Details

sample98.0ms

Algorithm

intervals

Results

35.0ms	205×	body	80	valid
13.0ms	16×	body	640	valid
12.0ms	11×	body	1280	valid
9.0ms	11×	body	160	valid
7.0ms	13×	body	320	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	16
1	123	16
2	294	16
3	1083	16
4	5001	16

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 0.8b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.4b	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
1.5b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.8b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`times-frac`
19×	`add-exp-log`
15×	`sqrt-prod`
13×	`unpow-prod-down`
11×	`associate-l`
8×	`add-cbrt-cube`
6×	`pow1` `prod-exp` `associate-/r*`
5×	`associate-r`
4×	`sqrt-div` `pow-exp` `add-log-exp`
3×	`pow-unpow` `flip3-+` `div-exp` `flip-+` `associate-/l*` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `associate-*r/` `associate-/r/` `div-inv` `distribute-lft-out`
1×	`cbrt-undiv` `distribute-rgt-in` `rem-sqrt-square` `pow-pow` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 110

Calls

4 calls:

3.0ms	(pow (sin kx) 2.0)
5.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
13.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series437.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin kx) 2.0)
170.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
113.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
136.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify71.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	593	1649
1	2411	1544
2	5001	1541

prune335.0ms

Filtered

122 candidates to 84 candidates (31.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	3	123

Merged error: 0.6b

Counts

123 → 3

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.4b	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
2.2b	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.8b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-exp-log`
72×	`prod-exp`
36×	`pow-exp`
33×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`div-exp`
24×	`times-frac`
22×	`associate-l`
17×	`unpow-prod-down`
15×	`sqrt-prod`
13×	`add-cbrt-cube`
12×	`pow-to-exp`
6×	`associate-r/` `associate-r` `associate-/r`
5×	`pow1` `distribute-rgt-in` `distribute-lft-in`
4×	`flip3-+` `sqrt-div` `cbrt-unprod` `flip-+` `add-log-exp`
3×	`div-inv` `associate-/l*` `unswap-sqr` `sqr-pow`
2×	`associate-/r/` `*-commutative` `distribute-lft-out`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 151

Calls

4 calls:

17.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
5.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
14.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

series524.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
168.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
110.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
134.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

simplify105.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	750	3124
1	3004	2790
2	5001	2787

prune494.0ms

Filtered

163 candidates to 96 candidates (41.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	163	3	166

Merged error: 0.6b

Counts

166 → 3

localize34.0ms

Local error

Found 4 expressions with local error:

7.8b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.6b	(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
8.6b	(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
8.6b	(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
12×	`add-sqr-sqrt` `sqrt-prod`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-div`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 63

Calls

4 calls:

2.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms	(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
3.0ms	(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
3.0ms	(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

series518.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
129.0ms	(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
128.0ms	(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
129.0ms	(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

simplify83.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	128	1365
1	403	1280
2	2167	1274
3	5002	1274

prune465.0ms

Filtered

75 candidates to 59 candidates (21.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	75	3	78

Merged error: 0.6b

Counts

78 → 3

localize7.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
Total	3	3

Merged error: 0.6b

Counts

3 → 3

regimes1.2s

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	32	22
1	32	22

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.2s	6242×	body	80	valid
560.0ms	503×	body	1280	valid
529.0ms	654×	body	640	valid
245.0ms	399×	body	320	valid
76.0ms	202×	body	160	valid

Details

sample98.0ms

simplify41.0ms

prune5.0ms

localize27.0ms

rewrite27.0ms

series437.0ms

simplify71.0ms

prune335.0ms

localize28.0ms

rewrite44.0ms

series524.0ms

simplify105.0ms

prune494.0ms

localize34.0ms

rewrite13.0ms

series518.0ms

simplify83.0ms

prune465.0ms

localize7.0ms

rewrite0.0ms

series0.0ms

simplify2.0ms

prune0.0ms

regimes1.2s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.0s

Profiling