Details

analyze1.4s

Algorithm: search

sample207.0ms

Algorithm

intervals

Results

128.0ms	121×	body	1280	valid
40.0ms	61×	body	640	valid
9.0ms	21×	body	320	valid
9.0ms	41×	body	80	valid
3.0ms	12×	body	160	valid

simplify52.0ms

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: 5.6b

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)))) (sin th))
0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
5.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-l`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
14×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

15.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (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)))

series108.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
19.0ms	(pow (sin kx) 2.0)
23.0ms	(pow (sin ky) 2.0)
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	425	1022
1	1522	960
2	5001	946

prune317.0ms

Filtered

78 candidates to 113 candidates (-44.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	102	11	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	11	114

Merged error: 3.9b

Counts

114 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))
0.3b	(pow (sin ky) 2.0)
0.3b	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
5.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
33×	`associate-l`
29×	`add-exp-log`
28×	`times-frac`
24×	`add-cube-cbrt`
22×	`sqrt-prod`
18×	`add-cbrt-cube`
13×	`pow1` `prod-exp`
11×	`unpow-prod-down`
8×	`distribute-lft-out`
7×	`cbrt-unprod`
5×	`unswap-sqr`
4×	`sqrt-div` `div-exp` `associate-r` `pow-prod-down` `add-log-exp`
3×	`pow-unpow`
2×	`cbrt-undiv` `rec-exp` `flip3-+` `1-exp` `associate-l/` `associate-/r/` `-commutative` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `associate-*r/` `pow-exp` `div-inv` `sqr-pow`

Counts

4 → 111

Calls

4 calls:

15.0ms	(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))
3.0ms	(pow (sin ky) 2.0)
16.0ms	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series130.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))
19.0ms	(pow (sin ky) 2.0)
42.0ms	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
21.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	443	1278
1	1840	1119
2	5001	1095

prune294.0ms

Filtered

80 candidates to 123 candidates (-53.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	122	12	134

Merged error: 3.9b

Counts

134 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

5.2b	(sqrt (+ (pow (sin kx) 2.0) (* (* (cbrt (pow (sin ky) 2.0)) (cbrt (pow (sin ky) 2.0))) (cbrt (pow (sin ky) 2.0)))))
15.4b	(cbrt (pow (sin ky) 2.0))
15.4b	(cbrt (pow (sin ky) 2.0))
15.4b	(cbrt (pow (sin ky) 2.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqrt-prod` `sqr-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt (+ (pow (sin kx) 2.0) (* (* (cbrt (pow (sin ky) 2.0)) (cbrt (pow (sin ky) 2.0))) (cbrt (pow (sin ky) 2.0)))))
2.0ms	(cbrt (pow (sin ky) 2.0))
2.0ms	(cbrt (pow (sin ky) 2.0))
2.0ms	(cbrt (pow (sin ky) 2.0))

series135.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sqrt (+ (pow (sin kx) 2.0) (* (* (cbrt (pow (sin ky) 2.0)) (cbrt (pow (sin ky) 2.0))) (cbrt (pow (sin ky) 2.0)))))
40.0ms	(cbrt (pow (sin ky) 2.0))
38.0ms	(cbrt (pow (sin ky) 2.0))
38.0ms	(cbrt (pow (sin ky) 2.0))

simplify74.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	215	722
1	602	679
2	2161	649
3	5001	643

prune305.0ms

Filtered

55 candidates to 72 candidates (-30.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	72	12	84

Merged error: 3.9b

Counts

84 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
5.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
30×	`cbrt-prod` `sqrt-prod`
25×	`add-sqr-sqrt`
24×	`times-frac`
22×	`add-cube-cbrt`
12×	`unpow-prod-down` `distribute-lft-out`
8×	`sqrt-div`
7×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 90

Calls

4 calls:

10.0ms	(cbrt (/ (sin ky) (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)))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(cbrt (/ (sin ky) (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)))
21.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify125.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	308	1314
1	909	1257
2	4097	1241
3	5003	1236

prune423.0ms

Filtered

68 candidates to 102 candidates (-50.0%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	102	12	114

Merged error: 3.9b

Counts

114 → 12

regimes1.2s

Accuracy

63.8% (0.5b remaining)

Error of 3.2b against oracle of 2.7b and baseline of 4.1b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	30
1	42	30

end0.0ms

analyze1.3s

Algorithm: search

sample6.2s

Algorithm

intervals

Results

4.0s	3696×	body	1280	valid
1.4s	2108×	body	640	valid
325.0ms	721×	body	320	valid
161.0ms	1191×	body	80	valid
87.0ms	284×	body	160	valid

Details

analyze1.4s

sample207.0ms

simplify52.0ms

prune5.0ms

localize15.0ms

rewrite30.0ms

series108.0ms

simplify45.0ms

prune317.0ms

localize16.0ms

rewrite44.0ms

series130.0ms

simplify52.0ms

prune294.0ms

localize21.0ms

rewrite13.0ms

series135.0ms

simplify74.0ms

prune305.0ms

localize23.0ms

rewrite33.0ms

series113.0ms

simplify125.0ms

prune423.0ms

regimes1.2s

bsearch2.0ms

simplify2.0ms

end0.0ms

analyze1.3s

sample6.2s

Profiling