Details

sample129.0ms

Algorithm

intervals

Results

68.0ms	86×	body	1280	valid
29.0ms	54×	body	640	valid
9.0ms	82×	body	80	valid
6.0ms	20×	body	320	valid
3.0ms	14×	body	160	valid

simplify51.0ms

Algorithm

egg-herbie

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize21.0ms

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)
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite68.0ms

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:

44.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
1.0ms	(pow (sin kx) 2.0)
1.0ms	(pow (sin ky) 2.0)
16.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series429.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
103.0ms	(pow (sin kx) 2.0)
109.0ms	(pow (sin ky) 2.0)
73.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

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

prune410.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.2b

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)))))
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite60.0ms

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:

12.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
70.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify96.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (85.0ms)

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

prune469.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.2b

localize27.0ms

Local error

Found 4 expressions with local error:

4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite64.0ms

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:

15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series298.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
70.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
75.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify128.0ms

Algorithm

egg-herbie

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

prune456.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 12.2b

localize33.0ms

Local error

Found 4 expressions with local error:

4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.1b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite64.0ms

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:

15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
71.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify128.0ms

Algorithm

egg-herbie

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

prune436.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 12.2b

regimes1.1s

Accuracy

55.2% (0.7b remaining)

Error of 12.0b against oracle of 11.3b and baseline of 12.9b

bsearch4.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	67
1	47	67

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.4s	2809×	body	1280	valid
866.0ms	1822×	body	640	valid
256.0ms	2289×	body	80	valid
225.0ms	706×	body	320	valid
83.0ms	374×	body	160	valid