Details

analyze613.0ms

Algorithm: search

sample100.0ms

Algorithm

intervals

Results

35.0ms	196×	body	80	valid
21.0ms	17×	body	1280	valid
17.0ms	20×	body	640	valid
8.0ms	13×	body	320	valid
4.0ms	10×	body	160	valid

simplify39.0ms

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

prune6.0ms

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: 1.3b

Counts

2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.6b	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
3.0b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.9b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite28.0ms

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))))))
14.0ms	(* (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)))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin kx) 2.0)
172.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
112.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
138.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	593	1648
1	2412	1544
2	5001	1541

prune362.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

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: 0.8b

Counts

123 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.9b	(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
21×	`sqrt-prod`
16×	`add-exp-log`
15×	`unpow-prod-down`
12×	`add-cube-cbrt`
11×	`associate-l`
8×	`sqrt-div` `associate-r`
7×	`pow1`
6×	`prod-exp` `add-cbrt-cube` `distribute-lft-out` `unswap-sqr`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `times-frac` `pow1/2` `pow-exp` `sqr-pow`
2×	`associate-*r/` `div-exp`
1×	`pow-to-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

16.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0ms	(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
136.0ms	(sqrt (+ 1.0 (* (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	460	1540
1	1400	1467
2	5002	1465

prune424.0ms

Filtered

69 candidates to 102 candidates (-47.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	102	3	105

Merged error: 0.8b

Counts

105 → 3

localize34.0ms

Local error

Found 4 expressions with local error:

9.9b	(sqrt (+ 1.0 (* (pow (* (cbrt (/ (* 2.0 l) Om)) (cbrt (/ (* 2.0 l) Om))) 2.0) (* (pow (cbrt (/ (* 2.0 l) Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
13.7b	(cbrt (/ (* 2.0 l) Om))
13.7b	(cbrt (/ (* 2.0 l) Om))
13.7b	(cbrt (/ (* 2.0 l) Om))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-div` `pow1/3` `sqrt-prod` `div-inv`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 63

Calls

4 calls:

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

series198.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(sqrt (+ 1.0 (* (pow (* (cbrt (/ (* 2.0 l) Om)) (cbrt (/ (* 2.0 l) Om))) 2.0) (* (pow (cbrt (/ (* 2.0 l) Om)) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
17.0ms	(cbrt (/ (* 2.0 l) Om))
17.0ms	(cbrt (/ (* 2.0 l) Om))
17.0ms	(cbrt (/ (* 2.0 l) Om))

simplify151.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (142.0ms)

Iter	Nodes	Cost
0	204	816
1	630	769
2	3860	762
3	5002	759

prune294.0ms

Filtered

60 candidates to 75 candidates (-25.0%)

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: 0.8b

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: 0.8b

Counts

3 → 3

regimes673.0ms

Accuracy

0% (0.1b remaining)

Error of 0.9b against oracle of 0.8b and baseline of 0.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	30
1	32	30

end0.0ms

analyze594.0ms

Algorithm: search

sample3.0s

Algorithm

intervals

Results

1.1s	6251×	body	80	valid
659.0ms	566×	body	1280	valid
618.0ms	566×	body	640	valid
243.0ms	416×	body	320	valid
77.0ms	201×	body	160	valid

Details

analyze613.0ms

sample100.0ms

simplify39.0ms

prune6.0ms

localize28.0ms

rewrite28.0ms

series441.0ms

simplify72.0ms

prune362.0ms

localize27.0ms

rewrite35.0ms

series314.0ms

simplify54.0ms

prune424.0ms

localize34.0ms

rewrite13.0ms

series198.0ms

simplify151.0ms

prune294.0ms

localize7.0ms

rewrite0.0ms

series0.0ms

simplify2.0ms

prune0.0ms

regimes673.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze594.0ms

sample3.0s

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