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

sample200.0ms

Algorithm

intervals

Results

135.0ms	126×	body	1280	valid
37.0ms	58×	body	640	valid
8.0ms	20×	body	320	valid
5.0ms	42×	body	80	valid
3.0ms	10×	body	160	valid

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4766	16
1	4766	16

prune18.0ms

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: 3.2b

Counts

2 → 2

localize15.0ms

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)
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite33.0ms

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)
2.0ms	(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)))

simplify78.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5228	1477

prune278.0ms

Filtered

77 candidates to 113 candidates (-46.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	102	11	113
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	103	12	115

Merged error: 2.3b

Counts

115 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2.0)
0.2b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
50×	`times-frac`
49×	`add-sqr-sqrt`
41×	`sqrt-prod`
40×	`add-cube-cbrt`
30×	`associate-r`
19×	`unpow-prod-down`
16×	`distribute-lft-out`
12×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `associate-/r*`
6×	`sqrt-div`
4×	`associate-/r/` `add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-l` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

3.0ms	(pow (sin kx) 2.0)
11.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
18.0ms	(* (sin ky) (/ (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)))

series124.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin kx) 2.0)
40.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
47.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5058	2219

prune277.0ms

Filtered

85 candidates to 145 candidates (-70.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	145	12	157

Merged error: 2.3b

Counts

157 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))
0.3b	(* (sin ky) (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))))
0.3b	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

370×	`times-frac`
293×	`*-un-lft-identity`
208×	`add-sqr-sqrt`
186×	`add-cube-cbrt`
132×	`sqrt-prod`
89×	`associate-r`
52×	`unpow-prod-down` `distribute-lft-out`
36×	`add-exp-log`
31×	`associate-/r*`
20×	`add-cbrt-cube`
15×	`div-exp`
11×	`associate-/l*`
10×	`div-inv`
8×	`pow1`
7×	`cbrt-undiv` `prod-exp` `unswap-sqr`
4×	`rec-exp` `sqrt-div` `1-exp` `add-log-exp`
3×	`associate-l` `cbrt-unprod`
2×	`frac-2neg` `flip3-+` `clear-num` `associate-/r/` `flip-+` `associate-/l/`
1×	`rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 322

Calls

4 calls:

11.0ms	(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))
32.0ms	(* (sin ky) (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))))
14.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series144.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))
48.0ms	(* (sin ky) (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))))
41.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify95.0ms

Algorithm

egg-herbie

Counts

334 → 334

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4957	6414
1	4957	6414

prune562.0ms

Filtered

164 candidates to 334 candidates (-103.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	334	0	334
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	334	12	346

Merged error: 2.3b

Counts

346 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
30×	`cbrt-prod` `sqrt-prod`
25×	`add-sqr-sqrt`
24×	`times-frac`
22×	`add-cube-cbrt`
12×	`unpow-prod-down` `distribute-lft-out`
8×	`sqrt-div`
7×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 90

Calls

4 calls:

13.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series112.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
21.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify65.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5542	1796

prune347.0ms

Filtered

68 candidates to 102 candidates (-50.0%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	102	12	114

Merged error: 2.3b

Counts

114 → 12

regimes854.0ms

Accuracy

0% (1.4b remaining)

Error of 4.0b against oracle of 2.6b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	16
1	15	16

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.9s	3667×	body	1280	valid
1.3s	2007×	body	640	valid
354.0ms	750×	body	320	valid
163.0ms	1260×	body	80	valid
95.0ms	316×	body	160	valid

Details

analyze1.4s

sample200.0ms

simplify58.0ms

prune18.0ms

localize15.0ms

rewrite33.0ms

series105.0ms

simplify78.0ms

prune278.0ms

localize17.0ms

rewrite45.0ms

series124.0ms

simplify84.0ms

prune277.0ms

localize19.0ms

rewrite89.0ms

series144.0ms

simplify95.0ms

prune562.0ms

localize22.0ms

rewrite40.0ms

series112.0ms

simplify65.0ms

prune347.0ms

regimes854.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.0s

Profiling