Details

analyze592.0ms

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

sample95.0ms

Algorithm

intervals

Results

33.0ms	195×	body	80	valid
23.0ms	28×	body	640	valid
18.0ms	16×	body	1280	valid
7.0ms	12×	body	320	valid
2.0ms	5×	body	160	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4882	29
1	4882	29

prune14.0ms

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

localize23.0ms

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))))))
2.9b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
10.7b	(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)
162.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
106.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
130.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4952	2674
1	4952	2674

prune333.0ms

Filtered

88 candidates to 122 candidates (-38.6%)

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

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 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)))
2.9b	(log (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
10.7b	(sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite34.0ms

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)))))

series575.0ms

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))))))
106.0ms	(* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
166.0ms	(log (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
137.0ms	(sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5006	3454

prune448.0ms

Filtered

98 candidates to 134 candidates (-36.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	133	3	136

Merged error: 0.8b

Counts

136 → 3

localize32.0ms

Local error

Found 4 expressions with local error:

3.1b	(log (sqrt (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
3.1b	(log (sqrt (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
10.7b	(sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
10.7b	(sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

54×	`log-pow`
52×	`sqrt-pow1`
48×	`exp-prod`
38×	`add-sqr-sqrt`
36×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
30×	`sqrt-prod`
12×	`log-prod`
10×	`pow1`
8×	`sqrt-div`
6×	`add-exp-log`
4×	`flip3-+` `pow1/2` `associate-/r/` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp` `div-inv`

Counts

4 → 112

Calls

4 calls:

9.0ms	(log (sqrt (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
9.0ms	(log (sqrt (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)))))
4.0ms	(sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series728.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(log (sqrt (exp (/ 1.0 (sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
229.0ms	(log (sqrt (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)))))
135.0ms	(sqrt (+ 1.0 (* (pow (* (/ 2.0 Om) l) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4955	3220
1	4955	3220

prune710.0ms

Filtered

94 candidates to 124 candidates (-31.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	124	3	127

Merged error: 0.8b

Counts

127 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
2.1b	(log (pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.4b	(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

3.0ms	(pow (sin ky) 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))))
12.0ms	(pow (exp (pow (* (/ 2.0 Om) l) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify41.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5153	1311

prune224.0ms

Filtered

62 candidates to 90 candidates (-45.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	90	3	93

Merged error: 0.8b

Counts

93 → 3

regimes569.0ms

Accuracy

0% (0.4b remaining)

Error of 1.0b against oracle of 0.7b and baseline of 1.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	31
1	30	31

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.2s	6212×	body	80	valid
571.0ms	497×	body	1280	valid
523.0ms	659×	body	640	valid
249.0ms	427×	body	320	valid
76.0ms	205×	body	160	valid

Details

analyze592.0ms

sample95.0ms

simplify57.0ms

prune14.0ms

localize23.0ms

rewrite29.0ms

series416.0ms

simplify65.0ms

prune333.0ms

localize30.0ms

rewrite34.0ms

series575.0ms

simplify56.0ms

prune448.0ms

localize32.0ms

rewrite30.0ms

series728.0ms

simplify64.0ms

prune710.0ms

localize27.0ms

rewrite24.0ms

series156.0ms

simplify41.0ms

prune224.0ms

regimes569.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.9s

Profiling