Details

sample416.0ms

Algorithm

intervals

Results

198.0ms	86×	body	1280	valid
78.0ms	59×	body	640	valid
22.0ms	30×	body	320	valid
18.0ms	72×	body	80	valid
5.0ms	9×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
7	2001
6	850
5	327
4	155
3	80
2	49
1	25
0	13

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
0.3b	(* (sin ky) (sin ky))
0.3b	(* (sin kx) (sin kx))
2.5b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite79.0ms

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:

27.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
11.0ms	(* (sin ky) (sin ky))
13.0ms	(* (sin kx) (sin kx))
25.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series733.0ms

Counts

4 → 12

Calls

4 calls:

558.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
23.0ms	(* (sin ky) (sin ky))
19.0ms	(* (sin kx) (sin kx))
133.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.5s

Counts

128 → 128

Iterations

Iter	Nodes
done	2000
3	2000
2	1848
1	442
0	191

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
2.5b	(sqrt (+ (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (sin kx))) (* (sin ky) (sin ky))))

rewrite83.0ms

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:

1.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
79.0ms	(sqrt (+ (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (sin kx))) (* (sin ky) (sin ky))))

series496.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(cbrt (sin kx))
124.0ms	(cbrt (sin kx))
142.0ms	(cbrt (sin kx))
105.0ms	(sqrt (+ (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (sin kx))) (* (sin ky) (sin ky))))

simplify1.6s

Counts

64 → 64

Iterations

Iter	Nodes
done	2001
4	2001
3	1925
2	582
1	189
0	81

prune982.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.1b

localize73.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
2.5b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
2.5b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
2.5b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
12×	`sqrt-div`
8×	`sin-mult`
7×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 86

Calls

4 calls:

24.0ms	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
23.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
24.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
14.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series554.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
105.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
133.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
115.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.3s

Counts

98 → 98

Iterations

Iter	Nodes
done	2001
3	2001
2	731
1	314
0	172

prune2.0s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 11.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin kx) (sin kx))
0.4b	(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
2.5b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
2.5b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite60.0ms

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:

14.0ms	(* (sin kx) (sin kx))
21.0ms	(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
12.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
12.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series444.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (sin kx) (sin kx))
202.0ms	(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
101.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
108.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.3s

Counts

129 → 129

Iterations

Iter	Nodes
done	2012
3	2012
2	1392
1	434
0	199

prune2.2s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 11.1b

regimes1.1s

Accuracy

0% (1.3b remaining)

Error of 12.5b against oracle of 11.2b and baseline of 12.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample11.7s

Algorithm

intervals

Results

6.5s	2634×	body	1280	valid
3.3s	1905×	body	640	valid
740.0ms	780×	body	320	valid
673.0ms	2313×	body	80	valid
302.0ms	368×	body	160	valid