Details

sample114.0ms

Algorithm

intervals

Results

60.0ms	85×	body	1280	valid
24.0ms	61×	body	640	valid
6.0ms	74×	body	80	valid
6.0ms	25×	body	320	valid
2.0ms	11×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	10
1	35	10
2	63	10
3	137	10
4	417	10
5	1798	10
6	5002	10
done	5002	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

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)
0.3b	(pow (sin kx) 2.0)
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite74.0ms

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:

34.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms	(pow (sin ky) 2.0)
4.0ms	(pow (sin kx) 2.0)
30.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
109.0ms	(pow (sin ky) 2.0)
107.0ms	(pow (sin kx) 2.0)
85.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify37.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	329	1021
1	1106	946
2	5002	943
done	5002	943

prune366.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
150×	`*-un-lft-identity`
99×	`add-sqr-sqrt`
98×	`add-cube-cbrt`
65×	`sqrt-prod`
32×	`unpow-prod-down`
28×	`associate-/r*`
26×	`distribute-lft-out`
17×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
7×	`div-exp`
6×	`pow-unpow`
5×	`div-inv`
4×	`add-log-exp`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow-to-exp` `rec-exp` `pow-pow` `sqrt-div` `1-exp` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `clear-num` `associate-/r/` `flip-+` `inv-pow`

Counts

4 → 187

Calls

4 calls:

39.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
3.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
28.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
109.0ms	(pow (sin ky) 2.0)
109.0ms	(pow (sin kx) 2.0)
84.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify70.0ms

Counts

199 → 199

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	642	2588
1	2882	2325
2	5003	2177
done	5003	2177

prune437.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite102.0ms

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

17.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
25.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
30.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
26.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
85.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
84.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
86.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify99.0ms

Counts

102 → 102

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	282	1291
1	819	1231
2	3475	1224
3	5002	1219
done	5002	1219

prune461.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 12.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky))) (cbrt (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky))))
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite241.0ms

Algorithm

rewrite-expression-head

Rules

160×	`cbrt-prod`
157×	`*-un-lft-identity`
142×	`add-sqr-sqrt`
136×	`times-frac`
101×	`sqrt-prod`
79×	`add-cube-cbrt`
43×	`swap-sqr`
36×	`distribute-lft-out`
31×	`associate-r` `associate-l`
30×	`unpow-prod-down`
16×	`unswap-sqr`
14×	`pow1`
6×	`add-exp-log` `pow1/3` `sqrt-div`
4×	`cbrt-div` `add-cbrt-cube` `div-inv` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 193

Calls

4 calls:

146.0ms	(* (cbrt (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky))) (cbrt (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky))))
26.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
25.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
28.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(* (cbrt (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky))) (cbrt (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky))))
83.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
83.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
85.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify71.0ms

Counts

205 → 205

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	371	4481
1	1267	4327
2	5002	4104
done	5002	4104

prune733.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 12.4b

regimes1.1s

Accuracy

0% (1.7b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	20
1	23	20
done	23	20

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.0s	2711×	body	1280	valid
777.0ms	1891×	body	640	valid
373.0ms	2308×	body	80	valid
216.0ms	793×	body	320	valid
52.0ms	297×	body	160	valid