Details

sample109.0ms

Algorithm

intervals

Results

56.0ms	82×	body	1280	valid
24.0ms	56×	body	640	valid
7.0ms	89×	body	80	valid
5.0ms	22×	body	320	valid
1.0ms	7×	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: 12.3b

localize15.0ms

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)
0.2b	(pow (sin ky) 2.0)
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite126.0ms

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:

83.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms	(pow (sin kx) 2.0)
4.0ms	(pow (sin ky) 2.0)
31.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
102.0ms	(pow (sin kx) 2.0)
102.0ms	(pow (sin ky) 2.0)
81.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify40.0ms

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	391	990
1	1382	928
2	5001	927
done	5001	927

prune415.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin ky) 2.0)
0.3b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
50×	`times-frac`
49×	`add-sqr-sqrt`
41×	`sqrt-prod`
40×	`add-cube-cbrt`
30×	`associate-r`
19×	`unpow-prod-down`
16×	`distribute-lft-out`
12×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `associate-/r*`
6×	`sqrt-div`
4×	`associate-/r/` `add-log-exp`
3×	`pow-unpow` `flip3-+` `associate-l` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `sqr-pow`

Counts

4 → 133

Calls

4 calls:

3.0ms	(pow (sin ky) 2.0)
36.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
84.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
27.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(pow (sin ky) 2.0)
140.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
157.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify55.0ms

Counts

145 → 145

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	412	1572
1	1810	1426
2	5002	1423
done	5002	1423

prune445.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 11.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite108.0ms

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:

19.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
28.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
30.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
27.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
83.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
82.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify92.0ms

Counts

102 → 102

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	282	1294
1	819	1231
2	3475	1224
3	5002	1219
done	5002	1219

prune471.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 11.2b

localize37.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
20×	`sqrt-prod`
12×	`add-sqr-sqrt`
8×	`pow1` `add-cube-cbrt` `unpow-prod-down` `sqrt-div` `distribute-lft-out`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

28.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
27.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
30.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
27.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
81.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
82.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify123.0ms

Counts

80 → 80

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	118	696
1	301	664
2	1019	664
3	4120	664
4	5001	664
done	5001	664

prune429.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 11.2b

regimes1.1s

Accuracy

0% (1.6b remaining)

Error of 12.8b against oracle of 11.3b and baseline of 12.8b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	56
1	29	56
done	29	56

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.9s	2756×	body	1280	valid
887.0ms	1833×	body	640	valid
196.0ms	747×	body	320	valid
196.0ms	2313×	body	80	valid
59.0ms	351×	body	160	valid