Details

analyze623.0ms

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

sample141.0ms

Algorithm

intervals

Results

35.0ms	200×	body	80	valid
21.0ms	18×	body	1280	valid
18.0ms	20×	body	640	valid
8.0ms	13×	body	320	valid
2.0ms	5×	body	160	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4882	29
1	4882	29

prune12.0ms

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: 1.8b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 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))))))
2.9b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.1b	(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 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))))))
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)))))

series549.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin ky) 2.0)
161.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
241.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
128.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4958	2674
1	4958	2674

prune340.0ms

Filtered

88 candidates to 122 candidates (-38.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	120	3	123

Merged error: 1.1b

Counts

123 → 3

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1.0 (sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.9b	(* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.8b	(log (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
10.1b	(sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`add-cube-cbrt` `times-frac`
25×	`log-pow`
24×	`exp-prod` `sqrt-prod`
18×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`prod-exp`
6×	`pow1` `sqrt-div` `associate-/r*`
5×	`associate-r` `associate-l`
4×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
3×	`unpow-prod-down` `log-prod` `pow-exp` `associate-/l*`
2×	`associate-*r/` `div-exp` `div-inv` `distribute-lft-out` `unswap-sqr` `sqr-pow`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `rem-log-exp` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 122

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
12.0ms	(* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms	(log (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
3.0ms	(sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series571.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
104.0ms	(* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
165.0ms	(log (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
135.0ms	(sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5006	3454

prune457.0ms

Filtered

98 candidates to 134 candidates (-36.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	134	3	137

Merged error: 1.1b

Counts

137 → 3

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* (/ 2.0 Om) l) 2.0)
0.3b	(pow (sin ky) 2.0)
2.9b	(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.5b	(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

rewrite27.0ms

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 ky) 2.0)
11.0ms	(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0ms	(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

series153.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(pow (* (/ 2.0 Om) l) 2.0)
18.0ms	(pow (sin ky) 2.0)
57.0ms	(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
64.0ms	(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))

simplify44.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4953	1342
1	4953	1342

prune232.0ms

Filtered

61 candidates to 91 candidates (-49.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	91	3	94

Merged error: 1.1b

Counts

94 → 3

regimes1.3s

Accuracy

0% (0.3b remaining)

Error of 0.9b against oracle of 0.6b and baseline of 0.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	29
1	28	29

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.1s	6229×	body	80	valid
619.0ms	526×	body	1280	valid
531.0ms	632×	body	640	valid
247.0ms	412×	body	320	valid
80.0ms	201×	body	160	valid

Details

analyze623.0ms

sample141.0ms

simplify57.0ms

prune12.0ms

localize29.0ms

rewrite29.0ms

series549.0ms

simplify62.0ms

prune340.0ms

localize33.0ms

rewrite35.0ms

series571.0ms

simplify55.0ms

prune457.0ms

localize31.0ms

rewrite27.0ms

series153.0ms

simplify44.0ms

prune232.0ms

regimes1.3s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.9s

Profiling