Details

sample108.0ms

Algorithm

intervals

Results

57.0ms	84×	body	1280	valid
22.0ms	55×	body	640	valid
7.0ms	26×	body	320	valid
7.0ms	80×	body	80	valid
2.0ms	11×	body	160	valid

simplify2.7s

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	3183	16
done	5000	16

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite39.0ms

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)
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series412.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
106.0ms	(pow (sin ky) 2.0)
104.0ms	(pow (sin kx) 2.0)
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.3s

Counts

112 → 112

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	170	1738
1	330	1550
2	815	1503
3	2660	1503
done	5000	1503

prune383.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2)
0.3b	(pow (sin kx) 2)
0.3b	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
3.7b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite76.0ms

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)
47.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
22.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series256.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin ky) 2)
18.0ms	(pow (sin kx) 2)
120.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
100.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify1.3s

Counts

127 → 127

Iterations

Useful iterations: 3 (463.0ms)

Iter	Nodes	Cost
0	190	1895
1	366	1664
2	849	1565
3	2385	1555
done	5000	1555

prune451.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 11.5b

localize25.0ms

Local error

Found 4 expressions with local error:

3.7b	(sqrt (/ 1 (+ (* (* (cbrt (pow (sin kx) 2)) (cbrt (pow (sin kx) 2))) (cbrt (pow (sin kx) 2))) (pow (sin ky) 2))))
14.8b	(cbrt (pow (sin kx) 2))
14.8b	(cbrt (pow (sin kx) 2))
14.8b	(cbrt (pow (sin kx) 2))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
21×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`sqrt-prod`
11×	`times-frac`
9×	`unpow-prod-down`
6×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/3` `unpow2` `sqr-pow`
2×	`associate-/r/`
1×	`pow-flip` `flip3-+` `pow1/2` `sqrt-div` `flip-+` `div-inv` `inv-pow`

Counts

4 → 78

Calls

4 calls:

49.0ms	(sqrt (/ 1 (+ (* (* (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))
1.0ms	(cbrt (pow (sin kx) 2))

series450.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(sqrt (/ 1 (+ (* (* (cbrt (pow (sin kx) 2)) (cbrt (pow (sin kx) 2))) (cbrt (pow (sin kx) 2))) (pow (sin ky) 2))))
112.0ms	(cbrt (pow (sin kx) 2))
112.0ms	(cbrt (pow (sin kx) 2))
115.0ms	(cbrt (pow (sin kx) 2))

simplify1.0s

Counts

90 → 90

Iterations

Useful iterations: 3 (264.0ms)

Iter	Nodes	Cost
0	135	1736
1	258	1591
2	576	909
3	1761	899
done	5000	899

prune386.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 11.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
3.6b	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
13.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series557.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt (sin kx))
97.0ms	(cbrt (sin kx))
95.0ms	(cbrt (sin kx))
267.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify976.0ms

Counts

60 → 60

Iterations

Useful iterations: 3 (200.0ms)

Iter	Nodes	Cost
0	81	818
1	187	744
2	481	620
3	1608	609
done	5000	609

prune255.0ms

Pruning

25 alts after pruning (23 fresh and 2 done)

Merged error: 11.5b

regimes1.1s

Accuracy

58.6% (0.8b remaining)

Error of 12.4b against oracle of 11.6b and baseline of 13.4b

bsearch4.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	57
1	41	57
done	41	57

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.0s	2736×	body	1280	valid
734.0ms	1776×	body	640	valid
242.0ms	2390×	body	80	valid
204.0ms	742×	body	320	valid
63.0ms	356×	body	160	valid