Details

sample523.0ms

Algorithm

intervals

Results

191.0ms	99×	body	1280	valid
113.0ms	57×	body	640	valid
19.0ms	73×	body	80	valid
14.0ms	21×	body	320	valid
3.0ms	6×	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

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
0.3b	(* (sin kx) (sin kx))
0.3b	(* (sin ky) (sin ky))
2.4b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite71.0ms

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:

26.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
11.0ms	(* (sin kx) (sin kx))
18.0ms	(* (sin ky) (sin ky))
13.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series350.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
24.0ms	(* (sin kx) (sin kx))
20.0ms	(* (sin ky) (sin ky))
110.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.8s

Counts

128 → 128

Iterations

Iter	Nodes
3	3803
2	1420
1	431
0	191

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.7b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
0.3b	(* (sin kx) (sin kx))
0.3b	(* (sin ky) (sin ky))
2.4b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
93×	`add-sqr-sqrt`
88×	`*-un-lft-identity` `add-cube-cbrt`
39×	`sqrt-prod`
22×	`associate-/r*`
20×	`pow1`
19×	`add-exp-log`
13×	`add-cbrt-cube`
7×	`div-exp`
6×	`swap-sqr` `associate-r` `associate-l`
5×	`div-inv`
4×	`insert-posit16` `sin-mult` `add-log-exp`
3×	`cbrt-undiv` `sqrt-div` `associate-/l*`
2×	`pow2` `rec-exp` `pow-plus` `1-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `sqr-sin` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `frac-add` `associate-/r/` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 186

Calls

4 calls:

13.0ms	(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
24.0ms	(* (sin kx) (sin kx))
13.0ms	(* (sin ky) (sin ky))
12.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series338.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
27.0ms	(* (sin kx) (sin kx))
21.0ms	(* (sin ky) (sin ky))
111.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify2.8s

Counts

198 → 198

Iterations

Iter	Nodes
2	2221
1	751
0	299

prune3.5s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 10.7b

localize59.0ms

Local error

Found 4 expressions with local error:

2.4b	(sqrt (+ (* (* (cbrt (* (sin kx) (sin kx))) (cbrt (* (sin kx) (sin kx)))) (cbrt (* (sin kx) (sin kx)))) (* (sin ky) (sin ky))))
15.0b	(cbrt (* (sin kx) (sin kx)))
15.0b	(cbrt (* (sin kx) (sin kx)))
15.0b	(cbrt (* (sin kx) (sin kx)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

22×	`sin-mult`
15×	`cbrt-div`
9×	`sqrt-div`
7×	`frac-add`
6×	`add-sqr-sqrt`
5×	`frac-times` `pow1` `-un-lft-identity` `associate-l/` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `associate-*r/` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 56

Calls

4 calls:

76.0ms	(sqrt (+ (* (* (cbrt (* (sin kx) (sin kx))) (cbrt (* (sin kx) (sin kx)))) (cbrt (* (sin kx) (sin kx)))) (* (sin ky) (sin ky))))
5.0ms	(cbrt (* (sin kx) (sin kx)))
9.0ms	(cbrt (* (sin kx) (sin kx)))
5.0ms	(cbrt (* (sin kx) (sin kx)))

series582.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sqrt (+ (* (* (cbrt (* (sin kx) (sin kx))) (cbrt (* (sin kx) (sin kx)))) (cbrt (* (sin kx) (sin kx)))) (* (sin ky) (sin ky))))
154.0ms	(cbrt (* (sin kx) (sin kx)))
139.0ms	(cbrt (* (sin kx) (sin kx)))
169.0ms	(cbrt (* (sin kx) (sin kx)))

simplify3.6s

Counts

68 → 68

Iterations

Iter	Nodes
4	5933
3	1810
2	693
1	294
0	132

prune1.4s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 10.7b

localize74.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (sin ky))
0.3b	(/ 1 (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
2.4b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
2.4b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

11.0ms	(* (sin ky) (sin ky))
37.0ms	(/ 1 (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
11.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
16.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series398.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (sin ky) (sin ky))
159.0ms	(/ 1 (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
103.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
110.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify2.0s

Counts

137 → 137

Iterations

Iter	Nodes
3	2539
2	1104
1	398
0	197

prune2.1s

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 10.7b

regimes1.0s

Accuracy

0% (1.2b remaining)

Error of 12.4b against oracle of 11.2b and baseline of 12.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	16
1	16
0	14

end0.0ms

sample11.5s

Algorithm

intervals

Results

5.8s	2752×	body	1280	valid
3.3s	1826×	body	640	valid
1.0s	733×	body	320	valid
872.0ms	2367×	body	80	valid
220.0ms	322×	body	160	valid