Details

sample330.0ms

Algorithm

intervals

Results

148.0ms	83×	body	1280	valid
63.0ms	66×	body	640	valid
15.0ms	73×	body	80	valid
14.0ms	23×	body	320	valid
5.0ms	11×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.2b	(* (sin ky) (sin ky))
0.2b	(* (sin kx) (sin kx))
3.8b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite149.0ms

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` `insert-posit16` `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 → 119

Calls

4 calls:

84.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
12.0ms	(* (sin ky) (sin ky))
20.0ms	(* (sin kx) (sin kx))
27.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series436.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
37.0ms	(* (sin ky) (sin ky))
32.0ms	(* (sin kx) (sin kx))
131.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify2.3s

Counts

131 → 131

Iterations

Iter	Nodes
3	4912
2	1697
1	550
0	214

prune1.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.2b	(* (sin ky) (sin ky))
0.2b	(* (sin kx) (sin kx))
3.8b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite162.0ms

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` `insert-posit16` `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 → 119

Calls

4 calls:

108.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
23.0ms	(* (sin ky) (sin ky))
15.0ms	(* (sin kx) (sin kx))
13.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
32.0ms	(* (sin ky) (sin ky))
31.0ms	(* (sin kx) (sin kx))
133.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify2.3s

Counts

131 → 131

Iterations

Iter	Nodes
3	4912
2	1697
1	550
0	214

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.5b

localize74.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin ky))
3.8b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.8b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.8b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

3.0ms	(cbrt (sin ky))
24.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
15.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
18.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series487.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt (sin ky))
105.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
106.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
99.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify3.5s

Counts

75 → 75

Iterations

Iter	Nodes
4	3914
3	1416
2	496
1	206
0	96

prune1.7s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 10.5b

localize88.0ms

Local error

Found 4 expressions with local error:

0.9b	(sqrt (* (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
4.3b	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.3b	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
4.3b	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-div`
22×	`sin-mult`
15×	`sqrt-div`
12×	`pow1`
11×	`flip3-+` `frac-add` `flip-+`
9×	`cbrt-prod` `frac-times` `sqrt-pow1` `pow1/3`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`associate-l/` `associate-r/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 80

Calls

4 calls:

82.0ms	(sqrt (* (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
10.0ms	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
10.0ms	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
18.0ms	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series917.0ms

Counts

4 → 12

Calls

4 calls:

546.0ms	(sqrt (* (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
125.0ms	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
135.0ms	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
110.0ms	(cbrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.8s

Counts

92 → 92

Iterations

Iter	Nodes
4	2889
3	1211
2	535
1	254
0	145

prune1.7s

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 10.5b

regimes1.3s

Accuracy

0% (1.8b remaining)

Error of 12.9b against oracle of 11.2b and baseline of 12.9b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	21
1	21
0	18

end0.0ms

sample11.9s

Algorithm

intervals

Results

6.8s	2745×	body	1280	valid
3.1s	1875×	body	640	valid
764.0ms	2312×	body	80	valid
681.0ms	733×	body	320	valid
201.0ms	335×	body	160	valid