Details

sample350.0ms

Algorithm

intervals

Results

179.0ms	91×	body	1280	valid
49.0ms	58×	body	640	valid
17.0ms	71×	body	80	valid
16.0ms	24×	body	320	valid
4.0ms	12×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	632
4	140
3	64
2	35
1	23
0	13

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite96.0ms

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×	`associate-/r*` `add-exp-log`
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` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 100

Calls

4 calls:

36.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms	(pow (sin kx) 2.0)
5.0ms	(pow (sin ky) 2.0)
47.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series643.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
144.0ms	(pow (sin kx) 2.0)
166.0ms	(pow (sin ky) 2.0)
143.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify727.0ms

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	1591
1	382
0	170

prune778.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.6b

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite141.0ms

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×	`flip3-+` `add-cbrt-cube` `add-exp-log` `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:

30.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
44.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
40.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
21.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series602.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
111.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
113.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
114.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.7s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	3607
2	844
1	289
0	160

prune1.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.6b

localize73.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin ky))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

2.0ms	(cbrt (sin ky))
45.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
43.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
53.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt (sin ky))
128.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
101.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
94.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify929.0ms

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
3	1796
2	503
1	179
0	81

prune700.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 8.6b

localize63.0ms

Local error

Found 4 expressions with local error:

2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

22.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
38.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
24.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
22.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series516.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
149.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
126.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
137.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify764.0ms

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
3	1299
2	334
1	121
0	54

prune756.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 8.6b

regimes2.0s

Accuracy

0% (1.7b remaining)

Error of 12.7b against oracle of 11.0b and baseline of 12.7b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	23
1	23
0	19

end0.0ms

sample9.7s

Algorithm

intervals

Results

5.3s	2672×	body	1280	valid
2.5s	1912×	body	640	valid
619.0ms	761×	body	320	valid
552.0ms	2276×	body	80	valid
228.0ms	379×	body	160	valid