Details

sample314.0ms

Algorithm

intervals

Results

117.0ms	84×	body	1280	valid
104.0ms	62×	body	640	valid
16.0ms	29×	body	320	valid
15.0ms	71×	body	80	valid
4.0ms	10×	body	160	valid

simplify5.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	16
1	23	16
2	35	16
3	64	16
4	136	16
5	311	16
6	1019	16
7	4223	16
done	5001	16

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
2.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite108.0ms

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×	`add-exp-log` `associate-/r*`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

53.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
4.0ms	(pow (sin kx) 2.0)
4.0ms	(pow (sin ky) 2.0)
39.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series732.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
157.0ms	(pow (sin kx) 2.0)
157.0ms	(pow (sin ky) 2.0)
170.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.0s

Counts

112 → 112

Iterations

Useful iterations: 2 (255.0ms)

Iter	Nodes	Cost
0	170	1738
1	328	1556
2	794	1503
3	2419	1503
done	5000	1503

prune573.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2.0)
0.3b	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b	(pow (sin ky) 2.0)
2.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
30×	`associate-r`
28×	`times-frac`
25×	`add-cube-cbrt`
22×	`sqrt-prod`
15×	`add-exp-log`
14×	`unpow-prod-down`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
5×	`unswap-sqr`
4×	`sqrt-div` `prod-exp` `add-log-exp`
3×	`associate-l`
2×	`pow-to-exp` `pow-pow` `flip3-+` `div-exp` `pow-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 106

Calls

4 calls:

8.0ms	(pow (sin kx) 2.0)
105.0ms	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.0ms	(pow (sin ky) 2.0)
54.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series742.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(pow (sin kx) 2.0)
237.0ms	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
181.0ms	(pow (sin ky) 2.0)
131.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.9s

Counts

118 → 118

Iterations

Useful iterations: 2 (326.0ms)

Iter	Nodes	Cost
0	198	1690
1	433	1384
2	1090	1284
3	3240	1284
done	5001	1284

prune569.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
2.4b	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
42.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series584.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (sin kx))
159.0ms	(cbrt (sin kx))
150.0ms	(cbrt (sin kx))
125.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify1.8s

Counts

60 → 60

Iterations

Useful iterations: 3 (510.0ms)

Iter	Nodes	Cost
0	81	818
1	187	744
2	478	620
3	1767	609
done	5001	609

prune476.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 10.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
30×	`cbrt-prod` `sqrt-prod`
25×	`add-sqr-sqrt`
24×	`times-frac`
22×	`add-cube-cbrt`
12×	`unpow-prod-down` `distribute-lft-out`
8×	`sqrt-div`
7×	`pow1`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 90

Calls

4 calls:

21.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
30.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
37.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
45.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series597.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
136.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
121.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
113.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	160	2119
1	282	1894
2	636	1807
3	1703	1797
done	5001	1791

prune644.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 10.9b

regimes1.6s

Accuracy

0% (1.6b remaining)

Error of 12.9b against oracle of 11.3b and baseline of 12.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	27
1	20	27
done	20	27

end0.0ms

sample9.5s

Algorithm

intervals

Results

5.1s	2639×	body	1280	valid
2.7s	1890×	body	640	valid
571.0ms	834×	body	320	valid
542.0ms	2351×	body	80	valid
106.0ms	286×	body	160	valid