Details

analyze620.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
49.9%	49.9%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
74.9%	25%	0.2%	7
74.9%	25%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
87.3%	12.5%	0.2%	11
87.3%	12.5%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

sample103.0ms

Algorithm

intervals

Results

34.0ms	199×	body	80	valid
32.0ms	25×	body	1280	valid
16.0ms	19×	body	640	valid
5.0ms	8×	body	320	valid
2.0ms	5×	body	160	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4882	29
1	4882	29

prune4.0ms

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: 1.3b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2.0)
0.4b	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) 2.0) (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0))))))
2.2b	(.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) 2.0) (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))
9.2b	(sqrt.f64 (+.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) 2.0) (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`
19×	`add-exp-log_binary64`
15×	`sqrt-prod_binary64`
13×	`unpow-prod-down_binary64`
11×	`associate-l_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-/r*_binary64` `pow1_binary64` `prod-exp_binary64`
5×	`associate-r_binary64`
4×	`add-log-exp_binary64` `pow-exp_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`pow-to-exp_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `div-inv_binary64`
1×	`pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

4 → 110

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 ky) 2.0)
10.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) 2.0) (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0))))))
15.0ms	(.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) 2.0) (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))
4.0ms	(sqrt.f64 (+.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) 2.0) (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))))

series553.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow.f64 (sin.f64 ky) 2.0)
222.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) 2.0) (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0))))))
127.0ms	(.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) 2.0) (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))
184.0ms	(sqrt.f64 (+.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) 2.0) (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5297	2653

prune196.0ms

Filtered

83 candidates to 122 candidates (-47.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	2	123

Merged error: 1.0b

Counts

123 → 2

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) (/.f64 2.0 2)) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)) (pow.f64 (/.f64 (.f64 2.0 l) Om) (*.f64 1/2 2.0)))))))
0.9b	(.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) (/.f64 2.0 2)) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)) (pow.f64 (/.f64 (.f64 2.0 l) Om) (*.f64 1/2 2.0))))
2.9b	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)) (pow.f64 (/.f64 (.f64 2.0 l) Om) (*.f64 1/2 2.0)))
9.2b	(sqrt.f64 (+.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) (/.f64 2.0 2)) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)) (pow.f64 (/.f64 (.f64 2.0 l) Om) (*.f64 1/2 2.0))))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-exp-log_binary64`
72×	`prod-exp_binary64`
36×	`pow-exp_binary64`
33×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
25×	`div-exp_binary64`
24×	`times-frac_binary64`
17×	`unpow-prod-down_binary64`
16×	`associate-l_binary64`
15×	`sqrt-prod_binary64`
13×	`add-cbrt-cube_binary64`
12×	`pow-to-exp_binary64` `associate-r_binary64`
6×	`associate-/r*_binary64`
5×	`pow1_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `flip-+_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
3×	`sqr-pow_binary64` `unswap-sqr_binary64` `associate-/l*_binary64` `div-inv_binary64`
2×	`distribute-lft-out_binary64` `associate-r/_binary64` `associate-/r/_binary64` `-commutative_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 145

Calls

4 calls:

8.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) (/.f64 2.0 2)) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)) (pow.f64 (/.f64 (.f64 2.0 l) Om) (*.f64 1/2 2.0)))))))
19.0ms	(.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) (/.f64 2.0 2)) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)) (pow.f64 (/.f64 (.f64 2.0 l) Om) (*.f64 1/2 2.0))))
16.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)) (pow.f64 (/.f64 (.f64 2.0 l) Om) (*.f64 1/2 2.0)))
5.0ms	(sqrt.f64 (+.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) (/.f64 2.0 2)) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)) (pow.f64 (/.f64 (.f64 2.0 l) Om) (*.f64 1/2 2.0))))))

series667.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(/.f64 1.0 (sqrt.f64 (+.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) (/.f64 2.0 2)) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)) (pow.f64 (/.f64 (.f64 2.0 l) Om) (*.f64 1/2 2.0)))))))
125.0ms	(.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) (/.f64 2.0 2)) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)) (pow.f64 (/.f64 (.f64 2.0 l) Om) (*.f64 1/2 2.0))))
132.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)) (pow.f64 (/.f64 (.f64 2.0 l) Om) (*.f64 1/2 2.0)))
182.0ms	(sqrt.f64 (+.f64 1.0 (.f64 (pow.f64 (/.f64 (.f64 2.0 l) Om) (/.f64 2.0 2)) (.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)) (pow.f64 (/.f64 (.f64 2.0 l) Om) (*.f64 1/2 2.0))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5414	3706

prune250.0ms

Filtered

95 candidates to 157 candidates (-65.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	157	2	159

Merged error: 1.0b

Counts

159 → 2

localize6.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify4.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	1	1
Total	2	2

Merged error: 1.0b

Counts

2 → 2

regimes697.0ms

Accuracy

0% (0.1b remaining)

Error of 0.8b against oracle of 0.7b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	41
1	36	41

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	6219×	body	80	valid
676.0ms	589×	body	1280	valid
537.0ms	626×	body	640	valid
233.0ms	376×	body	320	valid
83.0ms	190×	body	160	valid

Details

analyze620.0ms

sample103.0ms

simplify67.0ms

prune4.0ms

localize22.0ms

rewrite36.0ms

series553.0ms

simplify65.0ms

prune196.0ms

localize27.0ms

rewrite57.0ms

series667.0ms

simplify64.0ms

prune250.0ms

localize6.0ms

rewrite0.0ms

series0.0ms

simplify4.0ms

prune0.0ms

regimes697.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.9s

Profiling