Details

sample612.0ms

Algorithm

intervals

Results

164.0ms	91×	body	1280	valid
133.0ms	23×	body	320	valid
99.0ms	60×	body	640	valid
17.0ms	72×	body	80	valid
6.0ms	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize33.0ms

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))
0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
1.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite191.0ms

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:

126.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
8.0ms	(pow (sin kx) 2.0)
8.0ms	(pow (sin ky) 2.0)
44.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series671.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
162.0ms	(pow (sin kx) 2.0)
160.0ms	(pow (sin ky) 2.0)
120.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.1s

Counts

113 → 113

Iterations

Useful iterations: done (1.1s)

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

prune645.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin th) (/ (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)
1.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite201.0ms

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:

143.0ms	(* (sin th) (/ (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)
40.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series688.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(* (sin th) (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
159.0ms	(pow (sin kx) 2.0)
140.0ms	(pow (sin ky) 2.0)
112.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify4.4s

Counts

113 → 113

Iterations

Useful iterations: 2 (1.4s)

Iter	Nodes	Cost
0	195	1650
1	511	1470
2	3761	1379
done	5000	1379

prune713.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 10.4b

localize58.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
0.6b	(cbrt (sin kx))
1.8b	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite47.0ms

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))
41.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(cbrt (sin kx))
128.0ms	(cbrt (sin kx))
157.0ms	(cbrt (sin kx))
107.0ms	(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify3.4s

Counts

60 → 60

Iterations

Useful iterations: 3 (717.0ms)

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

prune497.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 10.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (cbrt (sin kx)))
0.7b	(cbrt (cbrt (sin kx)))
0.7b	(cbrt (cbrt (sin kx)))
1.8b	(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)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`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 → 57

Calls

4 calls:

3.0ms	(cbrt (cbrt (sin kx)))
4.0ms	(cbrt (cbrt (sin kx)))
4.0ms	(cbrt (cbrt (sin kx)))
122.0ms	(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)))

series567.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(cbrt (cbrt (sin kx)))
192.0ms	(cbrt (cbrt (sin kx)))
151.0ms	(cbrt (cbrt (sin kx)))
103.0ms	(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)))

simplify1.4s

Counts

69 → 69

Iterations

Useful iterations: 3 (476.0ms)

Iter	Nodes	Cost
0	90	1212
1	197	1125
2	546	881
3	2344	816
done	5001	816

prune390.0ms

Pruning

20 alts after pruning (17 fresh and 3 done)

Merged error: 10.4b

regimes1.2s

Accuracy

0% (1.4b remaining)

Error of 12.5b against oracle of 11.1b and baseline of 12.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	15	16
done	15	16

end0.0ms

sample9.7s

Algorithm

intervals

Results

6.0s	2792×	body	1280	valid
2.0s	1816×	body	640	valid
520.0ms	2351×	body	80	valid
506.0ms	704×	body	320	valid
172.0ms	337×	body	160	valid