Details

sample439.0ms

Algorithm

intervals

Results

174.0ms	94×	body	1280	valid
65.0ms	53×	body	640	valid
47.0ms	18×	body	320	valid
24.0ms	76×	body	80	valid
9.0ms	15×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize64.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.3b	(* (sin ky) (sin ky))
0.3b	(* (sin kx) (sin kx))
4.0b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
31×	`associate-r`
27×	`*-un-lft-identity` `add-cube-cbrt`
21×	`pow1`
20×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
9×	`associate-l`
6×	`sqrt-div` `swap-sqr` `sin-mult`
5×	`unswap-sqr`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`pow-prod-down` `associate-/r/` `*-commutative`
2×	`pow2` `flip3-+` `pow-plus` `frac-add` `pow-sqr` `pow-prod-up` `flip-+` `sqr-sin`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*r/` `div-inv`

Counts

4 → 115

Calls

4 calls:

76.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
16.0ms	(* (sin ky) (sin ky))
19.0ms	(* (sin kx) (sin kx))
24.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series435.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
33.0ms	(* (sin ky) (sin ky))
32.0ms	(* (sin kx) (sin kx))
156.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify2.6s

Counts

127 → 127

Iterations

Iter	Nodes
3	4976
2	1850
1	545
0	210

prune1.6s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.4b

localize36.0ms

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))))))
4.0b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.0b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite64.0ms

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×	`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 → 113

Calls

4 calls:

19.0ms	(* (sin kx) (sin kx))
18.0ms	(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
10.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
15.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series438.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (sin kx) (sin kx))
205.0ms	(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
88.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
110.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.1s

Counts

125 → 125

Iterations

Iter	Nodes
3	2608
2	1158
1	422
0	196

prune2.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.4b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin kx) (sin kx))
0.3b	(* (sin ky) (/ 1 (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
4.0b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.0b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
39×	`sqrt-prod`
37×	`associate-r`
33×	`*-un-lft-identity` `times-frac`
30×	`add-cube-cbrt`
15×	`pow1` `add-exp-log`
12×	`sqrt-div`
11×	`add-cbrt-cube`
8×	`unswap-sqr`
7×	`sin-mult`
6×	`associate-l`
5×	`prod-exp`
4×	`add-log-exp`
3×	`flip3-+` `swap-sqr` `frac-add` `associate-/r/` `cbrt-unprod` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `*-commutative`
1×	`pow2` `cbrt-undiv` `rec-exp` `pow-plus` `1-exp` `associate-*r/` `pow-sqr` `un-div-inv` `pow-prod-up` `sqr-sin` `div-inv`

Counts

4 → 120

Calls

4 calls:

19.0ms	(* (sin kx) (sin kx))
53.0ms	(* (sin ky) (/ 1 (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
10.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
11.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (sin kx) (sin kx))
178.0ms	(* (sin ky) (/ 1 (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))))

simplify3.9s

Counts

132 → 132

Iterations

Iter	Nodes
3	3482
2	1571
1	558
0	220

prune2.3s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 11.4b

localize96.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
4.0b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.0b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.0b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite70.0ms

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

Counts

4 → 82

Calls

4 calls:

22.0ms	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
21.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
12.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
13.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series588.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
96.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
135.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
132.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify3.5s

Counts

94 → 94

Iterations

Iter	Nodes
4	5373
3	1815
2	686
1	309
0	170

prune1.5s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 11.4b

regimes1.0s

Accuracy

0% (1.5b remaining)

Error of 12.7b against oracle of 11.1b and baseline of 12.7b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	19
1	19
0	16

end0.0ms

sample12.3s

Algorithm

intervals

Results

7.8s	2817×	body	1280	valid
2.6s	1844×	body	640	valid
904.0ms	722×	body	320	valid
624.0ms	2282×	body	80	valid
181.0ms	335×	body	160	valid