Details

sample411.0ms

Algorithm

intervals

Results

144.0ms	81×	body	1280	valid
59.0ms	61×	body	640	valid
44.0ms	12×	body	160	valid
17.0ms	82×	body	80	valid
13.0ms	20×	body	320	valid

simplify1.5s

Counts

1 → 1

Iterations

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

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
0.2b	(* (sin ky) (sin ky))
0.3b	(* (sin kx) (sin kx))
3.4b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite124.0ms

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:

40.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
32.0ms	(* (sin ky) (sin ky))
22.0ms	(* (sin kx) (sin kx))
25.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series359.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
21.0ms	(* (sin ky) (sin ky))
29.0ms	(* (sin kx) (sin kx))
134.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify2.3s

Counts

128 → 128

Iterations

Iter	Nodes
3	3659
2	1381
1	430
0	191

prune1.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))
0.2b	(* (sin ky) (sin ky))
0.3b	(* (sin kx) (sin kx))
3.4b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite82.0ms

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×	`sqrt-div` `swap-sqr` `associate-r` `associate-l` `sin-mult` `associate-/l*`
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	(/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))
16.0ms	(* (sin ky) (sin ky))
29.0ms	(* (sin kx) (sin kx))
15.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series388.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))
32.0ms	(* (sin ky) (sin ky))
35.0ms	(* (sin kx) (sin kx))
129.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.4s

Counts

128 → 128

Iterations

Iter	Nodes
3	3113
2	1233
1	436
0	188

prune2.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky))
0.3b	(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky)))
3.4b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.4b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

99×	`sqrt-prod`
85×	`add-sqr-sqrt`
63×	`times-frac`
50×	`*-un-lft-identity` `add-cube-cbrt`
31×	`associate-r`
24×	`sqrt-div`
12×	`unswap-sqr`
11×	`add-cbrt-cube` `add-exp-log`
10×	`sin-mult`
9×	`associate-l` `associate-/l*`
8×	`pow1`
5×	`flip3-+` `frac-add` `flip-+`
4×	`insert-posit16` `add-log-exp`
3×	`frac-times` `associate-/r` `associate-l/` `associate-/l/`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 162

Calls

4 calls:

26.0ms	(/ (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky))
94.0ms	(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky)))
21.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
13.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series581.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky))
217.0ms	(* (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ (sqrt (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky)))
106.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
92.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.9s

Counts

174 → 174

Iterations

Iter	Nodes
3	3984
2	1370
1	489
0	215

prune3.1s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 11.7b

localize110.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin ky))
3.4b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.4b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.4b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite58.0ms

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:

1.0ms	(cbrt (sin ky))
15.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
17.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
24.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series415.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt (sin ky))
106.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
101.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
101.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify3.3s

Counts

75 → 75

Iterations

Iter	Nodes
4	3842
3	1412
2	493
1	205
0	96

prune1.4s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 11.7b

regimes1.7s

Accuracy

0% (1.6b remaining)

Error of 12.6b against oracle of 11.0b and baseline of 12.6b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
2	21
1	21
0	16

end0.0ms

sample11.8s

Algorithm

intervals

Results

7.2s	2689×	body	1280	valid
2.6s	1867×	body	640	valid
828.0ms	2328×	body	80	valid
772.0ms	773×	body	320	valid
181.0ms	343×	body	160	valid