Details

sample77.0ms

Algorithm

intervals

Results

24.0ms	195×	body	80	valid
14.0ms	18×	body	1280	valid
12.0ms	22×	body	640	valid
6.0ms	16×	body	320	valid
1.0ms	5×	body	160	valid

simplify42.0ms

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: 1.8b

Counts

2 → 1

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 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))))))
2.9b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
11.3b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite25.0ms

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 ky) 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)))
7.0ms	(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 ky) 2.0)
386.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
380.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
319.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify147.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	210	295
1	739	295
2	3863	295
3	5001	295

prune131.0ms

Filtered

31 candidates to 22 candidates (71.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	2	32

Merged error: 1.4b

Counts

32 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

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)))))))
0.8b	(* (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))))
3.6b	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
11.3b	(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

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

Counts

4 → 34

Calls

4 calls:

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)))))))
15.0ms	(* (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))))
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))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

390.0ms	(/ 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)))))))
385.0ms	(* (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))))
392.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
318.0ms	(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))))))

simplify197.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	237	610
1	836	599
2	4814	599
3	5001	599

prune189.0ms

Filtered

46 candidates to 30 candidates (65.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	46	2	48

Merged error: 1.4b

Counts

48 → 2

localize7.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Merged error: 1.4b

Counts

2 → 2

regimes242.0ms

Accuracy

0% (0.1b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

bsearch0.0ms

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

773.0ms	6239×	body	80	valid
434.0ms	542×	body	1280	valid
369.0ms	664×	body	640	valid
138.0ms	362×	body	320	valid
49.0ms	193×	body	160	valid