Details

sample4.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 70.898438%

Results

135.0ms	122×	body	1280	valid
41.0ms	63×	body	640	valid
9.0ms	20×	body	320	valid
5.0ms	37×	body	80	valid
4.0ms	14×	body	160	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	10
1	35	10
2	63	10
3	137	10
4	417	10
5	1798	10
6	5002	10

prune4.0ms

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: 3.4b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
16×	`unpow-prod-down`
10×	`distribute-lft-out`
8×	`add-exp-log` `associate-/r*`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

10.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
11.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
18.0ms	(pow (sin kx) 2.0)
20.0ms	(pow (sin ky) 2.0)
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	363	1053
1	1249	978
2	5002	961

prune233.0ms

Filtered

70 candidates to 112 candidates (-60.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	102	10	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	10	113

Merged error: 2.5b

Counts

113 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky))) (sin th))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

166×	`times-frac`
127×	`*-un-lft-identity`
106×	`add-sqr-sqrt`
89×	`associate-l`
84×	`add-cube-cbrt`
52×	`sqrt-prod`
26×	`unpow-prod-down`
25×	`add-exp-log`
20×	`distribute-lft-out`
13×	`add-cbrt-cube`
9×	`pow1`
7×	`div-exp` `prod-exp` `unswap-sqr`
6×	`pow-unpow`
4×	`div-inv` `add-log-exp`
3×	`cbrt-undiv` `associate-r` `cbrt-unprod`
2×	`pow-to-exp` `rec-exp` `pow-pow` `sqrt-div` `1-exp` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `flip-+`

Counts

4 → 170

Calls

4 calls:

24.0ms	(* (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky))) (sin th))
2.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series103.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky))) (sin th))
17.0ms	(pow (sin kx) 2.0)
18.0ms	(pow (sin ky) 2.0)
23.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify79.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	685	1984
1	3093	1819
2	5001	1762

prune387.0ms

Filtered

127 candidates to 182 candidates (-43.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	179	3	182
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	181	11	192

Merged error: 2.4b

Counts

192 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin th) (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
150×	`*-un-lft-identity`
99×	`add-sqr-sqrt`
98×	`add-cube-cbrt`
65×	`sqrt-prod`
32×	`unpow-prod-down`
28×	`associate-/r*`
26×	`distribute-lft-out`
11×	`add-exp-log`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`pow-unpow`
5×	`div-inv`
4×	`add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`pow-to-exp` `pow-pow` `sqrt-div` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `clear-num` `associate-/r/` `flip-+`

Counts

4 → 181

Calls

4 calls:

14.0ms	(/ (sin th) (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
2.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
6.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series103.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (sin th) (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
18.0ms	(pow (sin kx) 2.0)
21.0ms	(pow (sin ky) 2.0)
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify82.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	721	2809
1	3041	2660
2	5002	2660

prune326.0ms

Filtered

111 candidates to 193 candidates (-73.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	193	11	204

Merged error: 2.4b

Counts

204 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
0.4b	(/ 1 (/ (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)) (sin th)))
3.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

888×	`times-frac`
542×	`*-un-lft-identity`
395×	`add-sqr-sqrt`
394×	`add-cube-cbrt`
185×	`sqrt-prod`
88×	`associate-/r*`
80×	`unpow-prod-down`
74×	`distribute-lft-out`
27×	`add-exp-log`
17×	`div-inv`
15×	`div-exp`
13×	`add-cbrt-cube`
8×	`pow1`
6×	`cbrt-undiv` `pow-unpow`
4×	`add-log-exp`
3×	`rec-exp` `1-exp` `associate-/l*`
2×	`pow-to-exp` `pow-pow` `sqrt-div` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `clear-num` `associate-/r/` `flip-+` `inv-pow`

Counts

4 → 431

Calls

4 calls:

2.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
25.0ms	(/ 1 (/ (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)) (sin th)))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series102.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin kx) 2.0)
21.0ms	(pow (sin ky) 2.0)
45.0ms	(/ 1 (/ (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)) (sin th)))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify100.0ms

Algorithm

egg-herbie

Counts

443 → 443

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1642	8816
1	5001	7956

prune630.0ms

Filtered

195 candidates to 443 candidates (-127.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	443	0	443
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	443	11	454

Merged error: 2.4b

Counts

454 → 11

regimes605.0ms

Accuracy

0% (1.4b remaining)

Error of 3.9b against oracle of 2.5b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	10
1	14	10

end0.0ms

sample10.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 70.898438%

Results

4.2s	3796×	body	1280	valid
1.4s	2018×	body	640	valid
305.0ms	684×	body	320	valid
158.0ms	1223×	body	80	valid
83.0ms	279×	body	160	valid

Details

sample4.3s

simplify50.0ms

prune4.0ms

localize15.0ms

rewrite29.0ms

series94.0ms

simplify41.0ms

prune233.0ms

localize18.0ms

rewrite45.0ms

series103.0ms

simplify79.0ms

prune387.0ms

localize17.0ms

rewrite33.0ms

series103.0ms

simplify82.0ms

prune326.0ms

localize19.0ms

rewrite73.0ms

series102.0ms

simplify100.0ms

prune630.0ms

regimes605.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample10.7s

Profiling