Details

sample187.0ms

Algorithm

intervals

Results

118.0ms	118×	body	1280	valid
43.0ms	73×	body	640	valid
5.0ms	13×	body	320	valid
5.0ms	44×	body	80	valid
2.0ms	8×	body	160	valid

simplify54.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 3.5b

Counts

2 → 1

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))))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite27.0ms

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:

11.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms	(pow (sin kx) 2.0)
2.0ms	(pow (sin ky) 2.0)
7.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
103.0ms	(pow (sin kx) 2.0)
104.0ms	(pow (sin ky) 2.0)
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	329	1021
1	1106	946
2	5001	943

prune342.0ms

Filtered

112 candidates to 70 candidates (62.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	101	11	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	11	113

Merged error: 2.6b

Counts

113 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite30.0ms

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-/l*`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-/r*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `flip-+` `associate-/l/` `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:

11.0ms	(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky))
3.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
10.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky))
105.0ms	(pow (sin kx) 2.0)
106.0ms	(pow (sin ky) 2.0)
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify145.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	327	1017
1	1117	969
2	4630	966
3	5001	966

prune323.0ms

Filtered

112 candidates to 71 candidates (63.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	112	11	123

Merged error: 2.6b

Counts

123 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2)
0.3b	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
0.3b	(pow (sin ky) 2)
3.2b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite38.0ms

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:

3.0ms	(pow (sin kx) 2)
17.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
3.0ms	(pow (sin ky) 2)
11.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series267.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (sin kx) 2)
119.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
24.0ms	(pow (sin ky) 2)
105.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify47.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	369	1075
1	1256	984
2	5001	947

prune342.0ms

Filtered

127 candidates to 75 candidates (59.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	127	11	138

Merged error: 2.6b

Counts

138 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
0.3b	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

185×	`sqrt-prod`
163×	`add-sqr-sqrt`
144×	`times-frac`
132×	`*-un-lft-identity`
72×	`add-cube-cbrt`
39×	`associate-r` `associate-l`
28×	`add-exp-log` `unswap-sqr`
24×	`unpow-prod-down` `distribute-lft-out`
18×	`add-cbrt-cube`
16×	`sqrt-div`
11×	`associate-/r*`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 225

Calls

4 calls:

53.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
13.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
12.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
168.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
73.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
80.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify107.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	682	4592
1	3293	4120
2	5001	3911

prune601.0ms

Filtered

237 candidates to 125 candidates (52.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	237	0	237
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	237	11	248

Merged error: 2.6b

Counts

248 → 11

regimes446.0ms

Accuracy

0% (1.2b remaining)

Error of 3.9b against oracle of 2.7b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	11
1	19	11

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.7s	3711×	body	1280	valid
1.4s	2013×	body	640	valid
307.0ms	720×	body	320	valid
152.0ms	1246×	body	80	valid
79.0ms	310×	body	160	valid

Details

sample187.0ms

simplify54.0ms

prune3.0ms

localize21.0ms

rewrite27.0ms

series420.0ms

simplify41.0ms

prune342.0ms

localize16.0ms

rewrite30.0ms

series432.0ms

simplify145.0ms

prune323.0ms

localize16.0ms

rewrite38.0ms

series267.0ms

simplify47.0ms

prune342.0ms

localize19.0ms

rewrite98.0ms

series443.0ms

simplify107.0ms

prune601.0ms

regimes446.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.9s

Profiling