Details

analyze1.4s

Algorithm: search

sample207.0ms

Algorithm

intervals

Results

134.0ms	130×	body	1280	valid
42.0ms	60×	body	640	valid
10.0ms	23×	body	320	valid
4.0ms	35×	body	80	valid
2.0ms	8×	body	160	valid

simplify51.0ms

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

prune5.0ms

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: 4.2b

Counts

2 → 1

localize16.0ms

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)
3.9b	(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:

14.0ms	(/ (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)
7.0ms	(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)
18.0ms	(pow (sin ky) 2.0)
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (31.0ms)

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

prune242.0ms

Filtered

70 candidates to 112 candidates (-60.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	101	11	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	11	113

Merged error: 2.9b

Counts

113 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.5b	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

100×	`sqrt-prod`
52×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
34×	`sqrt-pow1`
30×	`pow1`
28×	`sqrt-div`
20×	`add-cube-cbrt`
19×	`swap-sqr`
18×	`pow1/2`
15×	`unpow-prod-down`
14×	`distribute-lft-out`
11×	`associate-r` `associate-l`
9×	`pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `add-log-exp`
3×	`pow-unpow`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`pow2` `pow-to-exp` `pow-pow` `pow-plus` `sqrt-unprod` `pow-exp` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 142

Calls

4 calls:

2.0ms	(pow (sin ky) 2.0)
23.0ms	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin ky) 2.0)
19.0ms	(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
21.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify55.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	330	1472
1	1266	1371
2	5002	1333

prune298.0ms

Filtered

72 candidates to 154 candidates (-113.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	154	11	165

Merged error: 2.9b

Counts

165 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.4b	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

62×	`sqrt-prod`
56×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
33×	`times-frac`
32×	`add-cube-cbrt`
15×	`unpow-prod-down`
12×	`distribute-lft-out`
11×	`associate-/r*`
8×	`sqrt-div`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`pow-unpow` `flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `div-exp` `pow-exp` `clear-num` `div-inv` `sqr-pow`

Counts

4 → 112

Calls

4 calls:

2.0ms	(pow (sin ky) 2.0)
12.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
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 ky) 2.0)
46.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	373	1454
1	1305	1344
2	5001	1333

prune331.0ms

Filtered

75 candidates to 124 candidates (-65.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	123	12	135

Merged error: 2.9b

Counts

135 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
1.5b	(exp (log (pow (sin ky) 2.0)))
3.9b	(sqrt (+ (pow (sin kx) 2.0) (exp (log (pow (sin ky) 2.0)))))
13.9b	(log (pow (sin ky) 2.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`log-prod` `*-un-lft-identity`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`unpow-prod-down`
7×	`add-exp-log` `exp-sum`
6×	`pow1`
4×	`exp-prod` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `rem-log-exp` `sqr-pow`
2×	`pow-to-exp` `sqrt-div` `pow-exp` `log-pow`
1×	`rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `rem-exp-log` `distribute-lft-out`

Counts

4 → 70

Calls

4 calls:

3.0ms	(pow (sin ky) 2.0)
5.0ms	(exp (log (pow (sin ky) 2.0)))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (exp (log (pow (sin ky) 2.0)))))
3.0ms	(log (pow (sin ky) 2.0))

series85.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin ky) 2.0)
18.0ms	(exp (log (pow (sin ky) 2.0)))
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (exp (log (pow (sin ky) 2.0)))))
29.0ms	(log (pow (sin ky) 2.0))

simplify107.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	265	525
1	832	497
2	3150	465
3	5001	459

prune131.0ms

Filtered

51 candidates to 82 candidates (-60.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	82	12	94

Merged error: 2.9b

Counts

94 → 12

regimes829.0ms

Accuracy

0% (1.8b remaining)

Error of 4.3b against oracle of 2.6b and baseline of 4.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	19
1	17	19

end0.0ms

analyze1.2s

Algorithm: search

sample6.2s

Algorithm

intervals

Results

4.0s	3722×	body	1280	valid
1.3s	1966×	body	640	valid
329.0ms	741×	body	320	valid
168.0ms	1293×	body	80	valid
79.0ms	278×	body	160	valid

Details

analyze1.4s

sample207.0ms

simplify51.0ms

prune5.0ms

localize16.0ms

rewrite29.0ms

series94.0ms

simplify41.0ms

prune242.0ms

localize20.0ms

rewrite45.0ms

series77.0ms

simplify55.0ms

prune298.0ms

localize21.0ms

rewrite33.0ms

series102.0ms

simplify45.0ms

prune331.0ms

localize19.0ms

rewrite20.0ms

series85.0ms

simplify107.0ms

prune131.0ms

regimes829.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.2s

sample6.2s

Profiling