Details

analyze1.4s

Algorithm: search

sample216.0ms

Algorithm

intervals

Results

142.0ms	127×	body	1280	valid
42.0ms	62×	body	640	valid
12.0ms	26×	body	320	valid
4.0ms	33×	body	80	valid
2.0ms	8×	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

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: 2.6b

Counts

2 → 1

localize21.0ms

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))
0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
2.4b	(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 ky) 2.0)
2.0ms	(pow (sin kx) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series103.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
21.0ms	(pow (sin ky) 2.0)
19.0ms	(pow (sin kx) 2.0)
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify44.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (34.0ms)

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

prune275.0ms

Filtered

78 candidates to 113 candidates (-44.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	101	12	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	12	114

Merged error: 2.0b

Counts

114 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
0.3b	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
2.4b	(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 ky) 2.0)
2.0ms	(pow (sin kx) 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)))

series97.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin ky) 2.0)
17.0ms	(pow (sin kx) 2.0)
43.0ms	(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (35.0ms)

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

prune262.0ms

Filtered

79 candidates to 117 candidates (-48.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	113	4	117
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	116	13	129

Merged error: 2.0b

Counts

129 → 13

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)))))
0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
2.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite31.0ms

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:

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

series100.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
18.0ms	(pow (sin ky) 2.0)
20.0ms	(pow (sin kx) 2.0)
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (12.0ms)

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

prune230.0ms

Filtered

69 candidates to 113 candidates (-63.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	113	13	126

Merged error: 2.0b

Counts

126 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2)
0.3b	(pow (sin kx) 2)
0.6b	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (sin ky) (sin th)))
2.5b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
42×	`sqrt-prod`
32×	`times-frac`
31×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
24×	`associate-l`
18×	`unpow-prod-down`
13×	`pow1`
12×	`distribute-lft-out`
11×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`pow-unpow`
4×	`associate-/r/` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `sqrt-div` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `flip-+` `div-inv` `sin-mult` `unpow2` `sqr-pow`
1×	`frac-times` `pow-flip` `pow1/2` `associate-r/` `associate-r` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 114

Calls

4 calls:

2.0ms	(pow (sin ky) 2)
3.0ms	(pow (sin kx) 2)
16.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (sin ky) (sin th)))
10.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series81.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (sin ky) 2)
3.0ms	(pow (sin kx) 2)
48.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (sin ky) (sin th)))
27.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify49.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	434	1122
1	1508	1011
2	5002	973

prune180.0ms

Filtered

74 candidates to 126 candidates (-70.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	126	13	139

Merged error: 2.0b

Counts

139 → 13

regimes889.0ms

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	15	10
1	15	10

end0.0ms

analyze1.3s

Algorithm: search

sample6.5s

Algorithm

intervals

Results

4.3s	3813×	body	1280	valid
1.4s	2018×	body	640	valid
321.0ms	677×	body	320	valid
160.0ms	1220×	body	80	valid
83.0ms	272×	body	160	valid

Details

analyze1.4s

sample216.0ms

simplify50.0ms

prune5.0ms

localize21.0ms

rewrite30.0ms

series103.0ms

simplify44.0ms

prune275.0ms

localize19.0ms

rewrite31.0ms

series97.0ms

simplify46.0ms

prune262.0ms

localize15.0ms

rewrite31.0ms

series100.0ms

simplify56.0ms

prune230.0ms

localize19.0ms

rewrite35.0ms

series81.0ms

simplify49.0ms

prune180.0ms

regimes889.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.3s

sample6.5s

Profiling