Details

sample374.0ms

Algorithm

intervals

Results

185.0ms	75×	body	1280	valid
59.0ms	65×	body	640	valid
20.0ms	83×	body	80	valid
12.0ms	21×	body	320	valid
5.0ms	12×	body	160	valid

simplify5.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
16×	`unpow-prod-down`
10×	`distribute-lft-out`
8×	`add-exp-log` `associate-/r*`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

82.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.0ms	(pow (sin kx) 2.0)
7.0ms	(pow (sin ky) 2.0)
31.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series727.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
151.0ms	(pow (sin kx) 2.0)
203.0ms	(pow (sin ky) 2.0)
156.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.9s

Counts

112 → 112

Iterations

Useful iterations: 2 (221.0ms)

Iter	Nodes	Cost
0	170	1738
1	328	1556
2	794	1503
3	2419	1503
done	5000	1503

prune622.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
0.3b	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
30×	`associate-r`
28×	`times-frac`
25×	`add-cube-cbrt`
22×	`sqrt-prod`
15×	`add-exp-log`
14×	`unpow-prod-down`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
5×	`unswap-sqr`
4×	`sqrt-div` `prod-exp` `add-log-exp`
3×	`associate-l`
2×	`pow-to-exp` `pow-pow` `flip3-+` `div-exp` `pow-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 106

Calls

4 calls:

4.0ms	(pow (sin kx) 2.0)
4.0ms	(pow (sin ky) 2.0)
159.0ms	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
66.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series703.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(pow (sin kx) 2.0)
174.0ms	(pow (sin ky) 2.0)
211.0ms	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
137.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify3.2s

Counts

118 → 118

Iterations

Useful iterations: 2 (346.0ms)

Iter	Nodes	Cost
0	198	1690
1	433	1384
2	1095	1284
3	3270	1284
done	5002	1284

prune559.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.5b

localize37.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
15.5b	(cbrt (pow (sin kx) 2.0))
15.5b	(cbrt (pow (sin kx) 2.0))
15.5b	(cbrt (pow (sin kx) 2.0))

rewrite143.0ms

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:

127.0ms	(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))
4.0ms	(cbrt (pow (sin kx) 2.0))
6.0ms	(cbrt (pow (sin kx) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

116.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
277.0ms	(cbrt (pow (sin kx) 2.0))
292.0ms	(cbrt (pow (sin kx) 2.0))
356.0ms	(cbrt (pow (sin kx) 2.0))

simplify1.4s

Counts

72 → 72

Iterations

Useful iterations: 3 (377.0ms)

Iter	Nodes	Cost
0	96	1131
1	206	1059
2	456	739
3	1340	733
done	5000	733

prune649.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 9.5b

localize56.0ms

Local error

Found 4 expressions with local error:

15.5b	(cbrt (pow (sin kx) 2.0))
15.5b	(cbrt (pow (sin kx) 2.0))
15.5b	(cbrt (pow (sin kx) 2.0))
15.5b	(cbrt (pow (sin kx) 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp` `sqr-pow`

Counts

4 → 60

Calls

4 calls:

6.0ms	(cbrt (pow (sin kx) 2.0))
6.0ms	(cbrt (pow (sin kx) 2.0))
5.0ms	(cbrt (pow (sin kx) 2.0))
3.0ms	(cbrt (pow (sin kx) 2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

305.0ms	(cbrt (pow (sin kx) 2.0))
309.0ms	(cbrt (pow (sin kx) 2.0))
318.0ms	(cbrt (pow (sin kx) 2.0))
755.0ms	(cbrt (pow (sin kx) 2.0))

simplify2.0s

Counts

72 → 72

Iterations

Useful iterations: 3 (106.0ms)

Iter	Nodes	Cost
0	50	724
1	91	708
2	172	668
3	378	656
4	960	656
5	2590	656
done	5001	656

prune520.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 9.5b

regimes1.6s

Accuracy

64.3% (0.5b remaining)

Error of 11.9b against oracle of 11.4b and baseline of 12.7b

bsearch4.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	68
1	49	68
done	49	68

end0.0ms

sample9.0s

Algorithm

intervals

Results

4.5s	2729×	body	1280	valid
2.2s	1786×	body	640	valid
1.0s	2350×	body	80	valid
630.0ms	786×	body	320	valid
160.0ms	349×	body	160	valid