Details

sample432.0ms

Algorithm

intervals

Results

212.0ms	91×	body	1280	valid
50.0ms	57×	body	640	valid
13.0ms	21×	body	320	valid
13.0ms	69×	body	80	valid
8.0ms	18×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
7	3061
6	850
5	327
4	155
3	80
2	49
1	25
0	13

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
0.2b	(pow (sin kx) 2)
0.3b	(pow (sin ky) 2)
3.7b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite93.0ms

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` `insert-posit16` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 107

Calls

4 calls:

65.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
3.0ms	(pow (sin kx) 2)
3.0ms	(pow (sin ky) 2)
19.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
37.0ms	(pow (sin kx) 2)
28.0ms	(pow (sin ky) 2)
115.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify2.5s

Counts

119 → 119

Iterations

Iter	Nodes
done	5036
3	3826
2	1251
1	448
0	182

prune1.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.6b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.3b	(/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
0.3b	(* (sin ky) (sin ky))
3.7b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
38×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
28×	`associate-r`
25×	`sqrt-prod`
14×	`pow1`
13×	`add-cbrt-cube` `add-exp-log`
9×	`sqrt-div`
7×	`sin-mult`
6×	`associate-/r` `associate-l*` `associate-/r/`
4×	`insert-posit16` `add-log-exp` `unswap-sqr`
3×	`flip3-+` `swap-sqr` `frac-add` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`pow2` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `associate-*r/` `pow-sqr` `pow-prod-up` `sqr-sin`

Counts

4 → 134

Calls

4 calls:

93.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
39.0ms	(/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
22.0ms	(* (sin ky) (sin ky))
30.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series497.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
184.0ms	(/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
20.0ms	(* (sin ky) (sin ky))
92.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify2.3s

Counts

146 → 146

Iterations

Iter	Nodes
done	5000
2	1554
1	500
0	208

prune906.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 12.6b

localize68.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2)
0.5b	(* (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
3.7b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
3.7b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

100×	`sqrt-prod`
52×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
34×	`sqrt-pow1`
30×	`pow1`
28×	`sqrt-div`
20×	`add-cube-cbrt`
19×	`swap-sqr`
18×	`pow1/2`
15×	`unpow-prod-down`
14×	`distribute-lft-out`
11×	`associate-r` `associate-l`
9×	`pow-prod-up` `unswap-sqr`
8×	`flip3-+` `flip-+`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `insert-posit16` `add-log-exp`
3×	`pow-unpow`
2×	`rem-sqrt-square` `associate-l/` `associate-r/`
1×	`pow2` `pow-to-exp` `rem-square-sqrt` `pow-pow` `pow-plus` `sqrt-unprod` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `unpow2` `sqr-pow`

Counts

4 → 147

Calls

4 calls:

3.0ms	(pow (sin ky) 2)
129.0ms	(* (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
37.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
16.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (sin ky) 2)
128.0ms	(* (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
91.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
107.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify1.8s

Counts

159 → 159

Iterations

Iter	Nodes
done	5001
3	1837
2	774
1	356
0	165

prune1.1s

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 12.6b

localize116.0ms

Local error

Found 4 expressions with local error:

3.7b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
3.7b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
3.7b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
3.7b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite89.0ms

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-+` `insert-posit16` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

18.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
17.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
28.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
25.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
115.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
88.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
94.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify3.6s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
5	4929
4	1387
3	620
2	278
1	111
0	52

prune760.0ms

Pruning

18 alts after pruning (15 fresh and 3 done)

Merged error: 12.6b

regimes2.0s

Accuracy

0% (1.2b remaining)

Error of 12.7b against oracle of 11.4b and baseline of 12.7b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	14
1	14
0	12

end0.0ms

sample9.1s

Algorithm

intervals

Results

4.8s	2735×	body	1280	valid
2.8s	1852×	body	640	valid
581.0ms	766×	body	320	valid
477.0ms	2264×	body	80	valid
172.0ms	383×	body	160	valid