Details

sample191.0ms

Algorithm

intervals

Results

115.0ms	113×	body	1280	valid
37.0ms	64×	body	640	valid
13.0ms	35×	body	320	valid
4.0ms	37×	body	80	valid
2.0ms	7×	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

prune6.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 3.0b

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)
2.7b	(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)))

series111.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
18.0ms	(pow (sin kx) 2.0)
20.0ms	(pow (sin ky) 2.0)
24.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (35.0ms)

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

prune710.0ms

Filtered

113 candidates to 78 candidates (31.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	102	11	113
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	12	114

Merged error: 2.4b

Counts

114 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
0.3b	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

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

series101.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin kx) 2.0)
18.0ms	(pow (sin ky) 2.0)
43.0ms	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
22.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify49.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	427	1012
1	1607	935
2	5001	895

prune950.0ms

Filtered

117 candidates to 79 candidates (32.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	4	6	10
Picked	0	1	1
Done	0	1	1
Total	119	10	129

Merged error: 2.4b

Counts

129 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-r`
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-l` `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` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

17.0ms	(* (sin ky) (/ (sin th) (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)))

series104.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify57.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	471	980
1	2006	902
2	5001	902

prune544.0ms

Filtered

113 candidates to 68 candidates (39.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	114	9	123

Merged error: 2.4b

Counts

123 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.3b	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.2b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.2b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt`
11×	`associate-r`
10×	`sqrt-prod`
9×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
6×	`cbrt-div` `add-cbrt-cube` `distribute-lft-out`
4×	`add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-l` `flip-+` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/`
1×	`pow-to-exp` `pow-pow` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

2.0ms	(pow (sin ky) 2.0)
12.0ms	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin ky) 2.0)
40.0ms	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
32.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
28.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify149.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	364	1147
1	1204	1075
2	4865	1035
3	5001	1035

prune615.0ms

Filtered

89 candidates to 63 candidates (29.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	88	10	98

Merged error: 2.4b

Counts

98 → 10

regimes928.0ms

Accuracy

0% (1.4b remaining)

Error of 4.2b against oracle of 2.7b and baseline of 4.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.7s	3723×	body	1280	valid
1.2s	2012×	body	640	valid
283.0ms	725×	body	320	valid
139.0ms	1250×	body	80	valid
79.0ms	290×	body	160	valid

Details

sample191.0ms

simplify50.0ms

prune6.0ms

localize15.0ms

rewrite30.0ms

series111.0ms

simplify45.0ms

prune710.0ms

localize16.0ms

rewrite31.0ms

series101.0ms

simplify49.0ms

prune950.0ms

localize15.0ms

rewrite32.0ms

series104.0ms

simplify57.0ms

prune544.0ms

localize21.0ms

rewrite30.0ms

series118.0ms

simplify149.0ms

prune615.0ms

regimes928.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.7s

Profiling