Details

sample105.0ms

Algorithm

intervals

Results

57.0ms	85×	body	1280	valid
17.0ms	46×	body	640	valid
8.0ms	31×	body	320	valid
7.0ms	85×	body	80	valid
1.0ms	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: 13.1b

localize21.0ms

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 ky) 2.0)
0.2b	(pow (sin kx) 2.0)
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite116.0ms

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:

79.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
25.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
104.0ms	(pow (sin ky) 2.0)
107.0ms	(pow (sin kx) 2.0)
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.7s

Counts

113 → 113

Iterations

Useful iterations: 2 (159.0ms)

Iter	Nodes	Cost
0	180	1660
1	391	1562
2	1016	1469
3	3466	1469
done	5000	1469

prune417.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin th) (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.2b	(pow (sin ky) 2.0)
0.2b	(pow (sin kx) 2.0)
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite115.0ms

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:

76.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms	(pow (sin ky) 2.0)
4.0ms	(pow (sin kx) 2.0)
25.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
108.0ms	(pow (sin ky) 2.0)
106.0ms	(pow (sin kx) 2.0)
84.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.3s

Counts

113 → 113

Iterations

Useful iterations: 2 (199.0ms)

Iter	Nodes	Cost
0	195	1650
1	425	1466
2	1246	1375
3	4297	1375
done	5000	1375

prune370.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 12.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite99.0ms

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)))))
26.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
25.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
28.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
85.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
81.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
81.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify921.0ms

Counts

102 → 102

Iterations

Useful iterations: done (917.0ms)

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

prune484.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 12.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite99.0ms

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)))))
25.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
25.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
29.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
81.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify912.0ms

Counts

102 → 102

Iterations

Useful iterations: done (908.0ms)

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

prune410.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 12.3b

regimes1.1s

Accuracy

0% (1.3b remaining)

Error of 12.8b against oracle of 11.6b and baseline of 12.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.1s	2696×	body	1280	valid
696.0ms	1742×	body	640	valid
225.0ms	791×	body	320	valid
210.0ms	2396×	body	80	valid
63.0ms	375×	body	160	valid