Details

analyze1.4s

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

sample201.0ms

Algorithm

intervals

Results

127.0ms	122×	body	1280	valid
44.0ms	62×	body	640	valid
10.0ms	22×	body	320	valid
5.0ms	42×	body	80	valid
2.0ms	8×	body	160	valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4766	16
1	4766	16

prune17.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 4.7b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.2b	(pow (sin ky) 2.0)
0.2b	(pow (sin kx) 2.0)
4.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

17.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
2.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series105.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
18.0ms	(pow (sin ky) 2.0)
23.0ms	(pow (sin kx) 2.0)
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4942	1477
1	4942	1477

prune243.0ms

Filtered

77 candidates to 113 candidates (-46.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	105	8	113
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	105	10	115

Merged error: 2.7b

Counts

115 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2.0)
0.2b	(pow (sin kx) 2.0)
0.2b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
4.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite26.0ms

Algorithm

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:

2.0ms	(pow (sin ky) 2.0)
2.0ms	(pow (sin kx) 2.0)
11.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series97.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin ky) 2.0)
18.0ms	(pow (sin kx) 2.0)
40.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5287	1503

prune201.0ms

Filtered

70 candidates to 112 candidates (-60.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	112	10	122

Merged error: 2.7b

Counts

122 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
1.5b	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (sin th) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
4.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

101×	`sqrt-prod`
87×	`*-un-lft-identity`
66×	`times-frac`
53×	`add-sqr-sqrt`
51×	`add-cube-cbrt`
45×	`add-exp-log`
39×	`associate-l`
27×	`add-cbrt-cube`
20×	`prod-exp`
18×	`unpow-prod-down` `distribute-lft-out`
12×	`sqrt-div`
11×	`pow1` `div-exp` `associate-/r*`
10×	`cbrt-unprod`
6×	`cbrt-undiv`
4×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-r/` `pow-prod-down` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv`
1×	`frac-times` `frac-2neg` `associate-r` `associate-l/` `clear-num` `-commutative`

Counts

4 → 166

Calls

4 calls:

13.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
32.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (sin th) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series131.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
46.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (sin th) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
22.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5404	3426

prune424.0ms

Filtered

104 candidates to 178 candidates (-71.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	177	11	188

Merged error: 2.7b

Counts

188 → 11

localize26.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (/ 1 (sqrt (* (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))) (* (sin th) (/ (sin ky) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
4.9b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.9b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.9b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-exp-log`
27×	`*-un-lft-identity`
25×	`add-cbrt-cube`
24×	`associate-l`
20×	`prod-exp`
18×	`cbrt-div`
15×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
10×	`div-exp` `cbrt-unprod`
9×	`pow1` `flip3-+` `flip-+`
8×	`sqrt-div` `associate-/r/`
6×	`unpow-prod-down` `distribute-lft-out`
5×	`cbrt-undiv` `frac-times` `associate-*r/`
4×	`add-log-exp`
3×	`rec-exp` `pow1/3` `1-exp` `pow-prod-down` `associate-*l/` `sqrt-prod`
1×	`associate-r` `*-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

40.0ms	(* (/ 1 (sqrt (* (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))) (* (sin th) (/ (sin ky) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
7.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series134.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (/ 1 (sqrt (* (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))) (* (sin th) (/ (sin ky) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
27.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
27.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
31.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify61.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5365	2529

prune355.0ms

Filtered

76 candidates to 113 candidates (-48.7%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	112	12	124

Merged error: 2.7b

Counts

124 → 12

regimes1.1s

Accuracy

76.5% (0.3b remaining)

Error of 2.9b against oracle of 2.5b and baseline of 4.0b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	53
1	36	53

end0.0ms

analyze1.2s

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

sample6.1s

Algorithm

intervals

Results

4.0s	3681×	body	1280	valid
1.4s	2082×	body	640	valid
311.0ms	683×	body	320	valid
166.0ms	1274×	body	80	valid
82.0ms	280×	body	160	valid

Details

analyze1.4s

sample201.0ms

simplify59.0ms

prune17.0ms

localize16.0ms

rewrite32.0ms

series105.0ms

simplify85.0ms

prune243.0ms

localize15.0ms

rewrite26.0ms

series97.0ms

simplify58.0ms

prune201.0ms

localize19.0ms

rewrite70.0ms

series131.0ms

simplify70.0ms

prune424.0ms

localize26.0ms

rewrite65.0ms

series134.0ms

simplify61.0ms

prune355.0ms

regimes1.1s

bsearch2.0ms

simplify1.0ms

end0.0ms

analyze1.2s

sample6.1s

Profiling