Details

sample220.0ms

Algorithm

intervals

Results

146.0ms	126×	body	1280	valid
39.0ms	59×	body	640	valid
9.0ms	20×	body	320	valid
6.0ms	42×	body	80	valid
3.0ms	9×	body	160	valid

simplify1.3s

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	129	16
5	328	16
6	946	16
7	3348	16
done	5001	16

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: 3.5b

Counts

2 → 1

localize16.0ms

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)))

rewrite36.0ms

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)
9.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
20.0ms	(pow (sin kx) 2.0)
21.0ms	(pow (sin ky) 2.0)
25.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.0s

Counts

113 → 113

Iterations

Useful iterations: 3 (403.0ms)

Iter	Nodes	Cost
0	191	1706
1	434	1602
2	1260	1491
3	4366	1475
done	5000	1475

prune294.0ms

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

localize17.0ms

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)
20.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
12.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series145.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (sin ky) 2.0)
51.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
50.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
21.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify457.0ms

Counts

145 → 145

Iterations

Useful iterations: 2 (132.0ms)

Iter	Nodes	Cost
0	200	2654
1	438	2406
2	1595	2229
done	5001	2229

prune292.0ms

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

localize20.0ms

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)))

rewrite38.0ms

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)
15.0ms	(* (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)))
10.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series131.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (sin ky) 2.0)
48.0ms	(* (fabs (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
31.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
31.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify725.0ms

Counts

89 → 89

Iterations

Useful iterations: 3 (287.0ms)

Iter	Nodes	Cost
0	165	1876
1	370	1750
2	1049	1601
3	2888	1522
done	5001	1522

prune313.0ms

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)))

rewrite32.0ms

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)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (sin ky) 2.0)
21.0ms	(exp (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
31.0ms	(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
21.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify528.0ms

Counts

91 → 91

Iterations

Useful iterations: done (525.0ms)

Iter	Nodes	Cost
0	143	1416
1	275	1215
2	653	1132
3	1615	1120
done	5000	1118

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

regimes925.0ms

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

sample6.7s

Algorithm

intervals

Results

4.1s	3817×	body	1280	valid
1.4s	2008×	body	640	valid
548.0ms	684×	body	320	valid
162.0ms	1219×	body	80	valid
80.0ms	272×	body	160	valid

Details

sample220.0ms

simplify1.3s

prune5.0ms

localize16.0ms

rewrite36.0ms

series118.0ms

simplify1.0s

prune294.0ms

localize17.0ms

rewrite48.0ms

series145.0ms

simplify457.0ms

prune292.0ms

localize20.0ms

rewrite38.0ms

series131.0ms

simplify725.0ms

prune313.0ms

localize19.0ms

rewrite32.0ms

series94.0ms

simplify528.0ms

prune172.0ms

regimes925.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.7s

Profiling