Details

sample335.0ms

Algorithm

intervals

Results

108.0ms	82×	body	1280	valid
91.0ms	53×	body	640	valid
18.0ms	34×	body	320	valid
13.0ms	77×	body	80	valid
4.0ms	10×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	13	16
1	23	16
2	35	16
3	64	16
4	140	16
5	632	16
done	5000	16

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite214.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

135.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
7.0ms	(pow (sin kx) 2.0)
8.0ms	(pow (sin ky) 2.0)
58.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series671.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
175.0ms	(pow (sin kx) 2.0)
139.0ms	(pow (sin ky) 2.0)
123.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.2s

Counts

113 → 113

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	180	1660
1	449	1562
2	1841	1473
done	5000	1469

prune697.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2.0)
0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b	(pow (sin ky) 2.0)
3.9b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

4.0ms	(pow (sin kx) 2.0)
114.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.0ms	(pow (sin ky) 2.0)
43.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series734.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(pow (sin kx) 2.0)
260.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
183.0ms	(pow (sin ky) 2.0)
134.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.7s

Counts

113 → 113

Iterations

Useful iterations: 2 (795.0ms)

Iter	Nodes	Cost
0	195	1650
1	506	1485
2	2924	1375
done	5002	1375

prune596.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 11.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
3.9b	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite42.0ms

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:

2.0ms	(cbrt (sin kx))
2.0ms	(cbrt (sin kx))
1.0ms	(cbrt (sin kx))
36.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt (sin kx))
137.0ms	(cbrt (sin kx))
135.0ms	(cbrt (sin kx))
113.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify2.9s

Counts

60 → 60

Iterations

Useful iterations: 3 (642.0ms)

Iter	Nodes	Cost
0	81	818
1	191	744
2	597	620
3	3194	609
done	5000	609

prune563.0ms

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 11.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
3.9b	(sqrt (+ (* (pow (* (cbrt (sin kx)) (* (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx)))) (cbrt (cbrt (sin kx))))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite95.0ms

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))
2.0ms	(cbrt (sin kx))
90.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (* (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx)))) (cbrt (cbrt (sin kx))))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series551.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt (sin kx))
151.0ms	(cbrt (sin kx))
150.0ms	(cbrt (sin kx))
101.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (* (* (cbrt (cbrt (sin kx))) (cbrt (cbrt (sin kx)))) (cbrt (cbrt (sin kx))))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify2.9s

Counts

60 → 60

Iterations

Useful iterations: 3 (565.0ms)

Iter	Nodes	Cost
0	83	1071
1	197	975
2	625	728
3	3281	609
done	5001	609

prune496.0ms

Pruning

23 alts after pruning (21 fresh and 2 done)

Merged error: 11.1b

regimes1.8s

Accuracy

68% (0.4b remaining)

Error of 11.6b against oracle of 11.2b and baseline of 12.6b

bsearch4.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	30	53
1	37	53
done	37	53

end0.0ms

sample9.1s

Algorithm

intervals

Results

4.9s	2727×	body	1280	valid
1.9s	1815×	body	640	valid
1.0s	2306×	body	80	valid
527.0ms	764×	body	320	valid
250.0ms	388×	body	160	valid