Details

analyze1.2s (11.1%)

Algorithm

1×

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

sample202.0ms (1.8%)

Algorithm

1×

intervals

Results

123.0ms	115×	body	1280	valid
50.0ms	75×	body	640	valid
9.0ms	19×	body	320	valid
4.0ms	37×	body	80	valid
3.0ms	10×	body	160	valid

simplify73.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4766	16
1	4766	16

prune6.0ms (0.1%)

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

localize14.0ms (0.1%)

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)))

rewrite32.0ms (0.3%)

Algorithm

1×	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:

15.0ms	(/.f64 (sin.f64 ky) (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)))
3.0ms	(pow.f64 (sin.f64 ky) 2.0)
3.0ms	(pow.f64 (sin.f64 kx) 2.0)

series109.0ms (1%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0))))
25.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))
19.0ms	(pow.f64 (sin.f64 ky) 2.0)
18.0ms	(pow.f64 (sin.f64 kx) 2.0)

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4925	1503
1	4925	1503

prune209.0ms (1.9%)

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

localize16.0ms (0.1%)

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)))

rewrite40.0ms (0.4%)

Algorithm

1×	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)))
10.0ms	(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)

series105.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0))) (sin.f64 ky)))
24.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2.0) (pow.f64 (sin.f64 ky) 2.0)))
21.0ms	(pow.f64 (sin.f64 kx) 2.0)
18.0ms	(pow.f64 (sin.f64 ky) 2.0)

simplify88.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4932	3585
1	4932	3585

prune320.0ms (2.8%)

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

localize18.0ms (0.2%)

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)))

rewrite85.0ms (0.8%)

Algorithm

1×	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:

25.0ms	(/.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)))
8.0ms	(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)

series107.0ms (1%)

Counts

4 → 12

Calls

4 calls:

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)))
23.0ms	(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)
18.0ms	(pow.f64 (sin.f64 kx) 2.0)

simplify153.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

528 → 528

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4952	13838
1	4952	13838

prune1.2s (10.5%)

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

localize17.0ms (0.2%)

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 (0.4%)

Algorithm

1×	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:

18.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))
11.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))
10.0ms	(/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
3.0ms	(pow.f64 (sin.f64 ky) 2)

series112.0ms (1%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))
39.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))
24.0ms	(/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
4.0ms	(pow.f64 (sin.f64 ky) 2)

simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4925	1985
1	4925	1985

prune208.0ms (1.8%)

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

regimes645.0ms (5.7%)

Accuracy

Total 2.0b remaining (41.4%)

Threshold costs 0b (0%)

bsearch2.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	39
1	67	39

end0.0ms (0%)

sample6.1s (54.1%)

Algorithm

1×

intervals

Results

4.0s	3713×	body	1280	valid
1.3s	1985×	body	640	valid
340.0ms	750×	body	320	valid
159.0ms	1276×	body	80	valid
80.0ms	276×	body	160	valid

Details

analyze1.2s (11.1%)

sample202.0ms (1.8%)

simplify73.0ms (0.6%)

prune6.0ms (0.1%)

localize14.0ms (0.1%)

rewrite32.0ms (0.3%)

series109.0ms (1%)

simplify66.0ms (0.6%)

prune209.0ms (1.9%)

localize16.0ms (0.1%)

rewrite40.0ms (0.4%)

series105.0ms (0.9%)

simplify88.0ms (0.8%)

prune320.0ms (2.8%)

localize18.0ms (0.2%)

rewrite85.0ms (0.8%)

series107.0ms (1%)

simplify153.0ms (1.4%)

prune1.2s (10.5%)

localize17.0ms (0.2%)

rewrite48.0ms (0.4%)

series112.0ms (1%)

simplify53.0ms (0.5%)

prune208.0ms (1.8%)

regimes645.0ms (5.7%)

bsearch2.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.1s (54.1%)

Profiling