Details

sample73.0ms

Algorithm

intervals

Results

24.0ms	202×	body	80	valid
14.0ms	18×	body	1280	valid
11.0ms	20×	body	640	valid
4.0ms	11×	body	320	valid
1.0ms	5×	body	160	valid

simplify40.0ms

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 (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: 0.3b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.3b	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
1.1b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.4b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

4×	`sqrt-div`
3×	`flip3-+` `flip-+`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-l*` `associate-/r/` `div-inv` `sqr-pow`
1×	`pow-to-exp` `unpow-prod-down` `frac-2neg` `pow1/2` `clear-num` `*-commutative`

Counts

4 → 19

Calls

4 calls:

2.0ms	(pow (sin kx) 2.0)
7.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
8.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

103.0ms	(pow (sin kx) 2.0)
380.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
373.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
313.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify128.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	210	295
1	739	295
2	3848	295
3	5002	295

prune127.0ms

Filtered

31 candidates to 22 candidates (71.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	30	1	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	1	32

Merged error: 0.2b

Counts

32 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.3b	(/ 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)))))))
1.9b	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.4b	(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))))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

4×	`sqrt-div`
3×	`flip3-+` `flip-+`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-r/` `associate-l*` `associate-/r/` `div-inv` `sqr-pow`
1×	`pow-to-exp` `unpow-prod-down` `frac-2neg` `pow1/2` `clear-num` `*-commutative`

Counts

4 → 19

Calls

4 calls:

2.0ms	(pow (sin kx) 2.0)
10.0ms	(/ 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)))))))
8.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.0ms	(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))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

103.0ms	(pow (sin kx) 2.0)
377.0ms	(/ 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)))))))
393.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
311.0ms	(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))))))

simplify155.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	216	385
1	769	385
2	4285	385
3	5001	385

prune136.0ms

Filtered

31 candidates to 22 candidates (71.0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	31	1	32

Merged error: 0.2b

Counts

32 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	22
1	32	22

end0.0ms

sample2.0s

Algorithm

intervals

Results

755.0ms	6285×	body	80	valid
450.0ms	560×	body	1280	valid
337.0ms	601×	body	640	valid
142.0ms	361×	body	320	valid
50.0ms	193×	body	160	valid