Details

sample107.0ms

Algorithm

intervals

Results

54.0ms	72×	body	1280	valid
21.0ms	56×	body	640	valid
8.0ms	90×	body	80	valid
7.0ms	26×	body	320	valid
2.0ms	12×	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: 14.5b

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))))
0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite74.0ms

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:

37.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
26.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
105.0ms	(pow (sin ky) 2.0)
106.0ms	(pow (sin kx) 2.0)
83.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify37.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (28.0ms)

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

prune375.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
150×	`*-un-lft-identity`
99×	`add-sqr-sqrt`
98×	`add-cube-cbrt`
65×	`sqrt-prod`
32×	`unpow-prod-down`
28×	`associate-/r*`
26×	`distribute-lft-out`
17×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
7×	`div-exp`
6×	`pow-unpow`
5×	`div-inv`
4×	`add-log-exp`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow-to-exp` `rec-exp` `pow-pow` `sqrt-div` `1-exp` `pow-exp` `sqr-pow`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `clear-num` `associate-/r/` `flip-+` `inv-pow`

Counts

4 → 187

Calls

4 calls:

41.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
3.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
29.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
105.0ms	(pow (sin ky) 2.0)
113.0ms	(pow (sin kx) 2.0)
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	642	2588
1	2882	2325
2	5003	2177

prune446.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 13.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin ky)))
0.2b	(pow (sin ky) 2)
0.3b	(pow (sin kx) 2)
3.3b	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
150×	`*-un-lft-identity`
99×	`add-sqr-sqrt`
98×	`add-cube-cbrt`
65×	`sqrt-prod`
32×	`unpow-prod-down`
28×	`associate-/r*`
26×	`distribute-lft-out`
17×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
7×	`div-exp`
6×	`pow-unpow`
5×	`div-inv`
4×	`add-log-exp`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow-to-exp` `rec-exp` `pow-pow` `sqrt-div` `1-exp` `pow-exp` `unpow2` `sqr-pow`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `clear-num` `associate-/r/` `flip-+` `inv-pow`

Counts

4 → 189

Calls

4 calls:

43.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin ky)))
3.0ms	(pow (sin ky) 2)
3.0ms	(pow (sin kx) 2)
28.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ 1 (/ (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin ky)))
19.0ms	(pow (sin ky) 2)
19.0ms	(pow (sin kx) 2)
84.0ms	(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

simplify74.0ms

Algorithm

egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	639	2516
1	2726	2235
2	5001	2087

prune444.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 13.6b

localize21.0ms

Local error

Found 4 expressions with local error:

3.3b	(sqrt (+ (* (* (cbrt (pow (sin kx) 2)) (cbrt (pow (sin kx) 2))) (cbrt (pow (sin kx) 2))) (pow (sin ky) 2)))
16.6b	(cbrt (pow (sin kx) 2))
16.6b	(cbrt (pow (sin kx) 2))
16.6b	(cbrt (pow (sin kx) 2))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `sqrt-prod` `unpow2` `sqr-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 63

Calls

4 calls:

84.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2)) (cbrt (pow (sin kx) 2))) (cbrt (pow (sin kx) 2))) (pow (sin ky) 2)))
3.0ms	(cbrt (pow (sin kx) 2))
3.0ms	(cbrt (pow (sin kx) 2))
3.0ms	(cbrt (pow (sin kx) 2))

series421.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2)) (cbrt (pow (sin kx) 2))) (cbrt (pow (sin kx) 2))) (pow (sin ky) 2)))
117.0ms	(cbrt (pow (sin kx) 2))
112.0ms	(cbrt (pow (sin kx) 2))
114.0ms	(cbrt (pow (sin kx) 2))

simplify94.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	197	679
1	574	616
2	2569	601
3	5002	601

prune297.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 13.6b

regimes909.0ms

Accuracy

0% (1.4b remaining)

Error of 12.9b against oracle of 11.5b and baseline of 12.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	20
1	23	20

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.1s	2665×	body	1280	valid
734.0ms	1832×	body	640	valid
201.0ms	747×	body	320	valid
199.0ms	2388×	body	80	valid
70.0ms	368×	body	160	valid