Details

analyze640.0ms

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

39.0ms	197×	body	80	valid
25.0ms	30×	body	640	valid
9.0ms	8×	body	1280	valid
9.0ms	14×	body	320	valid
3.0ms	7×	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

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: 1.0b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (/ (* 2.0 l) Om) 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))))))
3.2b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.6b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
27×	`add-cube-cbrt`
24×	`add-exp-log` `times-frac`
17×	`unpow-prod-down`
15×	`sqrt-prod`
11×	`associate-l`
8×	`add-cbrt-cube`
7×	`prod-exp`
6×	`pow1` `pow-exp` `associate-/r*`
5×	`div-exp` `associate-r`
4×	`sqrt-div` `add-log-exp`
3×	`pow-unpow` `flip3-+` `flip-+` `div-inv` `associate-/l*` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `associate-*r/` `associate-/r/` `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 → 116

Calls

4 calls:

7.0ms	(pow (/ (* 2.0 l) Om) 2.0)
5.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
13.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.0ms	(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:

14.0ms	(pow (/ (* 2.0 l) Om) 2.0)
163.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
108.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
131.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5026	2803

prune370.0ms

Filtered

93 candidates to 128 candidates (-37.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	127	2	129

Merged error: 0.4b

Counts

129 → 2

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (cbrt (pow (sqrt (+ 1.0 (* (pow (* (/ l Om) 2.0) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3)))
3.2b	(* (pow (* (/ l Om) 2.0) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.6b	(sqrt (+ 1.0 (* (pow (* (/ l Om) 2.0) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
10.2b	(cbrt (pow (sqrt (+ 1.0 (* (pow (* (/ l Om) 2.0) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

90×	`cbrt-prod`
63×	`times-frac`
62×	`add-sqr-sqrt` `*-un-lft-identity`
58×	`add-cube-cbrt`
33×	`unpow-prod-down` `sqrt-prod`
30×	`cube-prod`
21×	`associate-/r*`
18×	`add-exp-log`
7×	`prod-exp` `add-cbrt-cube` `sqr-pow`
6×	`sqrt-div`
5×	`pow1` `cube-mult` `unpow3` `associate-r` `associate-l`
4×	`cube-div` `cbrt-div` `flip3-+` `flip-+` `add-log-exp`
3×	`pow-exp` `associate-/l*`
2×	`associate-*r/` `div-exp` `associate-/r/` `distribute-lft-out` `unswap-sqr`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow1/3` `clear-num` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `div-inv`

Counts

4 → 175

Calls

4 calls:

11.0ms	(/ 1.0 (cbrt (pow (sqrt (+ 1.0 (* (pow (* (/ l Om) 2.0) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3)))
12.0ms	(* (pow (* (/ l Om) 2.0) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.0ms	(sqrt (+ 1.0 (* (pow (* (/ l Om) 2.0) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
5.0ms	(cbrt (pow (sqrt (+ 1.0 (* (pow (* (/ l Om) 2.0) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

series521.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ 1.0 (cbrt (pow (sqrt (+ 1.0 (* (pow (* (/ l Om) 2.0) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3)))
106.0ms	(* (pow (* (/ l Om) 2.0) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
125.0ms	(sqrt (+ 1.0 (* (pow (* (/ l Om) 2.0) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
128.0ms	(cbrt (pow (sqrt (+ 1.0 (* (pow (* (/ l Om) 2.0) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

simplify90.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4976	5446
1	4976	5446

prune435.0ms

Filtered

100 candidates to 187 candidates (-87.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	187	2	189

Merged error: 0.4b

Counts

189 → 2

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.3b	(pow (* (/ l Om) 2.0) 2.0)
0.9b	(log (pow (exp (pow (* (/ l Om) 2.0) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.7b	(pow (exp (pow (* (/ l Om) 2.0) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite25.0ms

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:

3.0ms	(pow (sin ky) 2.0)
6.0ms	(pow (* (/ l Om) 2.0) 2.0)
5.0ms	(log (pow (exp (pow (* (/ l Om) 2.0) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
11.0ms	(pow (exp (pow (* (/ l Om) 2.0) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin ky) 2.0)
14.0ms	(pow (* (/ l Om) 2.0) 2.0)
64.0ms	(log (pow (exp (pow (* (/ l Om) 2.0) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
58.0ms	(pow (exp (pow (* (/ l Om) 2.0) 2.0)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify55.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5035	1332

prune239.0ms

Filtered

64 candidates to 91 candidates (-42.2%)

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: 0.4b

Counts

93 → 2

regimes529.0ms

Accuracy

0% (0.4b remaining)

Error of 1.1b against oracle of 0.7b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	32
1	31	32

end0.0ms

analyze631.0ms

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

sample3.1s

Algorithm

intervals

Results

1.2s	6182×	body	80	valid
783.0ms	523×	body	1280	valid
596.0ms	693×	body	640	valid
250.0ms	398×	body	320	valid
89.0ms	204×	body	160	valid

Details

analyze640.0ms

sample99.0ms

simplify57.0ms

prune11.0ms

localize23.0ms

rewrite32.0ms

series416.0ms

simplify52.0ms

prune370.0ms

localize28.0ms

rewrite37.0ms

series521.0ms

simplify90.0ms

prune435.0ms

localize28.0ms

rewrite25.0ms

series154.0ms

simplify55.0ms

prune239.0ms

regimes529.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze631.0ms

sample3.1s

Profiling