Details

sample113.0ms

Algorithm

intervals

Results

50.0ms	73×	body	1280	valid
29.0ms	75×	body	640	valid
10.0ms	26×	body	320	valid
7.0ms	73×	body	80	valid
2.0ms	9×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	23	16
2	35	16
3	64	16
4	136	16
5	311	16
6	1019	16
7	4223	16
done	5001	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

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))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite122.0ms

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:

81.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
4.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
31.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
102.0ms	(pow (sin kx) 2.0)
101.0ms	(pow (sin ky) 2.0)
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.7s

Counts

113 → 113

Iterations

Useful iterations: 2 (157.0ms)

Iter	Nodes	Cost
0	180	1660
1	391	1562
2	1016	1469
3	3467	1469
done	5000	1469

prune420.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.8b

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 kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite121.0ms

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:

80.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
30.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
106.0ms	(pow (sin kx) 2.0)
106.0ms	(pow (sin ky) 2.0)
84.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.6s

Counts

113 → 113

Iterations

Useful iterations: 2 (226.0ms)

Iter	Nodes	Cost
0	195	1650
1	426	1464
2	1332	1375
3	4965	1375
done	5000	1375

prune375.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite103.0ms

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:

17.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
27.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
26.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
29.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
84.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
81.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify941.0ms

Counts

102 → 102

Iterations

Useful iterations: done (937.0ms)

Iter	Nodes	Cost
0	160	2119
1	282	1894
2	636	1807
3	1703	1797
done	5001	1791

prune473.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 11.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (sin ky))
3.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`sqrt-prod`
11×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`unpow-prod-down` `sqrt-div` `distribute-lft-out`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow1/3`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt (sin ky))
27.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
27.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
30.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (sin ky))
83.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
83.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.7s

Counts

74 → 74

Iterations

Useful iterations: 3 (184.0ms)

Iter	Nodes	Cost
0	81	1037
1	175	899
2	403	866
3	1059	863
4	3229	863
done	5000	863

prune319.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 11.8b

regimes1.4s

Accuracy

56.5% (0.8b remaining)

Error of 12.0b against oracle of 11.2b and baseline of 13.1b

bsearch3.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	87
1	50	87
done	50	87

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.0s	2715×	body	1280	valid
783.0ms	1834×	body	640	valid
230.0ms	792×	body	320	valid
209.0ms	2318×	body	80	valid
64.0ms	341×	body	160	valid