Details

sample125.0ms

Algorithm

intervals

Results

65.0ms	90×	body	1280	valid
28.0ms	68×	body	640	valid
6.0ms	23×	body	320	valid
6.0ms	68×	body	80	valid
1.0ms	7×	body	160	valid

simplify50.0ms

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
done	5002	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.9b

localize20.0ms

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)
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite117.0ms

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 kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
26.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
103.0ms	(pow (sin kx) 2.0)
109.0ms	(pow (sin ky) 2.0)
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify39.0ms

Counts

113 → 113

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	391	990
1	1382	928
2	5001	927
done	5001	927

prune390.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.1b

localize20.0ms

Local error

Found 4 expressions with local error:

3.3b	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
16.9b	(cbrt (pow (sin kx) 2.0))
16.9b	(cbrt (pow (sin kx) 2.0))
16.9b	(cbrt (pow (sin kx) 2.0))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqrt-prod` `sqr-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 60

Calls

4 calls:

82.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
3.0ms	(cbrt (pow (sin kx) 2.0))
3.0ms	(cbrt (pow (sin kx) 2.0))
3.0ms	(cbrt (pow (sin kx) 2.0))

series662.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
192.0ms	(cbrt (pow (sin kx) 2.0))
194.0ms	(cbrt (pow (sin kx) 2.0))
196.0ms	(cbrt (pow (sin kx) 2.0))

simplify57.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	204	682
1	478	640
2	1705	640
3	5001	634
done	5001	634

prune346.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 10.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite101.0ms

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)))
30.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
82.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
74.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify92.0ms

Counts

102 → 102

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	282	1291
1	819	1231
2	3475	1224
3	5002	1219
done	5002	1219

prune426.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

14.0ms	(cbrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
26.0ms	(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)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(cbrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
75.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
82.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
83.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify55.0ms

Counts

81 → 81

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	181	788
1	478	746
2	1740	744
3	5001	740
done	5001	740

prune331.0ms

Pruning

22 alts after pruning (20 fresh and 2 done)

Merged error: 10.1b

regimes1.1s

Accuracy

0% (1.5b remaining)

Error of 12.9b against oracle of 11.3b and baseline of 12.9b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	31
1	19	31
done	19	31

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.0s	2719×	body	1280	valid
958.0ms	1892×	body	640	valid
229.0ms	760×	body	320	valid
217.0ms	2287×	body	80	valid
64.0ms	342×	body	160	valid