Details

analyze609.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
49.9%	49.9%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
74.9%	25%	0.2%	7
74.9%	25%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
87.3%	12.5%	0.2%	11
87.3%	12.5%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

sample99.0ms

Algorithm

intervals

Results

34.0ms	199×	body	80	valid
24.0ms	18×	body	1280	valid
21.0ms	26×	body	640	valid
3.0ms	6×	body	320	valid
3.0ms	7×	body	160	valid

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4882	29
1	4882	29

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 1.3b

Counts

2 → 1

localize27.0ms

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))))))
1.9b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.5b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite29.0ms

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)
6.0ms	(/ 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)))))

series416.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin kx) 2.0)
164.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
105.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
129.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4952	2674
1	4952	2674

prune329.0ms

Filtered

88 candidates to 122 candidates (-38.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Merged error: 0.8b

Counts

123 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* (/ 2.0 Om) l) 2.0)
0.3b	(pow (sin kx) 2.0)
0.9b	(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.9b	(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
13×	`unpow-prod-down`
12×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt`
11×	`pow-unpow`
9×	`pow1` `pow-pow`
8×	`log-prod`
6×	`pow-exp`
5×	`exp-prod` `sqr-pow`
4×	`pow-to-exp` `add-cbrt-cube` `add-log-exp`
3×	`rem-log-exp`
2×	`unpow-prod-up` `prod-exp` `distribute-lft-out`
1×	`div-exp` `pow-prod-down` `log-pow`

Counts

4 → 79

Calls

4 calls:

6.0ms	(pow (* (/ 2.0 Om) l) 2.0)
3.0ms	(pow (sin kx) 2.0)
5.0ms	(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
14.0ms	(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series150.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(pow (* (/ 2.0 Om) l) 2.0)
17.0ms	(pow (sin kx) 2.0)
63.0ms	(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
56.0ms	(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4951	1342
1	4951	1342

prune222.0ms

Filtered

61 candidates to 91 candidates (-49.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	91	2	93

Merged error: 0.8b

Counts

93 → 2

regimes1.2s

Accuracy

0% (0.4b remaining)

Error of 1.0b against oracle of 0.6b and baseline of 1.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	29
1	28	29

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.3s	6245×	body	80	valid
604.0ms	518×	body	1280	valid
529.0ms	635×	body	640	valid
237.0ms	394×	body	320	valid
83.0ms	208×	body	160	valid

Details

analyze609.0ms

sample99.0ms

simplify58.0ms

prune11.0ms

localize27.0ms

rewrite29.0ms

series416.0ms

simplify64.0ms

prune329.0ms

localize26.0ms

rewrite29.0ms

series150.0ms

simplify43.0ms

prune222.0ms

regimes1.2s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.0s

Profiling