Details

sample403.0ms

Algorithm

intervals

Results

182.0ms	88×	body	1280	valid
65.0ms	68×	body	640	valid
16.0ms	25×	body	320	valid
13.0ms	65×	body	80	valid
4.0ms	10×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
7	3061
6	850
5	327
4	155
3	80
2	49
1	25
0	13

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
0.2b	(pow (sin kx) 2)
0.3b	(pow (sin ky) 2)
3.6b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
16×	`unpow-prod-down`
10×	`distribute-lft-out`
8×	`associate-/r*` `add-exp-log`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 106

Calls

4 calls:

40.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
17.0ms	(pow (sin kx) 2)
7.0ms	(pow (sin ky) 2)
58.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
36.0ms	(pow (sin kx) 2)
36.0ms	(pow (sin ky) 2)
121.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify2.0s

Counts

118 → 118

Iterations

Iter	Nodes
done	5010
3	2546
2	999
1	383
0	171

prune793.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
0.2b	(* (sin kx) (sin kx))
0.3b	(* (sin ky) (sin ky))
3.6b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite111.0ms

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:

39.0ms	(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
13.0ms	(* (sin kx) (sin kx))
19.0ms	(* (sin ky) (sin ky))
27.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series406.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ 1 (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)))
33.0ms	(* (sin kx) (sin kx))
34.0ms	(* (sin ky) (sin ky))
140.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify2.8s

Counts

198 → 198

Iterations

Iter	Nodes
done	5000
2	2325
1	764
0	299

prune946.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.2b

localize87.0ms

Local error

Found 4 expressions with local error:

3.6b	(sqrt (+ (* (* (cbrt (pow (sin kx) 2)) (cbrt (pow (sin kx) 2))) (cbrt (pow (sin kx) 2))) (pow (sin ky) 2)))
12.4b	(cbrt (pow (sin kx) 2))
12.4b	(cbrt (pow (sin kx) 2))
12.4b	(cbrt (pow (sin kx) 2))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`unpow-prod-down`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3` `sqrt-prod` `unpow2` `sqr-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 67

Calls

4 calls:

105.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2)) (cbrt (pow (sin kx) 2))) (cbrt (pow (sin kx) 2))) (pow (sin ky) 2)))
3.0ms	(cbrt (pow (sin kx) 2))
4.0ms	(cbrt (pow (sin kx) 2))
6.0ms	(cbrt (pow (sin kx) 2))

series558.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2)) (cbrt (pow (sin kx) 2))) (cbrt (pow (sin kx) 2))) (pow (sin ky) 2)))
142.0ms	(cbrt (pow (sin kx) 2))
131.0ms	(cbrt (pow (sin kx) 2))
180.0ms	(cbrt (pow (sin kx) 2))

simplify1.9s

Counts

79 → 79

Iterations

Iter	Nodes
done	5002
3	1603
2	505
1	204
0	93

prune801.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 10.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
0.4b	(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
3.6b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.6b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
141×	`sqrt-prod`
126×	`times-frac`
78×	`*-un-lft-identity`
66×	`add-cube-cbrt`
34×	`associate-r` `associate-l`
28×	`add-exp-log` `unswap-sqr`
24×	`sqrt-div`
18×	`add-cbrt-cube`
10×	`sin-mult`
9×	`associate-/r*` `div-exp` `associate-/r/`
8×	`pow1` `prod-exp`
5×	`cbrt-undiv` `flip3-+` `frac-add` `flip-+`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 210

Calls

4 calls:

198.0ms	(* (/ 1 (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
26.0ms	(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
32.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
20.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series603.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (/ 1 (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))))
242.0ms	(/ (sin ky) (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
107.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
115.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify3.3s

Counts

222 → 222

Iterations

Iter	Nodes
done	5001
2	2352
1	749
0	271

prune1.1s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 10.2b

regimes2.0s

Accuracy

0% (1.5b remaining)

Error of 13.0b against oracle of 11.5b and baseline of 13.0b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	19
1	19
0	16

end0.0ms

sample8.9s

Algorithm

intervals

Results

5.7s	2646×	body	1280	valid
1.8s	1814×	body	640	valid
621.0ms	772×	body	320	valid
449.0ms	2393×	body	80	valid
127.0ms	375×	body	160	valid