Details

sample216.0ms

Algorithm

intervals

Results

136.0ms	126×	body	1280	valid
44.0ms	59×	body	640	valid
9.0ms	20×	body	320	valid
5.0ms	42×	body	80	valid
3.0ms	9×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	23	16
2	34	16
3	63	16
4	126	16
5	297	16
6	885	16
7	3190	16
done	5000	16

prune7.0ms

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: 3.5b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (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)
3.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite35.0ms

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:

17.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
26.0ms	(pow (sin kx) 2.0)
20.0ms	(pow (sin ky) 2.0)
21.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.1s

Counts

113 → 113

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	191	1706
1	426	1602
2	1149	1491
3	4250	1475
done	5000	1475

prune303.0ms

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: 2.3b

Counts

114 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
50×	`times-frac`
49×	`add-sqr-sqrt`
41×	`sqrt-prod`
40×	`add-cube-cbrt`
30×	`associate-r`
19×	`unpow-prod-down`
16×	`distribute-lft-out`
12×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `associate-/r*`
6×	`sqrt-div`
4×	`associate-/r/` `add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-l` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

3.0ms	(pow (sin ky) 2.0)
18.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
14.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series136.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin ky) 2.0)
48.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
49.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify895.0ms

Counts

145 → 145

Iterations

Useful iterations: 2 (216.0ms)

Iter	Nodes	Cost
0	200	2654
1	431	2364
2	1329	2229
done	5000	2229

prune297.0ms

Filtered

86 candidates to 145 candidates (-68.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	145	11	156

Merged error: 2.3b

Counts

156 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.4b	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.7b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.7b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite34.0ms

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:

3.0ms	(pow (sin ky) 2.0)
13.0ms	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series126.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (sin ky) 2.0)
42.0ms	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
33.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
31.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.3s

Counts

89 → 89

Iterations

Useful iterations: 3 (574.0ms)

Iter	Nodes	Cost
0	165	1876
1	366	1739
2	932	1601
3	2779	1522
done	5000	1522

prune318.0ms

Filtered

60 candidates to 89 candidates (-48.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	89	11	100

Merged error: 2.3b

Counts

100 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
1.2b	(exp (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
1.3b	(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

3.0ms	(pow (sin ky) 2.0)
10.0ms	(exp (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.0ms	(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (sin ky) 2.0)
20.0ms	(exp (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
26.0ms	(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
23.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify980.0ms

Counts

91 → 91

Iterations

Useful iterations: 3 (243.0ms)

Iter	Nodes	Cost
0	143	1416
1	271	1212
2	601	1140
3	1658	1120
done	5000	1120

prune172.0ms

Filtered

57 candidates to 91 candidates (-59.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	90	12	102

Merged error: 2.3b

Counts

102 → 12

regimes912.0ms

Accuracy

0% (1.3b remaining)

Error of 3.8b against oracle of 2.5b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	15	16
done	15	16

end0.0ms

sample6.3s

Algorithm

intervals

Results

4.0s	3817×	body	1280	valid
1.3s	2008×	body	640	valid
326.0ms	684×	body	320	valid
159.0ms	1219×	body	80	valid
78.0ms	272×	body	160	valid

Details

sample216.0ms

simplify3.1s

prune7.0ms

localize15.0ms

rewrite35.0ms

series117.0ms

simplify2.1s

prune303.0ms

localize16.0ms

rewrite48.0ms

series136.0ms

simplify895.0ms

prune297.0ms

localize19.0ms

rewrite34.0ms

series126.0ms

simplify1.3s

prune318.0ms

localize19.0ms

rewrite31.0ms

series89.0ms

simplify980.0ms

prune172.0ms

regimes912.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.3s

Profiling