Details

sample338.0ms

Algorithm

intervals

Results

134.0ms	101×	body	1280	valid
83.0ms	54×	body	640	valid
14.0ms	71×	body	80	valid
13.0ms	22×	body	320	valid
3.0ms	8×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
7	3496
6	1008
5	394
4	173
3	82
2	47
1	25
0	13

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
0.3b	(* (sin kx) (sin kx))
0.3b	(* (sin ky) (sin ky))
4.3b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

34.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
12.0ms	(* (sin kx) (sin kx))
18.0ms	(* (sin ky) (sin ky))
20.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
27.0ms	(* (sin kx) (sin kx))
20.0ms	(* (sin ky) (sin ky))
127.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify2.2s

Counts

128 → 128

Iterations

Iter	Nodes
3	3803
2	1420
1	431
0	191

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.8b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (sin ky))
0.4b	(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
4.3b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.3b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

20.0ms	(* (sin ky) (sin ky))
45.0ms	(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
24.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
25.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (sin ky) (sin ky))
185.0ms	(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
108.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
116.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify2.7s

Counts

129 → 129

Iterations

Iter	Nodes
3	3277
2	1099
1	403
0	195

prune1.6s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.8b

localize50.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
4.3b	(sqrt (+ (* (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (sin ky) (sin ky))))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 52

Calls

4 calls:

2.0ms	(cbrt (sin kx))
2.0ms	(cbrt (sin kx))
4.0ms	(cbrt (sin kx))
286.0ms	(sqrt (+ (* (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (sin ky) (sin ky))))

series543.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (sin kx))
156.0ms	(cbrt (sin kx))
123.0ms	(cbrt (sin kx))
127.0ms	(sqrt (+ (* (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (cbrt (sin kx)) (cbrt (sin kx)))) (* (sin ky) (sin ky))))

simplify5.8s

Counts

64 → 64

Iterations

Iter	Nodes
4	8159
3	1726
2	522
1	196
0	81

prune868.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 10.8b

localize73.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ (sin ky) (sqrt (fabs (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (sqrt (sqrt (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
4.3b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.8b	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.8b	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

498×	`times-frac`
465×	`sqrt-prod`
269×	`add-sqr-sqrt`
268×	`*-un-lft-identity` `add-cube-cbrt`
75×	`cbrt-prod`
22×	`associate-/l*`
14×	`div-inv`
12×	`associate-/r*`
9×	`cbrt-div` `add-cbrt-cube` `sqrt-div` `add-exp-log`
8×	`sin-mult`
5×	`pow1`
4×	`flip3-+` `frac-add` `flip-+` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/r/`
2×	`pow1/3`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 364

Calls

4 calls:

29.0ms	(/ (/ (sin ky) (sqrt (fabs (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (sqrt (sqrt (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
18.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
15.0ms	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
10.0ms	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series564.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(/ (/ (sin ky) (sqrt (fabs (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))) (sqrt (sqrt (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
82.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
124.0ms	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
134.0ms	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify2.4s

Counts

376 → 376

Iterations

Iter	Nodes
2	2926
1	1139
0	526

prune6.3s

Pruning

17 alts after pruning (14 fresh and 3 done)

Merged error: 10.8b

regimes1.1s

Accuracy

0% (1.6b remaining)

Error of 12.3b against oracle of 10.7b and baseline of 12.3b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	16
1	16
0	14

end0.0ms

sample11.9s

Algorithm

intervals

Results

6.5s	2755×	body	1280	valid
2.9s	1787×	body	640	valid
1.1s	756×	body	320	valid
888.0ms	2351×	body	80	valid
196.0ms	351×	body	160	valid