Details

sample356.0ms

Algorithm

intervals

Results

133.0ms	88×	body	1280	valid
35.0ms	54×	body	640	valid
12.0ms	23×	body	320	valid
11.0ms	80×	body	80	valid
4.0ms	11×	body	160	valid

simplify4.0s

Counts

1 → 1

Iterations

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

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.4b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
0.2b	(pow (sin ky) 2)
0.2b	(pow (sin kx) 2)
3.6b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite206.0ms

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:

135.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
7.0ms	(pow (sin ky) 2)
8.0ms	(pow (sin kx) 2)
47.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th))
22.0ms	(pow (sin ky) 2)
22.0ms	(pow (sin kx) 2)
134.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify2.5s

Counts

119 → 119

Iterations

Iter	Nodes
done	5020
3	3411
2	1237
1	448
0	182

prune901.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.5b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin th) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
0.2b	(pow (sin ky) 2)
0.2b	(pow (sin kx) 2)
3.6b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-r`
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-l` `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-r/` `-commutative` `div-inv`

Counts

4 → 107

Calls

4 calls:

114.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
4.0ms	(pow (sin ky) 2)
4.0ms	(pow (sin kx) 2)
39.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
21.0ms	(pow (sin ky) 2)
34.0ms	(pow (sin kx) 2)
135.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify2.5s

Counts

119 → 119

Iterations

Iter	Nodes
done	5028
3	3946
2	1478
1	506
0	195

prune817.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 10.5b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin kx) (sin kx))
0.3b	(/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
3.6b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite179.0ms

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:

22.0ms	(* (sin kx) (sin kx))
23.0ms	(/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
99.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
27.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series538.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (sin kx) (sin kx))
169.0ms	(/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
221.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
113.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify3.1s

Counts

146 → 146

Iterations

Iter	Nodes
done	5001
2	1891
1	518
0	212

prune989.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 10.5b

localize81.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
3.6b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
3.6b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
3.6b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite169.0ms

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-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 94

Calls

4 calls:

35.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
53.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
44.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
31.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series551.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
104.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
104.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
116.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify1.9s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
3	2124
2	680
1	280
0	159

prune768.0ms

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 10.5b

regimes2.1s

Accuracy

0% (1.4b remaining)

Error of 12.7b against oracle of 11.2b and baseline of 12.7b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	12

end0.0ms

sample9.2s

Algorithm

intervals

Results

5.1s	2716×	body	1280	valid
2.3s	1885×	body	640	valid
1.0s	751×	body	320	valid
441.0ms	2301×	body	80	valid
118.0ms	347×	body	160	valid