Details

sample428.0ms

Algorithm

intervals

Results

131.0ms	77×	body	1280	valid
114.0ms	65×	body	640	valid
28.0ms	23×	body	320	valid
20.0ms	77×	body	80	valid
8.0ms	14×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize58.0ms

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))
0.3b	(* (sin kx) (sin kx))
3.9b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite145.0ms

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))))))
19.0ms	(* (sin ky) (sin ky))
14.0ms	(* (sin kx) (sin kx))
23.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
26.0ms	(* (sin ky) (sin ky))
21.0ms	(* (sin kx) (sin kx))
150.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.0s

Counts

131 → 131

Iterations

Iter	Nodes
done	2002
2	2002
1	563
0	214

prune845.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin kx) (sin kx))
0.5b	(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
3.9b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.9b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
56×	`add-sqr-sqrt`
54×	`sqrt-div`
36×	`pow1`
34×	`sqrt-pow1`
22×	`*-un-lft-identity` `add-cube-cbrt`
21×	`sin-mult`
18×	`pow1/2` `swap-sqr`
12×	`associate-r` `associate-l`
10×	`flip3-+` `frac-add` `pow-prod-up` `flip-+` `unswap-sqr`
9×	`frac-times`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow-prod-down` `pow-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`associate-l/` `associate-r/`
2×	`pow2` `rem-sqrt-square` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`rem-square-sqrt` `sqrt-unprod` `sqr-sin`

Counts

4 → 153

Calls

4 calls:

12.0ms	(* (sin kx) (sin kx))
145.0ms	(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (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))))

series334.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (sin kx) (sin kx))
106.0ms	(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
97.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
107.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.3s

Counts

165 → 165

Iterations

Iter	Nodes
done	2001
3	2001
2	1145
1	410
0	191

prune960.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 12.1b

localize65.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
3.9b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.9b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.9b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite77.0ms

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:

12.0ms	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
24.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
24.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
16.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series525.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
96.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
115.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
98.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.2s

Counts

98 → 98

Iterations

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

prune837.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 12.1b

localize72.0ms

Local error

Found 4 expressions with local error:

3.9b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.9b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.9b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.9b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

24.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
25.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
24.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
33.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series482.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
115.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
113.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
117.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.1s

Counts

80 → 80

Iterations

Iter	Nodes
done	2000
4	2000
3	874
2	363
1	150
0	68

prune794.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 12.1b

regimes1.1s

Accuracy

0% (1.6b remaining)

Error of 13.1b against oracle of 11.5b and baseline of 13.1b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	16
1	16
0	14

end0.0ms

sample12.2s

Algorithm

intervals

Results

6.7s	2666×	body	1280	valid
3.4s	1855×	body	640	valid
779.0ms	787×	body	320	valid
771.0ms	2336×	body	80	valid
220.0ms	356×	body	160	valid