Details

sample113.0ms

Algorithm

intervals

Results

61.0ms	83×	body	1280	valid
23.0ms	57×	body	640	valid
7.0ms	83×	body	80	valid
6.0ms	22×	body	320	valid
2.0ms	11×	body	160	valid

simplify4.8s

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	128	16
5	325	16
6	1189	16
7	4392	16
done	5000	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize16.0ms

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)))

rewrite45.0ms

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:

20.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.0ms	(pow (sin ky) 2.0)
2.0ms	(pow (sin kx) 2.0)
19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
105.0ms	(pow (sin ky) 2.0)
106.0ms	(pow (sin kx) 2.0)
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify3.3s

Counts

112 → 112

Iterations

Useful iterations: 2 (109.0ms)

Iter	Nodes	Cost
0	170	1738
1	337	1574
2	1062	1503
3	4941	1503
done	5000	1503

prune619.0ms

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)))

rewrite48.0ms

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:

24.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
1.0ms	(pow (sin ky) 2)
1.0ms	(pow (sin kx) 2)
18.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
18.0ms	(pow (sin ky) 2)
18.0ms	(pow (sin kx) 2)
76.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify2.8s

Counts

114 → 114

Iterations

Useful iterations: 3 (599.0ms)

Iter	Nodes	Cost
0	165	1738
1	331	1528
2	1052	1433
3	4989	1421
done	5000	1421

prune388.0ms

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)) (cbrt (pow (sin kx) 2))) (cbrt (pow (sin kx) 2))) (pow (sin ky) 2)))
16.2b	(cbrt (pow (sin kx) 2))
16.2b	(cbrt (pow (sin kx) 2))
16.2b	(cbrt (pow (sin kx) 2))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

24×	`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` `unpow2` `sqr-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 63

Calls

4 calls:

50.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2)) (cbrt (pow (sin kx) 2))) (cbrt (pow (sin kx) 2))) (pow (sin ky) 2)))
1.0ms	(cbrt (pow (sin kx) 2))
1.0ms	(cbrt (pow (sin kx) 2))
2.0ms	(cbrt (pow (sin kx) 2))

series412.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2)) (cbrt (pow (sin kx) 2))) (cbrt (pow (sin kx) 2))) (pow (sin ky) 2)))
111.0ms	(cbrt (pow (sin kx) 2))
114.0ms	(cbrt (pow (sin kx) 2))
111.0ms	(cbrt (pow (sin kx) 2))

simplify1.3s

Counts

75 → 75

Iterations

Useful iterations: 3 (283.0ms)

Iter	Nodes	Cost
0	91	1143
1	200	1039
2	579	654
3	2336	644
done	5001	644

prune328.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.4b

localize17.0ms

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))))

rewrite82.0ms

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:

2.0ms	(pow (sin ky) 2)
2.0ms	(pow (sin kx) 2)
53.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
21.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series262.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin ky) 2)
21.0ms	(pow (sin kx) 2)
118.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
104.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify3.6s

Counts

127 → 127

Iterations

Useful iterations: 3 (790.0ms)

Iter	Nodes	Cost
0	190	1895
1	375	1681
2	1204	1565
3	4416	1555
done	5000	1555

prune373.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.4b

regimes653.0ms

Accuracy

0% (1.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.0s	2684×	body	1280	valid
749.0ms	1759×	body	640	valid
225.0ms	821×	body	320	valid
207.0ms	2389×	body	80	valid
63.0ms	347×	body	160	valid