Details

sample428.0ms

Algorithm

intervals

Results

158.0ms	92×	body	1280	valid
62.0ms	53×	body	640	valid
54.0ms	29×	body	320	valid
18.0ms	72×	body	80	valid
5.0ms	10×	body	160	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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize47.0ms

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))
3.5b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite71.0ms

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:

33.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
10.0ms	(* (sin ky) (sin ky))
11.0ms	(* (sin kx) (sin kx))
13.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
36.0ms	(* (sin ky) (sin ky))
36.0ms	(* (sin kx) (sin kx))
136.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify2.2s

Counts

128 → 128

Iterations

Iter	Nodes
3	3659
2	1381
1	430
0	191

prune1.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.5b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin ky) (sin ky))
0.3b	(* (sin ky) (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
0.3b	(* (sin kx) (sin kx))
3.5b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
31×	`associate-r`
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-l`
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-*r/` `un-div-inv` `div-inv`

Counts

4 → 124

Calls

4 calls:

11.0ms	(* (sin ky) (sin ky))
83.0ms	(* (sin ky) (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
23.0ms	(* (sin kx) (sin kx))
24.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series345.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (sin ky) (sin ky))
171.0ms	(* (sin ky) (/ 1 (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
35.0ms	(* (sin kx) (sin kx))
118.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify1.5s

Counts

136 → 136

Iterations

Iter	Nodes
3	3203
2	1467
1	551
0	216

prune2.0s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 11.5b

localize72.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
3.5b	(sqrt (+ (* (* (sin kx) (* (cbrt (sin kx)) (cbrt (sin kx)))) (cbrt (sin kx))) (* (sin ky) (sin ky))))

rewrite129.0ms

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))
125.0ms	(sqrt (+ (* (* (sin kx) (* (cbrt (sin kx)) (cbrt (sin kx)))) (cbrt (sin kx))) (* (sin ky) (sin ky))))

series567.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt (sin kx))
133.0ms	(cbrt (sin kx))
157.0ms	(cbrt (sin kx))
102.0ms	(sqrt (+ (* (* (sin kx) (* (cbrt (sin kx)) (cbrt (sin kx)))) (cbrt (sin kx))) (* (sin ky) (sin ky))))

simplify6.0s

Counts

64 → 64

Iterations

Iter	Nodes
4	8921
3	1806
2	552
1	189
0	81

prune1.1s

Pruning

22 alts after pruning (20 fresh and 2 done)

Merged error: 11.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
3.5b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.5b	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
3.5b	(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:

17.0ms	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
24.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
23.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
13.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

series544.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(cbrt (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))))
92.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
84.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))
104.0ms	(sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))

simplify3.3s

Counts

98 → 98

Iterations

Iter	Nodes
4	5664
3	1873
2	694
1	310
0	172

prune1.9s

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 11.4b

regimes1.5s

Accuracy

0% (1.3b remaining)

Error of 12.7b against oracle of 11.3b and baseline of 12.7b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	19
1	19
0	14

end0.0ms

sample12.5s

Algorithm

intervals

Results

7.2s	2805×	body	1280	valid
3.1s	1823×	body	640	valid
934.0ms	784×	body	320	valid
753.0ms	2234×	body	80	valid
195.0ms	354×	body	160	valid