Details

sample528.0ms

Algorithm

intervals

Results

290.0ms	87×	body	1280	valid
68.0ms	63×	body	640	valid
50.0ms	79×	body	80	valid
10.0ms	15×	body	320	valid
6.0ms	12×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
7	3444
6	999
5	390
4	174
3	84
2	49
1	25
0	13

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize42.0ms

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))
4.8b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite69.0ms

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:

20.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
21.0ms	(* (sin ky) (sin ky))
11.0ms	(* (sin kx) (sin kx))
14.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series364.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
21.0ms	(* (sin ky) (sin ky))
21.0ms	(* (sin kx) (sin kx))
152.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify2.4s

Counts

128 → 128

Iterations

Iter	Nodes
3	3659
2	1381
1	430
0	191

prune1.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.0b

localize42.0ms

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 ky) (sin ky))
0.3b	(* (sin kx) (sin kx))
4.8b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite94.0ms

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:

27.0ms	(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
22.0ms	(* (sin ky) (sin ky))
26.0ms	(* (sin kx) (sin kx))
12.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series346.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
27.0ms	(* (sin ky) (sin ky))
19.0ms	(* (sin kx) (sin kx))
112.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify741.0ms

Counts

198 → 198

Iterations

Iter	Nodes
2	2068
1	750
0	299

prune2.9s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 13.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (sin ky))
0.3b	(* (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky))
0.3b	(* (sin kx) (sin kx))
4.8b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
31×	`associate-l`
29×	`*-un-lft-identity`
27×	`add-cube-cbrt`
22×	`times-frac`
21×	`pow1`
17×	`add-exp-log`
14×	`sqrt-prod`
13×	`add-cbrt-cube`
9×	`associate-r`
7×	`unswap-sqr`
6×	`sqrt-div` `swap-sqr` `prod-exp` `sin-mult`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow-prod-down` `associate-/r/` `*-commutative`
2×	`pow2` `flip3-+` `pow-plus` `div-exp` `frac-add` `pow-sqr` `pow-prod-up` `flip-+` `sqr-sin`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-*l/` `div-inv`

Counts

4 → 123

Calls

4 calls:

13.0ms	(* (sin ky) (sin ky))
82.0ms	(* (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky))
21.0ms	(* (sin kx) (sin kx))
22.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series322.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (sin ky) (sin ky))
151.0ms	(* (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky))
25.0ms	(* (sin kx) (sin kx))
109.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify3.5s

Counts

135 → 135

Iterations

Iter	Nodes
3	5182
2	1945
1	510
0	205

prune1.9s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 13.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
4.8b	(sqrt (+ (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (sin kx))) (* (sin ky) (sin ky))))

rewrite72.0ms

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))
67.0ms	(sqrt (+ (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (sin kx))) (* (sin ky) (sin ky))))

series545.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (sin kx))
123.0ms	(cbrt (sin kx))
172.0ms	(cbrt (sin kx))
99.0ms	(sqrt (+ (* (* (cbrt (sin kx)) (cbrt (sin kx))) (* (cbrt (sin kx)) (sin kx))) (* (sin ky) (sin ky))))

simplify5.1s

Counts

64 → 64

Iterations

Iter	Nodes
4	6859
3	1946
2	584
1	189
0	81

prune1.0s

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 13.0b

regimes1.4s

Accuracy

0% (1.3b remaining)

Error of 12.3b against oracle of 10.9b and baseline of 12.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	19
1	19
0	14

end0.0ms

sample12.5s

Algorithm

intervals

Results

6.8s	2772×	body	1280	valid
3.7s	1833×	body	640	valid
767.0ms	2267×	body	80	valid
705.0ms	783×	body	320	valid
238.0ms	345×	body	160	valid