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

sample170.0ms

Algorithm

intervals

Results

126.0ms	149×	body	1024	valid
21.0ms	40×	body	512	valid
6.0ms	22×	body	256	valid
6.0ms	45×	body	128	valid

simplify82.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5169	26

prune2.0ms

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: 2.7b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
2.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

18.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
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)))

series615.0ms

Counts

4 → 12

Calls

4 calls:

394.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
25.0ms	(pow.f64 (sin.f64 kx) 2)
26.0ms	(pow.f64 (sin.f64 ky) 2)
170.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify73.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4953	2288
1	4953	2288

prune141.0ms

Filtered

75 candidates to 115 candidates (-53.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	103	12	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	12	116

Merged error: 2.4b

Counts

116 → 12

localize14.0ms

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 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
2.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)
23.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (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)))

series608.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow.f64 (sin.f64 kx) 2)
24.0ms	(pow.f64 (sin.f64 ky) 2)
397.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
163.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify56.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5052	2129

prune103.0ms

Filtered

65 candidates to 115 candidates (-76.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	116	11	127

Merged error: 2.4b

Counts

127 → 11

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
2.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
2.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
2.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
20×	`sqrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
8×	`distribute-lft-out_binary64` `unpow-prod-down_binary64` `cbrt-prod_binary64` `sqrt-div_binary64`
7×	`pow1_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`cbrt-div_binary64`
1×	`pow1/3_binary64`

Counts

4 → 69

Calls

4 calls:

9.0ms	(cbrt.f64 (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)))
9.0ms	(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)))

series691.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
167.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
150.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
159.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify82.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4902	1705
1	4902	1705

prune149.0ms

Filtered

54 candidates to 81 candidates (-50.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	80	12	92

Merged error: 2.4b

Counts

92 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
1.3b	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
2.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
2.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

101×	`sqrt-prod_binary64`
87×	`*-un-lft-identity_binary64`
66×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
51×	`add-cube-cbrt_binary64`
39×	`associate-l_binary64`
36×	`add-exp-log_binary64`
27×	`add-cbrt-cube_binary64`
18×	`distribute-lft-out_binary64` `unpow-prod-down_binary64`
15×	`prod-exp_binary64`
12×	`sqrt-div_binary64`
11×	`associate-/r*_binary64` `pow1_binary64`
10×	`cbrt-unprod_binary64`
7×	`div-exp_binary64`
6×	`cbrt-undiv_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `associate-/r/_binary64` `flip-+_binary64`
3×	`pow-prod-down_binary64` `associate-r/_binary64` `rec-exp_binary64` `associate-/l_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`
1×	`associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 163

Calls

4 calls:

14.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
40.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (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)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

356.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
426.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
173.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
147.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify105.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4963	5508
1	4963	5508

prune206.0ms

Filtered

100 candidates to 175 candidates (-75.0%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	174	1	175
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	174	13	187

Merged error: 2.4b

Counts

187 → 13

regimes332.0ms

Accuracy

0% (1.8b remaining)

Error of 4.7b against oracle of 2.8b and baseline of 4.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	84
1	23	84

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.9s	4598×	body	1024	valid
763.0ms	1481×	body	512	valid
180.0ms	1347×	body	128	valid
173.0ms	557×	body	256	valid
33.0ms	17×	body	2048	valid

Details

analyze1.3s

sample170.0ms

simplify82.0ms

prune2.0ms

localize15.0ms

rewrite43.0ms

series615.0ms

simplify73.0ms

prune141.0ms

localize14.0ms

rewrite48.0ms

series608.0ms

simplify56.0ms

prune103.0ms

localize28.0ms

rewrite49.0ms

series691.0ms

simplify82.0ms

prune149.0ms

localize20.0ms

rewrite98.0ms

series1.1s

simplify105.0ms

prune206.0ms

regimes332.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample5.3s

Profiling