Details

analyze1.4s (12.3%)

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

sample212.0ms (1.8%)

Algorithm

1×

intervals

Results

137.0ms	126×	body	1280	valid
46.0ms	66×	body	640	valid
8.0ms	18×	body	320	valid
5.0ms	41×	body	80	valid
1.0ms	5×	body	160	valid

simplify60.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4766	16
1	4766	16

prune20.0ms (0.2%)

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: 3.8b

Counts

2 → 2

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
16×	`unpow-prod-down`
10×	`distribute-lft-out`
8×	`add-exp-log` `associate-/r*`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

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

series111.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
25.0ms	(pow (sin kx) 2.0)
21.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
20.0ms	(pow (sin ky) 2.0)

simplify62.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4941	1503
1	4941	1503

prune356.0ms (3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	101	11	112
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	102	12	114

Merged error: 3.1b

Counts

114 → 12

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
16×	`unpow-prod-down`
10×	`distribute-lft-out`
8×	`add-exp-log` `associate-/r*`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

15.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)

series102.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
20.0ms	(pow (sin kx) 2.0)
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
20.0ms	(pow (sin ky) 2.0)

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4962	1511
1	4962	1511

prune354.0ms (3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	107	5	112
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	111	13	124

Merged error: 3.0b

Counts

124 → 13

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

180×	`times-frac`
150×	`*-un-lft-identity`
99×	`add-sqr-sqrt`
98×	`add-cube-cbrt`
65×	`sqrt-prod`
32×	`unpow-prod-down`
28×	`associate-/r*`
26×	`distribute-lft-out`
17×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
7×	`div-exp`
6×	`pow-unpow`
5×	`div-inv`
4×	`add-log-exp`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow-to-exp` `rec-exp` `pow-pow` `sqrt-div` `1-exp` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `clear-num` `associate-/r/` `flip-+` `inv-pow`

Counts

4 → 187

Calls

4 calls:

17.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
10.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)

series101.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
23.0ms	(pow (sin ky) 2.0)
21.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
20.0ms	(pow (sin kx) 2.0)

simplify64.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5053	3593

prune629.0ms (5.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	198	1	199
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	199	13	212

Merged error: 3.0b

Counts

212 → 13

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
30×	`associate-r`
28×	`times-frac`
25×	`add-cube-cbrt`
22×	`sqrt-prod`
15×	`add-exp-log`
14×	`unpow-prod-down`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
5×	`unswap-sqr`
4×	`sqrt-div` `prod-exp` `add-log-exp`
3×	`associate-l`
2×	`pow-to-exp` `pow-pow` `flip3-+` `div-exp` `pow-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 106

Calls

4 calls:

21.0ms	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)

series103.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
21.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
20.0ms	(pow (sin kx) 2.0)
20.0ms	(pow (sin ky) 2.0)

simplify61.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4932	1336
1	4932	1336

prune306.0ms (2.6%)

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: 3.0b

Counts

131 → 13

regimes952.0ms (8.1%)

Accuracy

Total 1.3b remaining (36%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	18
1	18	18

end0.0ms (0%)

sample6.5s (55.6%)

Algorithm

1×

intervals

Results

4.3s	3843×	body	1280	valid
1.4s	2005×	body	640	valid
316.0ms	686×	body	320	valid
161.0ms	1164×	body	80	valid
93.0ms	302×	body	160	valid

Details

analyze1.4s (12.3%)

sample212.0ms (1.8%)

simplify60.0ms (0.5%)

prune20.0ms (0.2%)

localize17.0ms (0.1%)

rewrite30.0ms (0.3%)

series111.0ms (0.9%)

simplify62.0ms (0.5%)

prune356.0ms (3%)

localize16.0ms (0.1%)

rewrite32.0ms (0.3%)

series102.0ms (0.9%)

simplify65.0ms (0.6%)

prune354.0ms (3%)

localize18.0ms (0.2%)

rewrite43.0ms (0.4%)

series101.0ms (0.9%)

simplify64.0ms (0.5%)

prune629.0ms (5.3%)

localize20.0ms (0.2%)

rewrite39.0ms (0.3%)

series103.0ms (0.9%)

simplify61.0ms (0.5%)

prune306.0ms (2.6%)

regimes952.0ms (8.1%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample6.5s (55.6%)

Profiling