Details

sample623.0ms

Algorithm

intervals

Results

456.0ms	85×	body	1280	valid
50.0ms	62×	body	640	valid
11.0ms	75×	body	80	valid
9.0ms	19×	body	320	valid
5.0ms	15×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
4.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-l`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
14×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

91.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
38.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series689.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
169.0ms	(pow (sin kx) 2.0)
169.0ms	(pow (sin ky) 2.0)
110.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.2s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
2	1861
1	451
0	181

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b	(pow (sin ky) 2.0)
0.3b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
4.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
50×	`times-frac`
49×	`add-sqr-sqrt`
41×	`sqrt-prod`
40×	`add-cube-cbrt`
30×	`associate-r`
19×	`unpow-prod-down`
16×	`distribute-lft-out`
12×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `associate-/r*`
6×	`sqrt-div`
4×	`associate-/r/` `add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-l` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`pow-to-exp` `rem-sqrt-square` `clear-num` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `pow-exp` `associate-r/` `-commutative` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

112.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms	(pow (sin ky) 2.0)
54.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
41.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series653.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
153.0ms	(pow (sin ky) 2.0)
173.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
90.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify3.4s

Counts

145 → 145

Iterations

Iter	Nodes
done	5000
2	3086
1	471
0	195

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.3b	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
4.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

141×	`add-sqr-sqrt`
133×	`sqrt-prod`
111×	`times-frac`
94×	`*-un-lft-identity`
50×	`add-cube-cbrt`
39×	`associate-r` `associate-l`
28×	`unswap-sqr`
27×	`add-exp-log`
19×	`unpow-prod-down`
16×	`add-cbrt-cube` `distribute-lft-out`
12×	`sqrt-div`
9×	`pow1`
8×	`div-exp` `prod-exp`
4×	`cbrt-undiv` `flip3-+` `associate-/r/` `cbrt-unprod` `flip-+` `add-log-exp`
3×	`pow-unpow`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `div-inv`
1×	`frac-times` `pow-to-exp` `pow-pow` `pow-prod-down` `associate-l/` `pow-exp` `associate-r/` `*-commutative` `sqr-pow`

Counts

4 → 181

Calls

4 calls:

5.0ms	(pow (sin ky) 2.0)
215.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
43.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
41.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series639.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(pow (sin ky) 2.0)
219.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
119.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
128.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify4.0s

Counts

193 → 193

Iterations

Iter	Nodes
done	5001
2	4591
1	761
0	254

prune1.5s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 9.1b

localize112.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite122.0ms

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:

15.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
35.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
46.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
22.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series628.0ms

Counts

4 → 12

Calls

4 calls:

259.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
131.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
126.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
112.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.1s

Counts

102 → 102

Iterations

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

prune836.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 9.1b

regimes2.9s

Accuracy

58% (0.7b remaining)

Error of 11.8b against oracle of 11.1b and baseline of 12.8b

bsearch5.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	43
1	43
0	32

end0.0ms

sample9.2s

Algorithm

intervals

Results

4.5s	2710×	body	1280	valid
2.7s	1845×	body	640	valid
590.0ms	367×	body	160	valid
536.0ms	766×	body	320	valid
524.0ms	2312×	body	80	valid