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

sample206.0ms

Algorithm

intervals

Results

126.0ms	115×	body	1280	valid
51.0ms	75×	body	640	valid
9.0ms	19×	body	320	valid
5.0ms	37×	body	80	valid
3.0ms	10×	body	160	valid

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4766	16
1	4766	16

prune7.0ms

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: 4.9b

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 kx) 2.0)
0.3b	(pow.f64 (sin.f64 ky) 2.0)
4.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

rewrite28.0ms

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:

11.0ms	(/.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 kx) 2.0)
3.0ms	(pow.f64 (sin.f64 ky) 2.0)
7.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

series104.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0))))
20.0ms	(pow.f64 (sin.f64 kx) 2.0)
19.0ms	(pow.f64 (sin.f64 ky) 2.0)
23.0ms	(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

prune163.0ms

Filtered

70 candidates to 112 candidates (-60.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	100	12	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	12	113

Merged error: 2.7b

Counts

113 → 12

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 kx) 2.0)
0.3b	(pow.f64 (sin.f64 ky) 2.0)
4.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

rewrite39.0ms

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:

15.0ms	(/.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 kx) 2.0)
3.0ms	(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)))

series101.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0))) (sin.f64 ky)))
17.0ms	(pow.f64 (sin.f64 kx) 2.0)
18.0ms	(pow.f64 (sin.f64 ky) 2.0)
23.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4932	3585
1	4932	3585

prune180.0ms

Filtered

94 candidates to 199 candidates (-111.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	195	4	199
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	198	13	211

Merged error: 2.7b

Counts

211 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2.0)
0.2b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))) (/.f64 1 (sin.f64 ky)))
0.3b	(pow.f64 (sin.f64 ky) 2.0)
4.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

rewrite78.0ms

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`
2×	`pow-to-exp_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 → 516

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 kx) 2.0)
24.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))) (/.f64 1 (sin.f64 ky)))
3.0ms	(pow.f64 (sin.f64 ky) 2.0)
7.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

series104.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow.f64 (sin.f64 kx) 2.0)
47.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))) (/.f64 1 (sin.f64 ky)))
18.0ms	(pow.f64 (sin.f64 ky) 2.0)
23.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))

simplify156.0ms

Algorithm

egg-herbie

Counts

528 → 528

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4952	13838
1	4952	13838

prune378.0ms

Filtered

175 candidates to 528 candidates (-201.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	527	1	528
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	529	12	541

Merged error: 2.7b

Counts

541 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
0.3b	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))
0.3b	(pow.f64 (sin.f64 ky) 2)
4.6b	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64` `times-frac_binary64`
45×	`sqrt-prod_binary64`
36×	`add-cube-cbrt_binary64`
24×	`associate-r_binary64`
23×	`unpow-prod-down_binary64`
20×	`distribute-lft-out_binary64`
11×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-/r/_binary64`
5×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`inv-pow_binary64` `div-exp_binary64` `pow-flip_binary64` `sqrt-div_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `pow-pow_binary64` `sqr-pow_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `rec-exp_binary64` `pow-exp_binary64` `-commutative_binary64`

Counts

4 → 138

Calls

4 calls:

10.0ms	(/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
18.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))
3.0ms	(pow.f64 (sin.f64 ky) 2)
10.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))

series107.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
44.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))
4.0ms	(pow.f64 (sin.f64 ky) 2)
34.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))

simplify51.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4925	1985
1	4925	1985

prune122.0ms

Filtered

81 candidates to 150 candidates (-85.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	150	12	162

Merged error: 2.6b

Counts

162 → 12

regimes643.0ms

Accuracy

-44.1% (2.0b remaining)

Error of 4.9b against oracle of 2.8b and baseline of 4.2b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	39
1	67	39

end0.0ms

sample6.2s

Algorithm

intervals

Results

4.0s	3713×	body	1280	valid
1.4s	1985×	body	640	valid
332.0ms	750×	body	320	valid
165.0ms	1276×	body	80	valid
78.0ms	276×	body	160	valid

Details

analyze1.3s

sample206.0ms

simplify72.0ms

prune7.0ms

localize15.0ms

rewrite28.0ms

series104.0ms

simplify64.0ms

prune163.0ms

localize15.0ms

rewrite39.0ms

series101.0ms

simplify84.0ms

prune180.0ms

localize17.0ms

rewrite78.0ms

series104.0ms

simplify156.0ms

prune378.0ms

localize15.0ms

rewrite48.0ms

series107.0ms

simplify51.0ms

prune122.0ms

regimes643.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample6.2s

Profiling