Details

sample96.0ms

Algorithm

intervals

Results

36.0ms	208×	body	80	valid
22.0ms	21×	body	1280	valid
15.0ms	19×	body	640	valid
3.0ms	5×	body	320	valid
1.0ms	3×	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: 1.0b

Counts

2 → 1

localize29.0ms

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))))))
2.2b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
9.2b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite30.0ms

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 ky) 2.0)
6.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
15.0ms	(* (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)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

103.0ms	(pow (sin ky) 2.0)
378.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
378.0ms	(* (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)))))

simplify75.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	505	1608
1	2047	1504
2	5003	1501

prune431.0ms

Filtered

122 candidates to 83 candidates (68.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	2	123

Merged error: 0.8b

Counts

123 → 2

localize32.0ms

Local error

Found 4 expressions with local error:

9.2b	(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))))))
15.5b	(cbrt (/ (* 2.0 l) Om))
15.5b	(cbrt (/ (* 2.0 l) Om))
15.5b	(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))

series727.0ms

Counts

4 → 12

Calls

4 calls:

456.0ms	(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))))))
89.0ms	(cbrt (/ (* 2.0 l) Om))
90.0ms	(cbrt (/ (* 2.0 l) Om))
92.0ms	(cbrt (/ (* 2.0 l) Om))

simplify149.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (140.0ms)

Iter	Nodes	Cost
0	193	799
1	579	752
2	3641	744
3	5001	741

prune377.0ms

Filtered

75 candidates to 60 candidates (80.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	75	2	77

Merged error: 0.8b

Counts

77 → 2

localize6.0ms

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

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: 0.8b

Counts

2 → 2

regimes241.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.6b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	26
1	33	26

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	6236×	body	80	valid
572.0ms	520×	body	1280	valid
515.0ms	635×	body	640	valid
221.0ms	388×	body	320	valid
83.0ms	221×	body	160	valid

Details

sample96.0ms

simplify42.0ms

prune5.0ms

localize29.0ms

rewrite30.0ms

series1.2s

simplify75.0ms

prune431.0ms

localize32.0ms

rewrite13.0ms

series727.0ms

simplify149.0ms

prune377.0ms

localize6.0ms

rewrite0.0ms

series0.0ms

simplify2.0ms

prune0.0ms

regimes241.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.7s

Profiling