Details

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 92.926025%

Results

38.0ms	198×	body	80	valid
19.0ms	15×	body	1280	valid
18.0ms	20×	body	640	valid
9.0ms	15×	body	320	valid
3.0ms	8×	body	160	valid

simplify39.0ms

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

prune6.0ms

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

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(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))))))
2.5b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.1b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite27.0ms

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)
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)))
3.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series418.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin ky) 2.0)
160.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
112.0ms	(* (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)))))

simplify71.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	593	1648
1	2412	1544
2	5002	1541

prune358.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	3	123

Merged error: 0.6b

Counts

123 → 3

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1.0 (cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3)))
2.5b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.1b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
12.2b	(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

90×	`cbrt-prod`
66×	`add-sqr-sqrt` `times-frac`
64×	`*-un-lft-identity`
60×	`add-cube-cbrt`
40×	`unpow-prod-down`
33×	`sqrt-prod`
30×	`cube-prod`
21×	`associate-/r*`
18×	`add-exp-log`
11×	`associate-l`
7×	`add-cbrt-cube` `sqr-pow`
6×	`sqrt-div` `prod-exp`
5×	`pow1` `cube-mult` `unpow3` `associate-r`
4×	`cube-div` `cbrt-div` `flip3-+` `flip-+` `add-log-exp`
3×	`div-exp` `pow-exp` `associate-/l*` `unswap-sqr`
2×	`associate-*r/` `associate-/r/` `div-inv` `distribute-lft-out`
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`

Counts

4 → 182

Calls

4 calls:

9.0ms	(/ 1.0 (cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3)))
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)))))
5.0ms	(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

series522.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ 1.0 (cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3)))
107.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
126.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
130.0ms	(cbrt (pow (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) 3))

simplify89.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	670	3750
1	2548	3261
2	5002	3189

prune482.0ms

Filtered

101 candidates to 194 candidates (-92.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	194	3	197

Merged error: 0.6b

Counts

197 → 3

localize29.0ms

Local error

Found 4 expressions with local error:

7.1b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.1b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.9b	(sqrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
7.9b	(sqrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-pow1`
6×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

2.0ms	(sqrt (+ 1.0 (* (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)))))
3.0ms	(sqrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
3.0ms	(sqrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

series496.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
126.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
122.0ms	(sqrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
122.0ms	(sqrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

simplify86.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	134	1188
1	428	1146
2	2260	1146
3	5001	1146

prune362.0ms

Filtered

62 candidates to 84 candidates (-35.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	84	3	87

Merged error: 0.6b

Counts

87 → 3

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

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
Total	3	3

Merged error: 0.6b

Counts

3 → 3

regimes1.0s

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	31	18
1	31	18

end0.0ms

sample4.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 92.926025%

Results

1.4s	6244×	body	80	valid
648.0ms	539×	body	1280	valid
553.0ms	657×	body	640	valid
211.0ms	351×	body	320	valid
82.0ms	209×	body	160	valid

Details

sample1.8s

simplify39.0ms

prune6.0ms

localize28.0ms

rewrite27.0ms

series418.0ms

simplify71.0ms

prune358.0ms

localize28.0ms

rewrite36.0ms

series522.0ms

simplify89.0ms

prune482.0ms

localize29.0ms

rewrite13.0ms

series496.0ms

simplify86.0ms

prune362.0ms

localize6.0ms

rewrite0.0ms

series0.0ms

simplify2.0ms

prune0.0ms

regimes1.0s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample4.9s

Profiling