Details

sample114.0ms

Algorithm

intervals

Results

60.0ms	88×	body	1280	valid
25.0ms	61×	body	640	valid
6.0ms	76×	body	80	valid
5.0ms	19×	body	320	valid
2.0ms	12×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	10
1	35	10
2	63	10
3	137	10
4	417	10
5	1798	10
6	5002	10
done	5002	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize16.0ms

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)
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite80.0ms

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:

34.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
4.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
34.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
101.0ms	(pow (sin kx) 2.0)
105.0ms	(pow (sin ky) 2.0)
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify37.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	329	1021
1	1106	946
2	5002	943
done	5002	943

prune365.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
0.3b	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite118.0ms

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:

3.0ms	(pow (sin kx) 2.0)
4.0ms	(pow (sin ky) 2.0)
78.0ms	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
29.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(pow (sin kx) 2.0)
105.0ms	(pow (sin ky) 2.0)
139.0ms	(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify53.0ms

Counts

118 → 118

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	449	931
1	2141	850
2	5001	809
done	5001	809

prune382.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.2b

localize23.0ms

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 (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite32.0ms

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))
27.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt (sin kx))
97.0ms	(cbrt (sin kx))
97.0ms	(cbrt (sin kx))
80.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify74.0ms

Counts

60 → 60

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	183	512
1	496	483
2	2171	477
3	5002	476
done	5002	476

prune316.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite99.0ms

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:

17.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
26.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
27.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
26.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify94.0ms

Counts

102 → 102

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	282	1291
1	819	1231
2	3475	1224
3	5002	1219
done	5002	1219

prune384.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 11.2b

regimes1.0s

Accuracy

0% (1.6b remaining)

Error of 12.5b against oracle of 10.9b and baseline of 12.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	31
1	28	31
done	28	31

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.0s	2761×	body	1280	valid
906.0ms	1851×	body	640	valid
205.0ms	2326×	body	80	valid
204.0ms	734×	body	320	valid
59.0ms	328×	body	160	valid