Details

sample111.0ms

Algorithm

intervals

Results

56.0ms	83×	body	1280	valid
27.0ms	57×	body	640	valid
7.0ms	83×	body	80	valid
6.0ms	22×	body	320	valid
2.0ms	11×	body	160	valid

simplify2.3s

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	126	16
5	297	16
6	884	16
7	3178	16
done	5000	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

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))))
0.2b	(pow (sin ky) 2.0)
0.2b	(pow (sin kx) 2.0)
4.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite41.0ms

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:

19.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.0ms	(pow (sin ky) 2.0)
1.0ms	(pow (sin kx) 2.0)
16.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series396.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
99.0ms	(pow (sin ky) 2.0)
101.0ms	(pow (sin kx) 2.0)
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.0s

Counts

112 → 112

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	170	1738
1	330	1550
2	819	1503
3	2663	1503
done	5000	1503

prune388.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
0.2b	(pow (sin ky) 2)
0.2b	(pow (sin kx) 2)
4.7b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite43.0ms

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-+` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 102

Calls

4 calls:

20.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
1.0ms	(pow (sin ky) 2)
1.0ms	(pow (sin kx) 2)
17.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
18.0ms	(pow (sin ky) 2)
21.0ms	(pow (sin kx) 2)
73.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify1.1s

Counts

114 → 114

Iterations

Useful iterations: 3 (389.0ms)

Iter	Nodes	Cost
0	165	1738
1	323	1504
2	803	1433
3	2680	1421
done	5000	1421

prune354.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.4b

localize20.0ms

Local error

Found 4 expressions with local error:

4.7b	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
16.2b	(cbrt (pow (sin kx) 2.0))
16.2b	(cbrt (pow (sin kx) 2.0))
16.2b	(cbrt (pow (sin kx) 2.0))

rewrite50.0ms

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:

45.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
1.0ms	(cbrt (pow (sin kx) 2.0))
1.0ms	(cbrt (pow (sin kx) 2.0))
1.0ms	(cbrt (pow (sin kx) 2.0))

series650.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(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))
193.0ms	(cbrt (pow (sin kx) 2.0))
188.0ms	(cbrt (pow (sin kx) 2.0))

simplify561.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (144.0ms)

Iter	Nodes	Cost
0	96	1131
1	206	1059
2	461	739
3	1300	733
done	5001	733

prune348.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2)
0.2b	(pow (sin kx) 2)
0.3b	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
4.9b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
45×	`sqrt-prod`
41×	`add-sqr-sqrt`
34×	`times-frac`
28×	`add-cube-cbrt`
24×	`associate-l`
18×	`unpow-prod-down`
12×	`distribute-lft-out`
10×	`pow1`
8×	`add-exp-log`
6×	`pow-unpow` `add-cbrt-cube`
4×	`associate-/r/` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `associate-r`
2×	`pow-to-exp` `pow-pow` `flip3-+` `sqrt-div` `pow-exp` `flip-+` `div-inv` `unpow2` `sqr-pow`
1×	`pow-flip` `pow1/2` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `inv-pow`

Counts

4 → 115

Calls

4 calls:

1.0ms	(pow (sin ky) 2)
1.0ms	(pow (sin kx) 2)
52.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
21.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series258.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(pow (sin ky) 2)
19.0ms	(pow (sin kx) 2)
116.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
103.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify1.1s

Counts

127 → 127

Iterations

Useful iterations: 3 (406.0ms)

Iter	Nodes	Cost
0	190	1895
1	366	1664
2	852	1565
3	2373	1555
done	5001	1555

prune350.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.4b

regimes749.0ms

Accuracy

0% (1.3b remaining)

Error of 13.0b against oracle of 11.7b and baseline of 13.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	17
1	17	17
done	17	17

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.2s	2684×	body	1280	valid
722.0ms	1759×	body	640	valid
231.0ms	821×	body	320	valid
226.0ms	2389×	body	80	valid
67.0ms	347×	body	160	valid