates to 114 candidates (-70.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	101	13	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	13	115

Merged error: 3.3b

Counts

115 → 13

localize15.0ms

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)))
0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
4.4b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite44.0ms

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`
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 → 189

Calls

4 calls:

17.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
3.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/.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)
21.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify77.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5002	3463

prune127.0ms

Filtered

91 candidates to 201 candidates (-120.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	202	12	214

Merged error: 3.3b

Counts

214 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
0.3b	(*.f64 (sin.f64 ky) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.4b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
30×	`associate-r_binary64`
28×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
22×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
14×	`unpow-prod-down_binary64`
9×	`pow1_binary64` `add-cbrt-cube_binary64`
8×	`distribute-lft-out_binary64`
6×	`pow-unpow_binary64`
5×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `prod-exp_binary64` `sqrt-div_binary64`
3×	`associate-l_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `div-exp_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 108

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)
24.0ms	(*.f64 (sin.f64 ky) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(pow.f64 (sin.f64 kx) 2)
4.0ms	(pow.f64 (sin.f64 ky) 2)
40.0ms	(*.f64 (sin.f64 ky) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
21.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify55.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4949	1266
1	4949	1266

prune87.0ms

Filtered

66 candidates to 120 candidates (-81.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	121	11	132

Merged error: 3.3b

Counts

132 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

4.4b	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (pow.f64 (sin.f64 ky) 2)))
19.2b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
19.2b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
19.2b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`unpow-prod-down_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`unpow2_binary64` `pow1/3_binary64` `sqr-pow_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 63

Calls

4 calls:

17.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))

series85.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (pow.f64 (sin.f64 ky) 2)))
23.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
20.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
21.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))

simplify59.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4887	648
1	4887	648

prune56.0ms

Filtered

54 candidates to 75 candidates (-38.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	75	11	86

Merged error: 3.3b

Counts

86 → 11

regimes472.0ms

Accuracy

0% (1.3b remaining)

Error of 3.9b against oracle of 2.6b and baseline of 3.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	18
1	19	18

end0.0ms

sample6.2s

Algorithm

intervals

Results

4.0s	3681×	body	1280	valid
1.4s	2033×	body	640	valid
329.0ms	727×	body	320	valid
167.0ms	1236×	body	80	valid
91.0ms	323×	body	160	valid

Details

analyze1.4s

sample195.0ms

simplify69.0ms

prune3.0ms

localize14.0ms

rewrite31.0ms

series73.0ms

simplify37.0ms

prune124.0ms

localize15.0ms

rewrite44.0ms

series67.0ms

simplify77.0ms

prune127.0ms

localize15.0ms

rewrite43.0ms

series69.0ms

simplify55.0ms

prune87.0ms

localize22.0ms

rewrite27.0ms

series85.0ms

simplify59.0ms

prune56.0ms

regimes472.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.2s

Profiling