Details

sample117.0ms

Algorithm

intervals

Results

66.0ms	89×	body	1280	valid
23.0ms	58×	body	640	valid
7.0ms	26×	body	320	valid
6.0ms	72×	body	80	valid
2.0ms	11×	body	160	valid

simplify50.0ms

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: 11.7b

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))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
4.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite31.0ms

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:

15.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
106.0ms	(pow (sin kx) 2.0)
112.0ms	(pow (sin ky) 2.0)
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

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

prune443.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite34.0ms

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:

10.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(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)))
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
81.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify102.0ms

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

prune502.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 10.6b

localize31.0ms

Local error

Found 4 expressions with local error:

4.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite32.0ms

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:

7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
74.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
82.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
82.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify124.0ms

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

prune490.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 10.6b

localize36.0ms

Local error

Found 4 expressions with local error:

4.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.8b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.8b	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
10×	`cbrt-prod` `add-sqr-sqrt` `sqrt-prod`
8×	`add-cube-cbrt` `unpow-prod-down` `distribute-lft-out`
6×	`pow1`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 64

Calls

4 calls:

7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
99.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
98.0ms	(cbrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	177	736
1	517	694
2	1979	690
3	5001	684

prune482.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 10.6b

regimes1.2s

Accuracy

0% (1.8b remaining)

Error of 12.6b against oracle of 10.9b and baseline of 12.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	57
1	33	57

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.2s	2713×	body	1280	valid
803.0ms	1864×	body	640	valid
204.0ms	2351×	body	80	valid
204.0ms	748×	body	320	valid
58.0ms	324×	body	160	valid