Details

sample117.0ms

Algorithm

intervals

Results

65.0ms	87×	body	1280	valid
24.0ms	63×	body	640	valid
6.0ms	70×	body	80	valid
5.0ms	20×	body	320	valid
3.0ms	16×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

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)
0.3b	(pow (sin ky) 2.0)
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite69.0ms

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:

48.0ms	(* (/ (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)
15.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
108.0ms	(pow (sin kx) 2.0)
108.0ms	(pow (sin ky) 2.0)
80.0ms	(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

prune422.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite61.0ms

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)))))
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)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(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)))
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify97.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (86.0ms)

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

prune487.0ms

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 11.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin ky))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt (sin ky))
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)))
18.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(cbrt (sin ky))
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	171	583
1	424	554
2	1478	552
3	5002	551

prune438.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 11.9b

localize26.0ms

Local error

Found 4 expressions with local error:

3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.4b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite63.0ms

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)))
17.0ms	(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)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
76.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
78.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify127.0ms

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

prune378.0ms

Pruning

26 alts after pruning (25 fresh and 1 done)

Merged error: 11.9b

regimes1.5s

Accuracy

57.9% (0.7b remaining)

Error of 12.1b against oracle of 11.4b and baseline of 13.0b

bsearch4.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	50
1	40	50

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.0s	2711×	body	1280	valid
932.0ms	1903×	body	640	valid
205.0ms	779×	body	320	valid
195.0ms	2259×	body	80	valid
60.0ms	348×	body	160	valid