Details

sample113.0ms

Algorithm

intervals

Results

58.0ms	77×	body	1280	valid
26.0ms	61×	body	640	valid
7.0ms	85×	body	80	valid
6.0ms	23×	body	320	valid
2.0ms	10×	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: 13.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b	(pow (sin kx) 2.0)
0.2b	(pow (sin ky) 2.0)
5.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
16×	`unpow-prod-down`
10×	`distribute-lft-out`
8×	`add-exp-log` `associate-/r*`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

25.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
17.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
101.0ms	(pow (sin kx) 2.0)
104.0ms	(pow (sin ky) 2.0)
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	329	1021
1	1106	946
2	5002	943

prune410.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.4b

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)))))
5.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite69.0ms

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)))))
17.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
17.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
20.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(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)))
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify101.0ms

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

prune517.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 12.4b

localize32.0ms

Local error

Found 4 expressions with local error:

5.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
5.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite72.0ms

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:

19.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
17.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
17.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
17.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
77.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
73.0ms	(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

prune494.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 12.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2)
0.2b	(pow (sin ky) 2)
0.3b	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
5.3b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
45×	`sqrt-prod`
41×	`add-sqr-sqrt`
34×	`times-frac`
28×	`add-cube-cbrt`
24×	`associate-l`
18×	`unpow-prod-down`
12×	`distribute-lft-out`
10×	`pow1`
8×	`add-exp-log`
6×	`pow-unpow` `add-cbrt-cube`
4×	`associate-/r/` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `associate-r`
2×	`pow-to-exp` `pow-pow` `flip3-+` `sqrt-div` `pow-exp` `flip-+` `div-inv` `unpow2` `sqr-pow`
1×	`pow-flip` `pow1/2` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `inv-pow`

Counts

4 → 115

Calls

4 calls:

2.0ms	(pow (sin kx) 2)
2.0ms	(pow (sin ky) 2)
54.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
25.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series258.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin kx) 2)
18.0ms	(pow (sin ky) 2)
117.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
105.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify50.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	369	1076
1	1262	985
2	5002	948

prune395.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 12.4b

regimes950.0ms

Accuracy

0% (1.7b remaining)

Error of 13.3b against oracle of 11.5b and baseline of 13.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	57
1	30	57

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.2s	2716×	body	1280	valid
762.0ms	1794×	body	640	valid
225.0ms	760×	body	320	valid
222.0ms	2381×	body	80	valid
64.0ms	349×	body	160	valid