Details

analyze1.3s

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

sample210.0ms

Algorithm

intervals

Results

133.0ms	126×	body	1280	valid
49.0ms	66×	body	640	valid
8.0ms	18×	body	320	valid
5.0ms	41×	body	80	valid
1.0ms	5×	body	160	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4766	16
1	4766	16

prune8.0ms

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: 3.9b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0))))
0.2b	(pow.f64 (sin.f64 ky) 2.0)
0.3b	(pow.f64 (sin.f64 kx) 2.0)
3.6b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

rewrite29.0ms

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` `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 → 100

Calls

4 calls:

12.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0))))
3.0ms	(pow.f64 (sin.f64 ky) 2.0)
3.0ms	(pow.f64 (sin.f64 kx) 2.0)
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0))))
18.0ms	(pow.f64 (sin.f64 ky) 2.0)
23.0ms	(pow.f64 (sin.f64 kx) 2.0)
26.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

simplify64.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4925	1503
1	4925	1503

prune172.0ms

Filtered

70 candidates to 112 candidates (-60.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	99	13	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	13	113

Merged error: 3.1b

Counts

113 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0))) (sin.f64 ky)))
0.2b	(pow.f64 (sin.f64 ky) 2.0)
0.3b	(pow.f64 (sin.f64 kx) 2.0)
3.6b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

rewrite42.0ms

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` `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 → 187

Calls

4 calls:

18.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0))) (sin.f64 ky)))
3.0ms	(pow.f64 (sin.f64 ky) 2.0)
3.0ms	(pow.f64 (sin.f64 kx) 2.0)
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0))) (sin.f64 ky)))
19.0ms	(pow.f64 (sin.f64 ky) 2.0)
18.0ms	(pow.f64 (sin.f64 kx) 2.0)
25.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

simplify87.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4932	3585
1	4932	3585

prune181.0ms

Filtered

93 candidates to 199 candidates (-114.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	197	2	199
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	199	13	212

Merged error: 3.1b

Counts

212 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2.0)
0.3b	(pow.f64 (sin.f64 kx) 2.0)
0.3b	(*.f64 (sin.f64 ky) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))))
3.6b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

rewrite37.0ms

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` `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 → 106

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 ky) 2.0)
3.0ms	(pow.f64 (sin.f64 kx) 2.0)
19.0ms	(*.f64 (sin.f64 ky) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

series114.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow.f64 (sin.f64 ky) 2.0)
18.0ms	(pow.f64 (sin.f64 kx) 2.0)
48.0ms	(*.f64 (sin.f64 ky) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))))
27.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

simplify60.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5148	1332

prune132.0ms

Filtered

69 candidates to 118 candidates (-71.0%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	118	13	131

Merged error: 3.1b

Counts

131 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

3.6b	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2.0)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2.0))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2.0))) (pow.f64 (sin.f64 ky) 2.0)))
13.7b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2.0))
13.7b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2.0))
13.7b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2.0))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

21×	`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×	`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 → 60

Calls

4 calls:

17.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2.0)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2.0))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2.0))) (pow.f64 (sin.f64 ky) 2.0)))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2.0))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2.0))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2.0))

series148.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2.0)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2.0))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2.0))) (pow.f64 (sin.f64 ky) 2.0)))
40.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2.0))
42.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2.0))
40.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5087	727

prune90.0ms

Filtered

58 candidates to 72 candidates (-24.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	72	13	85

Merged error: 3.1b

Counts

85 → 13

regimes676.0ms

Accuracy

0% (1.3b remaining)

Error of 3.6b against oracle of 2.3b and baseline of 3.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	18
1	18	18

end0.0ms

sample6.3s

Algorithm

intervals

Results

4.2s	3843×	body	1280	valid
1.3s	2005×	body	640	valid
301.0ms	686×	body	320	valid
153.0ms	1164×	body	80	valid
83.0ms	302×	body	160	valid

Details

analyze1.3s

sample210.0ms

simplify74.0ms

prune8.0ms

localize15.0ms

rewrite29.0ms

series116.0ms

simplify64.0ms

prune172.0ms

localize15.0ms

rewrite42.0ms

series127.0ms

simplify87.0ms

prune181.0ms

localize16.0ms

rewrite37.0ms

series114.0ms

simplify60.0ms

prune132.0ms

localize18.0ms

rewrite27.0ms

series148.0ms

simplify55.0ms

prune90.0ms

regimes676.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.3s

Profiling